Essays on Information and
Climate Change
Ian Temperton
Visiting Business Fellow
Smith School of Enterprise and the Environment
2011
Essays on Information and Climate Change
Information and Climate Change
I work for an investment and investment banking firm specialising in mobilising capital into the
development of the low-carbon economy. I spend my time advising clients on the decisions which
we all hope in aggregate will contribute to the prevention of dangerous climate change and
everything that goes with that. Over the last year or so I have also had the privilege of spending
time at the Smith School of Enterprise and the Environment at Oxford, where I have used my time to
muse on some of the issues of what I observe in my day job.
This set of short essays is an attempt to share the thoughts I have had over this period. Structuring
my work in this way has allowed me to, I hope, create some rounded pieces on individual topics on
the role of information in climate change and climate change finance during the limited periods I
have to pursue this research. I hope that for the busy reader this may also prove to be a helpful
format.
The unifying theme of this set of essays is information and its vital role in the financing of the
transition to a low-carbon economy. Despite the fact that information is all around us in the modern
world, it is still a somewhat esoteric concept to most people. As we will see in the coming essays,
within the study of information are many concepts related to those that determine the physics of
the energy system and hence the transformation of the Earth’s systems that we fear and those of
the energy system that we need.
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Essay One looks at the physical characteristics of the low-carbon economy and relates them
to the forms of investment decision which we will require in order to build that sustainable
energy system;
Essay Two looks at the key characteristics of investment decisions and how they relate (or
don’t relate) to the forms of incentives which are often established to leverage capital into
the low carbon economy;
Essay Three uses simple derivatives theory to explain how information is costly and how
systems designed to elicit information (such as cap-and-trade schemes) are not efficient
instruments for incentivising large-scale investment;
Essay Four explains the four real purposes of cap-and-trade schemes in my view:
observation, accounting, communication, and facilitating international climate
disagreements;
Essay Five assesses whether the ways we look at justifying the protection of the planet
through analysis really work and uses derivatives to provide a few hopefully useful new
thoughts;
Essay Six attempts to bring the themes of entropy, information and derivatives together in a
way which assesses the current financial architecture for climate change related investments
and makes recommendations as to how we might make this more effective. It is my view
that the climate change community is its own worst enemy in the way it deals with
information and finance;
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These essays are written with a view to being something of a guide to the reader and in particular
the business person and policy-maker. I have therefore kept the amount of algebra in the main
essays to almost zero and there are very few numerical examples except in Essay Three. I have
attempted to explain assumptions and methods in great detail, so someone who can vaguely
remember school maths will be able to follow the essays, and someone who can vaguely remember
university maths (applied I hasten to add) can almost certainly follow the Mathematical Appendix.
The Mathematical Appendix is included for a number of reasons. Firstly, it puts some formal rigour
behind a lot of the statements in the essays. Secondly, it allows some of those statements to be
made generally and precisely based on their exact assumptions. And finally, it allowed me to prove
to myself that I could still do a bit of calculus as my brain approaches forty.
I have also included a Bibliography which the reader will find varied and interesting. It includes
references to a lot of very good work in derivative, information theory, thermodynamics and climate
change. Because I am not an academic and I decided not to write this like an academic paper then
my references are probably not complete and rigorous. I apologise if you thought you should have
been there.
I apologise to the international reader who might think a few of my examples and cultural references
are rather British. The fact is that I am.
I would like to thank [ ].
All errors and omissions remain, of course, entirely mine.
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Contents
Information and Climate Change ............................................................................................................ 1
Essay One: Stuff and Things and Less of Both, Information and the Low-Carbon Economy ................ 4
Essay Two: The Characteristics of Trading Systems and their use in Investment Decisions and System
Optimisation ......................................................................................................................................... 17
On Which Side of the Balance Sheet do Trading Systems Sit? ......................................................... 18
Asset Mismatch in Trading Systems.................................................................................................. 21
Defining Average and Marginal Cost Investments............................................................................ 25
Price versus Quantity ........................................................................................................................ 27
Stuff and Things, and Energy and Entropy ........................................................................................ 29
Essay Three: Why cap-and-trade systems don’t lead to investment decisions ................................... 32
Derivatives ........................................................................................................................................ 32
NewClear investment decisions ........................................................................................................ 33
NewClear Options ............................................................................................................................. 36
Further Option Insights ..................................................................................................................... 42
Insights from Real Life....................................................................................................................... 44
Why cap-and-trade schemes don’t lead to investment decisions.................................................... 46
Essay Four: Observation, accounting, communication and climate disagreements ........................... 47
Observation....................................................................................................................................... 47
Accounting ........................................................................................................................................ 51
Communication ................................................................................................................................. 55
Climate disagreements ..................................................................................................................... 58
Observation, accounting, communication and climate disagreements ........................................... 60
Essay Five: Risk Management for the Planet ....................................................................................... 63
Four elements of climate change analysis ........................................................................................ 63
Risk Management for the Planet ...................................................................................................... 67
Essay Six: Information and Climate Change ......................................................................................... 76
Mathematical Appendix........................................................................................................................ 94
Bibliography ........................................................................................................................................ 114
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Essay One: Stuff and Things and Less of Both, Information and the
Low-Carbon Economy
We are currently using up a store of energy which was built up for us in the Earth some hundreds of
millions of years ago, and which itself took millions of years to create1. The stores of hydrocarbon
energy (coal, oil, gas etc.) which were created and stored over those vast periods of time have been
used up at an ever accelerating rate over the past 250 years as our human race has used this energy
to impose changes on the planet which improve it for our kind.
Climate change is fundamentally about the risks that this abrupt use of our planetary energy store
brings, and the changes to the planet which are potentially associated with it.
As generally understood, our energy system causes the emission of carbon dioxide and other gases
which have such properties that they trap ever more of the sun’s energy within the Earth’s
atmosphere as it is re-emitted from the Earth’s surface. The Earth therefore becomes warmer with
all the well-documented risks which come with that abrupt change in atmospheric composition and
its associated warming.
Deutscher2 looks at the climate change and energy issue as a problem of entropy; effectively as a
process of the release of the capacity for useful work which the sun’s energy created in the Earth all
those hundreds of millions years ago. Entropy is an esoteric concept which we will address in its
many forms as we go through these essays. For the moment, we can think of it in its
thermodynamic sense as a measure of the capacity to do useful work. (Actually as the entropy of a
system increases then its capacity to do useful work reduces).
The first law of thermodynamics tells us that energy is always conserved and hence it is not true to
say that the problem we face today is that we are using up energy, instead we are using up the
Earth’s store of capacity to do useful work.
During prehistoric times the sun’s energy combined with the chemistry of plants and animals caused
a massive storage of energy, and that energy was stored in a way where it has a massive capacity to
do useful work: this being the Earth’s stores of coal, oil, gas and other hydrocarbons.
The second law of thermodynamics3 tells us that overall entropy must always increase or stay the
same and it is worth, at this point, introducing another interpretation of entropy which is the degree
of order in a system. A lowering of the entropy of a system is associated with the creation of greater
order in that system and hence the capacity for useful work. However the second law tells us that,
while a sub-system may see a reduction in entropy, overall entropy can only increase or stay the
same4.
1
See (Southwood, 2003) for an interesting discussion on the history of the planet.
See (Deutscher, 2008)
3
For the history of the second law see (Magie, 1902)
4
For introductions to thermodynamics see (Atkins, 2010), (Fermi, 1936), and (Ness, 1969)
2
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We can therefore see the activities of humankind over the past 250 years or so as being to use up
energy stored in the Earth to create greater order in the human-dominated sub-system of planet
Earth. However in doing so it is necessarily causing an increase in overall entropy.5 The imposition
of human order on the Earth, by the use of this pre-historically stored capacity to do useful work is
therefore returning the non-human dominated parts of the planet (in particular the atmosphere and
the oceans) to a pre-historic state of higher entropy and hence greater disorder and this means it is
heating up.
We can see the Earth’s massive stores of useful energy as the source of the reduction in the overall
entropy of the rest of the planet, and the creation, storage, use, and emission of that store as a
transition for the planet from a state of higher entropy (disorder); to one of greater order; and back
to disorder again.
This all probably does seem a bit esoteric: isn’t climate change all about carbon dioxide (and other
less important greenhouse gases)? Yes. In the above explanation of the enormous thermodynamic
cycle which the Earth is going through, there is the implicit assumption that the reduction in the
entropy of the planet all those hundreds of millions of years ago was achieved at the expense of an
increase in the entropy of the rest of the Universe, whereas now, as we release that stored capacity
for useful work, we implicitly assume that the associated increase in entropy is constrained within
the Earth’s systems (atmosphere, oceans etc.). This is indeed because of the role of carbon. Carbon
and its combination with hydrogen to form the many and varied hydrocarbons on which all forms of
life and the majority of current energy sources depend, is the medium for this storage of the
capacity for useful work and its release. Carbon dioxide is the primary chemical product of that
human induced energy release, and carbon dioxide has the property of reducing the capacity of the
Earth to pass heat to the rest of the Universe. Hence we are back to the important and commonly
understood issue of climate change: that carbon dioxide prevents the emission of heat to the wider
Universe from Earth, but in our second law-based understanding of the problem, this property has
the effect of making the Earth more and more of a closed system. It is this closing of the system
which means that the imposition of human order on the planet cannot take place solely at the
expense of greater disorder in the wider Universe, and instead it takes place at the expense of
greater disorder in the non-human dominated part of the Earth’s system. It is the growing disorder
we create around us which we should be fearful of when we think about climate change and our
energy system.
This planetary view of stored energy taking us between different states of entropy will be useful at a
more micro level later in this essay.
It would appear then that a sustainable energy system for the human habitation of Earth would be
one in which we instantaneously harnessed the sun’s energy to create order in our human subsystem and the associated disorder (entropy) created by that action was immediately despatched
into the wider Universe as heat emitted from the Earth’s atmosphere rather than retained within it.
This would mean not changing the chemistry of the atmosphere such that we close off our ability to
discharge disorder into the wider Universe.
5
This is analogous perhaps to the idea that we only have a certain ration of tonnes of CO 2 that we can afford
to safely put into the atmosphere, see (Allen, et al., 2009) and (Meinshausen, et al., 2009)
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Our challenge is to cease using up the Earth’s stored capacity for useful work, because in doing so
we are restoring the planet’s systems to a state of higher entropy in which they existed in prehistoric
times, and we have grave fears that such a system may not have the capacity to sustain human
habitation of the form we would like, and in the quantity we envisage.
In a later essay we will discuss the weaknesses in the ability of the human race to observe and act on
climate change in sufficient time to mitigate the worst threats of global warming. Another way to
look at this, in the terms we are currently using, is that while we believe that we have created
greater order in the human-dominated sub-system of the planet in the last 250 years, as we have
seen exponential growth in population and living standards (in many parts of the world), we have
created associated disorder in the wider planet’s systems, and we may well discover that we require
ever increasing amounts of energy to preserve order in the human-dominated sub-system, given the
increase in the overall entropy of the planet.
In the terminology of climate change we might consider mitigation investments to be actions which
prevent us from increasing the overall entropy of the planet, and adaptation investments as being
those which attempt to maintain order in the human-dominated sub-systems of the planet against
the general disorder created in the overall planet system.
So what of stuff and things6?
If we are to transform our energy system from one which increases the overall entropy of the planet
to one which provides the same or greater level of human utility while preserving the state of
entropy of the planet then we need to transition from an energy system which is based on stuff, to
one which is based on things. We will see that this means that climate change mitigation is
therefore a capital investment problem and an information problem.
The modern energy economy and the wider economy which that energy economy powers has
developed over the last few hundred years through the release of energy from the stuff which was
created as a store of energy all those hundreds of millions of years ago. That stuff, being
hydrocarbons (coal, oil, gas etc.) found in the Earth’s crust, has been extracted, processed and its
effluent emitted to the atmosphere. The job of the energy industry, and in particular the electricity
and utility industries, in that time has been simply to process stuff (primarily by combustion), and
hence increase the state of entropy of the overall planet, while creating order in the humandominated sub-system of the planet.
Things create or use energy without the need to process any or as much stuff as had previously been
the case. Wind turbines and solar panels for instance are things which harness energy from wind
and from solar irradiation respectively without processing stuff found in the Earth’s surface.
We need to move to an energy system which harnesses the sun’s energy instantaneously and
creates order within the human sub-system while creating the associated disorder in the wider
Universe and not trapped within the planet’s atmosphere creating warming. This simply cannot
involve using the stuff that is the Earth’s store of energy.
6
With special thanks to Rick Jefferys of ConocoPhilips who set me off on stuff and things quite a while ago.
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So the energy business cannot be an industry that mines and burns the stuff which is stored in the
planet, but instead it must install and manage things which create an equivalently useful energy
system.
There are two reasons why this transition is very hard: one is to do with stuff and the other is to do
with things.
Firstly, you will note above that I described an ideal energy system as one in which the sun’s energy
is instantaneously harnessed and created into useful energy for human-kind. The problem here is
that our desire to use energy is not perfectly correlated with the sun’s delivery of that energy to our
locality. Because we have an energy system based on stuff, we have taken for granted two
characteristics of stuff which are extremely valuable. The first is that in most cases it is a very
effective store of energy (energy dense in both weight and volume terms) and hence this stuff-based
energy has the in-built capacity to deliver energy when we need it. A stuff-based energy system
therefore has the inherent ability to match energy delivery and use in the temporal dimension. The
second related characteristic is that this stuff can, in most cases, be relatively easily transported and
hence energy use can occur at a different place to the place where the stuff is found. A stuff-based
energy system has an in-built capacity to match energy delivery and use in the spatial dimension.
Matching energy delivery and use in space and time is much harder in a thing-based energy system.
Secondly, things tend to be more capital intensive than stuff. Hence the capital required to be
deployed is greater and the decisions are more irreversible. This irreversibility, as we will see in a
later essay, is a disincentive to investment decision making.
In my opinion, irrespective of the relative costs of the hydrocarbon (stuff) based energy system and
a low or zero carbon (thing-based) energy system, solving these two fundamental problems is the
key to the migration to that low-carbon economy.
It is perhaps worth a moment discussing the elements of stuff-based and thing-based energy
systems, simply to illustrate the differences and the importance of the above two issues.
First please note what should be obvious and that is that electricity isn’t either stuff or a thing:
electrons are not created or used in an electrical system despite the imprecise language we often
use in the industry.
So compare a coal-fired power station and a wind farm. The coal-fired power station uses stuff
(coal) and burns it to create electricity and in the process increases the entropy of the system
outside the power station. The coal can come from many different places on the planet and it can
have been mined at any time before it is burned and stored in the mean time. A coal-fired power
station costs say around £1,500 / kW7 to build in the western world and hence has a capital intensity
of annual electricity production (given that it can generate most of the year) of 18p8 per annual kWh
of installed production. The cost per unit of providing electrical energy from it is determined by the
recovery of this capital cost at a reasonable return and the cost of purchasing the coal (stuff) to be
7
Actually, thankfully no-one as built one in the UK for a while so who knows, but this is not a bad number for
illustrative purposes
8
That’s £1,500 / kW divided by 8760 which is the number of hours in a year and then divided by 0.95 to
account for the fact that you can’t run a plant all year (all times 100 to get from £ to pence, of course).
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processed over the life of the plant. The cost of the coal will be a substantial part of that overall
cost. A wind farm creates electrical energy when the wind blows and as importantly when the wind
blows at its specific location. A wind farm off the coast of the UK today will cost around £3,000 /
kW9 and as it will generate about 35% of the time the capital cost is about 97p10 per annual kWh of
installed production. It costs relatively little to run, and obviously does not have to pay for its fuel
which is completely free (the wind). Hence we can see that in the case of these two widely used
dirty and clean forms of electrical energy generation, one is temporally and spatially flexible and the
other isn’t, and one has a substantially greater upfront investment cost than the other. One
processes stuff and the other is a thing. Whatever their respective actual costs per unit of electricity,
we can see the obvious issues in transitioning to power generation based on things rather than
stuff11.
In the above comparison we could have used a gas or oil-fired power station for our emitting power
station (the stuff processor) and a solar power plant or even nuclear power plant for the thing and
the illustration would have been the same (nuclear has a few of its own characteristics but it is highly
capital intensive and the stuff it uses is not of the hydrocarbon sort, and we can argue that the stuff
you might think is stuff decays of its own accord, and hence we will consider it a thing).
In the home let’s think of a few of the ways we consume energy. Traditional incandescent light
bulbs are very cheap to invest in but use a lot of energy over their lifetimes. Whereas LED or
compact fluorescent light bulbs are considerably more expensive to invest in as they include a lot
more clever kit than a tungsten coil in a vacuum, but they use a fraction of the energy over the life of
the bulb. When we heat our homes we have the option of either investing upfront in insulation,
draught exclusion etc. and then we will use less energy over the lifetime of the house, or we can
simply use more energy when it is needed and not make the upfront investment in such things. I
heat water in my home using a solar thermal water system and a boiler for when the sun is not
sufficient. The solar thermal system was expensive to install upfront but has zero running cost,
whereas the boiler was cheaper upfront but then uses natural gas (stuff) as it needs it over its
lifetime to heat the water for the house.
Even within the household example we have the spatial and temporal issue. From an energy system
perspective, if I install an LED or compact fluorescent light bulb in a room, then if I hardly use the
room that capital has been invested inflexibly in providing the option of cheap marginal cost lighting
in that room by the investment of substantial capital. If I had installed a standard light bulb then the
overall energy system would have to have the capacity to deliver me more power when I wanted it,
but if I hardly used the room then that capital in energy production can be easily diverted to other
uses. Hence the move to more efficient lighting systems is capital intensive and reduces the spatial
and temporal flexibility of the overall investment in the energy system. One can make a similar
argument for my solar thermal water heating system and for the energy efficiency investments
described above. As well as being capital intensive they are temporally and spatially less flexible
than investments in greater stuff-based energy production.
9
This is a good guess – I assure you.
£3,000 / kW divided by 8760 hours divided by the 35% load factor and times by 100 to get into pence.
11
See (Helm, Wardlaw, & Caldecott, Delivering a 21st Century Infrastucture for Britain, 2009) for one of the
many expositions of the capital intensity of the move to a low-carbon economy in the UK for instance.
10
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There are many more examples, but by now I hope it is clear that the transition to a low-carbon
economy needs a transition from stuff to things, and that that transition will involve a capital
intensive period of investment in the energy system of the world. Climate change (or its prevention)
is largely a capital problem.
Information has several vital roles in this transition. The first is for society to know what things to
invest in, and ensuring that that information gets to the agents of investment. This is vitally
important but we will leave it for a subsequent essay. The second is to ensure that we reduce the
investment burden of the transition to a thing-based energy system by the information being
available to build the optimum set of things, and third is the ability to optimise the thing-based
energy system in such a way as to be able to deliver people energy at the time and place they wish
to use it.
Information has played a very important role in transformations of the energy system in the past. In
Europe and some other parts of the world, there has been a process of liberalisation of the energy
markets12. This process has involved many different elements but one of the important ones is the
ability of users to change their energy supplier. In the era before advanced information systems this
would have seemed absurd. The cost of having a new supplier put a second (or third or subsequent)
electrical or natural gas grid connection into a home in order to allow the change in supplier for the
user would clearly be greater than the benefit of changing supplier even if the supplier provided
cheaper electricity or gas. Hence before information technology was available, the cost of things
(like grids) meant that even if someone had cheaper stuff (say natural gas) it was impractical for
users to be able to access that cheaper supply. The growth in the ability of information systems
created the opportunity for different suppliers to deliver energy down the same pipes and wires. In
other words, the same basic infrastructure could be used by different suppliers to supply to the
same user because there were (are) now information systems capable of reconciling the generation
or production of energy put into the grid by a supplier and its use by different households. Energy
liberalisation, often seen as a major political endeavour, would have been completely impossible
without the advances in information technology which were available from the 1990s onwards, and
this is a classic example of information being able to facilitate the development of an entirely new
approach to energy supply without the need for excessive amounts of investment in infrastructure
(things).
Prior to the 1990s energy supply was clearly a “natural monopoly” because the information systems
were not available for it to be anything else. If you turned on a light in your house then that would
make a minor difference to the frequency of the overall electrical system which would cause an
increase in generation at a power station on the system. The electrical system had no knowledge of
who had created the need for more power, and the frequency and its electro-magnetic impact was
the only form of short-term communication available to a power system. By the late 1990s
computing power was such that it was now possible to allow competition between suppliers and
hence it is now possible to reconcile commercially the demand of an individual company’s customers
and that company’s generation, despite the fact that all suppliers and consumers are connected to
12
See (Helm, Energy, the State and the Market. British Energy Policy Since 1979, 2003) for an excellent history
of the liberalisation of the UK energy market.
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the same grid system. (However, of course instantaneously, we still rely on the frequency to control
the physical system).
In the future information will play a bigger and bigger role in the energy system and to achieve our
low-carbon goals, it simply must.
A stuff-based energy system has the advantage of temporal and spatial flexibility for one overarching
reason and that is because stuff (hydrocarbons) are already inherently low entropy energy sources,
(in other words they contain a high specific capacity to do useful work). This is the reason why they
are so energy dense, and why they are so easy to transport and store (giving spacial and temporal
flexibility). It requires a very low fraction of their inherent capacity for useful work to be expended
in order to store them over long periods or transport them over long distances. All that work was
done many hundreds of millions of years ago when the sun’s energy was used to create a store of
the capacity for useful work in the Earth’s crust and an associated reduction in the entropy of the
atmosphere. We owe much to the forests and sea-creatures of pre-historic times.
Within the stuff-based energy system which we have developed to date we have implicitly relied on
this pre-historic accident, and hence we have never had to overcome the challenges facing a thingbased system. Within a stuff-based energy system the costs of storage and transportation are
sufficiently small that we almost ignore them, whereas in a thing-based system we will see that
transportation and storage have real and noticeable costs which present the greatest challenge and
the greatest use for information.
The simple fact is that our energy use is not directly related to the instantaneous incidence of the
sun’s energy on the Earth and hence if we are to move to a thing-based energy system then we need
to create the capacity in that system to store energy, and more generally, have the ability to reduce
the entropy of the energy system at certain times and in certain places to suit our needs.
A purely thing-based energy system is clearly inherently chaotic (highly disordered and high
entropy). Imagine for a moment that we did not have a stuff-based system to begin with and
instead we simply wired up a load of wind turbines, solar panels, solar water heaters and other
energy capture things, with a simple grid, and with lighting and space and water heating for a
population of a town or country with no access to stuff. The result would be madness. People
would foolishly try to switch on their lights when there was no incident solar energy to create
electricity for the grid; they would try to take a warm shower when the wind wasn’t blowing; and
heat their homes on still and cloudy days. We are also pre-supposing that our energy community is
in a windy and sunny place, but if they are not, they may stand no chance of sourcing their energy
needs from the system we have put in place.
Such a system is clearly highly disordered and chaotic, and hence high entropy. You will also observe
that our capacity to do useful work within such a system is also much reduced from where it is
today, hence suggesting that this is a high-entropy system.
So if we are to have any chance of developing a thing-based energy system we need to find a way to
impose order in that system, or in other words, reduce the entropy of the system.
It is interesting to observe that in the same way as human’s imposing their form of order on the
world causes potentially dangerous disorder in the wider planet’s system, increasing the penetration
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of things in the stuff-based energy system similarly creates greater disorder in that energy system
which much be dealt with in some way. Many of the investments which those of us concerned
about climate change propose have the hidden cost of the disorder which they impose on the
energy system, and many of the objections which people against those investment have (wind and
solar are intermittent, energy efficient investments are a waste of money etc.) are actually true
reflections of the unresolved issue of maintaining our energy system at its current or lower state of
entropy (order)13.
We have but one mechanism for bringing down the state of entropy of our thing-based energy
system and that is information. There are however two complementary physical investments which
allow for information to be more effectively used in the reduction of entropy of the energy system.
They are system scale and physical storage.
Let’s deal with scale first14. Pretty much the state of the art in energy policy making at present is to
say that renewable energy intermittency (which is what people generally call the highly disordered
energy system one creates with renewable energy) can be overcome by large amounts of
interconnection. In other words, by physically connecting energy systems together then when
energy is not available in one place, it will be available in another and can be transported to the
place it is needed. Hence interconnection deals with the spatial inflexibility of our thing-based
energy system.
Unfortunately it simply isn’t true that making a system bigger reduces its entropy. However, it does
allow for a greater degree of information and the ability to use that information more affectively
over a greater space.
If I tried to power my house simply from the incident solar and solar generated natural energy in the
area of my part of south west London I would undoubtedly not be able to match precisely the spatial
and temporal demand for energy use in my house. Hence it seems logical that there will be benefits
in pooling the energy capture of a wider system and also providing the ability for the idiosyncratic
activities of energy users to balance each other out, however this is only the case if the systems exist
to manage that system in a way which achieves this.
It is absolutely true that interconnection is a vital part of the low-carbon and sustainable energy
system, and it is clear that a more interconnected system allows the greater use of information in
the reduction of the entropy of the overall system. However interconnection is only facilitation of
information usage in the energy system across space. It is not the answer in itself.
13
So at various times in these essays I will try to make myself very unpopular with the environmental
movement. Here is the first big one. Grid parity is rubbish. Many advocates of small-scale renewable and
other power generation like to compare their costs to the delivered cost of grid power at a space and time in
the system (usually the most expensive point). The simple fact is that in the energy system, if you are energy
capture, you are energy capture, and unless you can manage without the rest of the system to support you
and reduce the system entropy so that your energy is in a useful form then you should be compared with
other forms of energy capture. Hence a solar panel is not a more rational investment because I plug it in at my
house rather than next to a major sub-station. There will be outrage in the local health food shop, but it is
true, I am afraid.
14
See (Supergrid) for instance.
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Next let’s think about energy storage. Today we take storage largely for granted as it was gifted to
us by the forests and seas of the distant past. The energy industry does have massive teams and
investments seeking to reduce the costs of transportation and storage and there are many very large
and important companies in the field of energy logistics. However, at a macro, system-design level,
we largely take it for granted. At a high level storage and transport are a small reduction in the
available capacity for useful work of the Earth’s energy store which we are prepared to pay in order
to create the spatial and temporal flexibility which we need in order to live the ordered existence
which we have become used to.
In a thing-based system storage is a real and substantial issue. We need to find a way to use the
energy we instantaneously harvest to create a store which can be used at future times and can
potentially also be moved to different places. Hence we will use some of our precious harvested
energy, and hence the capacity of some of our energy harvesting things, to reduce the entropy of
part of our energy system, hence necessarily creating disorder in the wider universe, in order that
we will have the capacity, in some future time and place, to use that energy to impose order on
some part of the human dominated sub-system and then again create further disorder in the wider
universe.
If this sounds like a big ask then it is, and efficient energy storage is the holy grail of the energy
system. With the exception of harnessing the rainfall and melt-water in topologically advantaged
areas for hydropower, large-scale, low-cost storage of non-carbon based energy has so far eluded
science, and as we can see from this discussion, such a system has no small thermodynamic hill to
climb compared to the stuff-based approach we have become used to.
For the purposes of this essay, we will assume that non-carbon energy storage is going to be
expensive, but possible to some degree.
Given the enabling technologies of interconnection and storage above, the true source of entropy
reduction in the thing-based energy system is information. Now it so happens that as well as being a
measure of the capacity for useful work, and the state of disorder in a system, entropy is also a
concept in information theory. Often known as Shannon Entropy15, entropy in information theory is
a measure of the uncertainty associated with a random variable; or one can see it as the information
content of a random variable; or equivalently the information which one is missing if one does not
know the value of a random variable. More of this in later essays, but for the moment, it should
actually come as no surprise that entropy is a concept in information theory as it is hopefully
intuitive that knowledge of a system can be used to bring order to that system.
So information can help reduce the entropy of a thing-based energy system by allowing the control
of that system in a way which maximises the utility of the user while minimising the resources
required to deliver that utility. For instance, the system can learn habits and have preferences
expressed by the users in ways which allow the system to be optimised. The information on the
available resource is vital: are we expecting a sunny day; a windy month; an early thawing in the
mountains? This provides information on the available resource on which the system can take
actions to store, preserve or expend available energy today. On the consumption side, people’s
consumption habits, preferences and requirements can be understood in a way which allows the
15
See (Shannon & Weaver, 1963)
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optimum use of energy while maintaining the same level of utility and hence order in the human
world.
Within the optimisation of the energy system we prefer to have the highest possible bandwidth for
this information. It is extreme events which will be the biggest issue for the thing-based energy
system and hence it is vitally important that the operator of the system is in receipt of as much
information as is possible.
It is likely that one key mechanism for the transmission of this information will be in a price signal,
where people express their preferences for energy use at different places and at different times in
the form of the price they may pay for energy at that place and time. One interesting facet of our
thing-based energy system, which we will explore further in the next essay, is that in order to have
the greatest about of information on which to optimise the energy system, the high bandwidth
required in that system is consistent actually which much wider volatility in short-term energy
pricing. In other words we want as much information as possible and the extreme information on
energy needs and production is likely to be the most valuable, because black-outs, for instance, are
extreme and highly disruptive events which will need extreme information to help those who run
the system to avoid.
Greater volatility in short-term energy prices and greater communication of extreme events may
seem like a state of greater chaos and disorder not the state of greater order which we are looking
for in our energy system. This is also a common misconception when people first see the definition
of entropy in information theory as they see that the greater the uncertainty the greater the entropy
but the higher the information content. Intuitively it would seem more likely that better information
may lead to a lower state of disorder and chaos. This is true and the reason for the confusion is that
people forget to consider the receiver of the information and the resolution of uncertainty that they
benefit from as they receive that information. Hence, better explained, we can say that a system of
high bandwidth and high information uncertainty delivers higher value pieces of information to the
receiver of that information and hence reduces their level of uncertainty and hence entropy as they
receive that potentially high value information16.
Within the thing-based energy system the receiver of information is either a central system
controller, or within our liberalised view of the energy market, a market place in which the various
producers and suppliers of energy interact, and in which the energy system is optimised in space and
time. In order for this optimisation (whether by a central controller or a market) to reduce the
entropy of a thing-based system to the level of a stuff-based system, and hence provide for the
spatial and temporal flexibility which its users have come to take for granted, then we need the
maximum bandwidth for that information and hence the maximum uncertainty and potential value
of the information content of what is transmitted. If price is the main communication mechanism
(as it would be in a market system and as is likely to be the case) then we must design a system for
maximum uncertainty and hence volatility in the energy price.
16
Two of the best texts you will find on information theory and its application and relationship to other
physical concepts are (Vedral, 2010) and (Seife, 2006). If you read nothing else after reading these essays,
read these books.
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As noted above, we will explore this issue in greater depth in the next essay, but those who are well
versed in current thinking in energy policy will immediately note that the need for greater price
volatility in a low-carbon energy system is in complete contradiction to the current mode of thinking
among energy economists and policy-makers.
Information does not come for free, it clearly needs to be measured or procured and then
communicated, processed, and actions taken based on that information. So for instance my
willingness not to heat my water tank on a weekday needs to be communicated either by me
directly telling someone or by my habits being observed. The state of my water tank might need to
be measured, and the energy that that allows to be made available in the system, might, for
instance, be used to charge up someone’s electric car in Germany who has expressed a desire to pay
to make sure that they have enough charge for tomorrow’s school run. All this requires more things
and hence more investment, and hence even in the case of the information elements of a thingbased energy system we continue to need more and more capital intensive investment in
measurement, control and processing systems.
So what about less? So far we have not spoken much about how all this leads to less stuff and
things.
Clearly this whole essay has been about the need to move from a stuff to a thing-based energy
system and hence in the process having less stuff and replacing it with more things. The
development of interconnection, storage and information systems all require the further investment
in things, and hence the fundamental question for the design of a low-carbon energy system is about
the right mix of five forms of investment.
These five are: energy harnessing devices (solar panels, wind turbines, nuclear reactors); energy
usage devices (focussing in particular on the investments that use energy more efficiently);
interconnection; physical storage; and information systems.
The first two, as described previously, create disorder in the energy system and hence while they
replace the stuff-based system as an energy source, they do not recreate the low entropy state
which we so take for granted in our current stuff-based system. Our three new sources of
investment required for entropy reduction are the replacement for the free-ride we are currently
taking on the pre-historic entropy reduction of the planet and the associated storage of the capacity
to do useful work. None of interconnection, physical storage or information systems harness energy
in fact in all cases they dissipate it.
We wish to create a system which provides sufficient energy and sufficient capacity to use that
energy effectively for the creation of human utility, and we wish to create that system at lowest cost
and full in the knowledge that all five of the areas requiring investment are highly capital intensive
and hence come with a substantial capital burden.
Information plays a vital role in these decisions. We need the information to understand what to
invest in; we need to be able to understand the trade-offs between energy harvesting and energy
use; and we need to be able to understand the trade-offs between the relative abilities of our three
new forms of entropy reduction investment to achieve their goals cost effectively. Vital in all of this
is understanding the extent to which information allows us to operate an optimised and more
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effective energy system which provides the same or better capacity for useful work than the one we
have today. As with the transition to a liberalised market in the 1990s and 2000s, information has
an unrivalled ability to reduce the capital intensity of this transition in the world’s energy systems.
Over these few pages we have begun to explore the vital role of information in the transition to a
more sustainable energy future. This essay has hopefully highlighted a number of things about the
existing and future energy systems which are difficult and challenging, but which we are much better
placed to deal with if we understand and confront them.
This essay has discussed the current stuff-based energy system on which we are all dependent. This
stuff (the Earth’s hydrocarbon reserves) is a store of useful energy (low-entropy state) which was
gifted to us by pre-historic times, as the world went through a reduction in its overall entropy
powered by the sun. Since the start of the industrial revolution the human race has sought to
impose its own order on the planet by reversing this reduction in the entropy of the planet on which
we live and in doing so has released disorder into the planet’s systems which has been retained,
rather than shared with the wider universe, because of the associated emissions of carbon dioxide.
We are therefore faced with ever increasing demands for energy to both maintain and increase our
current utility, but also to protect our current standard of living from the disorder we have wrought
in the non-human systems of the planet.
Our stuff-based energy system has taken the gift of low entropy for granted, but a sustainable, thingbased system will need to invest to both harness energy and deliver it to humans in a form which
has the capacity to deliver useful work. Information is crucial to delivering this low-entropy
sustainable energy system at lowest cost, and is similarly essential in then operating that system in
the most highly ordered (lowest entropy) state.
Of the numerous consequences of this line of thinking a small number are worth highlighting.
A low-carbon, sustainable, thing-based energy system needs substantially more volatile and
information-rich pricing signals than the stuff-based systems that we have today. This is clearly
contrary to much current thinking in the sector and will be discussed further in later essays.
At the core of the debate between those who love and loathe renewable energy sources in
particular, is actually the issue of entropy. Such forms of power generation may be clean but they
impose an as yet un-priced state of disorder on the rest of the system. This is an inevitable
consequence of a thing-based system and so those who loathe them clearly do not have a better
and sustainable answer, but those who love them are often caught ignoring the major challenges of
the migration to a sustainable energy future.
Clean energy may or may not be cheap compared to our existing dirty forms of energy, but one thing
is for sure and that is that entropy reduction in the energy system is going to be a lot more difficult
and almost certainly more expensive than under a hydrocarbon-based system.
Stuff comes in a low-entropy (ordered) state; things create disorder.
Energy efficiency investments, as well as all their other issues, similarly reduce the spatial and
temporal flexibility of the energy system and create disorder in the rest of the system.
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Given the state of current and historical emissions, adaptation investment is necessary, but it is in no
way a substitute for the development of a low-carbon energy system (mitigation).
We have to understand how we overcome the capital intensity and investment issues in investing in
things for a sustainable energy system and ensure that that system is spatially and temporally
flexible and hence delivers the capacity for useful work for human-kind. Information is perhaps the
cheapest and most important element in that transition and in managing the system once we have
made the transition. The application of ideas involving information in the area of financing the lowcarbon economy are myriad and we will continue to explore them in the coming essays.
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Essay Two: The Characteristics of Trading Systems and their use in
Investment Decisions and System Optimisation
The previous essay discussed what all people with a basic knowledge of physics know and that is that
there is little point in energy unless it is useful and that useful work in a system is measured by the
entropy of that system. We identified that a thing-based energy system will need investment in the
capture of energy which has the potential to be useful, and investment in creating a system which
can turn that captured energy into useful work.
Easy! You might say all we need to do is to find a clever physicist to design the system and then get
the government to build it. This is indeed an option, but it is certainly a far cry from the current
situation in the energy market. In most advanced economies there is a degree of liberalisation of
the energy market and certainly the whole narrative around climate change finance is very much
one of leveraging private capital and so increasingly we have seen systems evolve where policymakers attempt to create incentives for private actors to make those investments. Hence in this
essay we are going to explore some of the characteristics of the price signals and incentive systems
which have been developed in pursuit of a low-carbon energy system and see how they serve our
greater purpose. We will divert for a while from our fundamental theme of information in order to
lay the basic groundwork for a discussion of its role in financial decision making, but we shall return
to the fundamental role of information in finance once way have explored a number of basic
financial concepts.
First an important note on government. People often treat government as some form of over-riding,
omnipotent being that can achieve anything (this thought is particularly prevalent among both those
who have never met anyone who works in one, and those that have worked in one for too long).
Hence often commentators, when they have no other option that works, assume that the
government should “just do it”. This is, of course, flawed. For our purposes the government (any
government) is just another economic agent. If it were to be engaged directly in the energy market
it would raise money in various ways from its populous and from international capital markets and
would invest it the things we need in a new energy system. This is no different from a private sector
actor passing on the cost of its investments to its customers and similarly accessing the international
capital markets. Also if the government has the right capabilities and its people are appropriately
incentivised then they may make a good job of investing in the energy sector, as may a private
sector player, and if they don’t they probably won’t. As we move to a low-carbon energy system we
need to decide what the right agents are for the efficient deployment of the vast amount of capital
required to fund that transformation and how those agents receive and react to the information
which tells them what to do and how to do it. Our fundamental informational problems do not
change whether we pick the government or the private sector as the agent.
In the mainstream energy sector, particularly in the utility sector, the model which has evolved over
recent decades is one in which the agents of investment in and management of the energy system
are not directly instruments of government, but are to varying degrees in the private sector or
operate as if they are. The UK is an extreme case where there is almost no government ownership
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of utilities; only some sub-sectors of the utility market are directly regulated by government or
pseudo-government bodies (grids are directly regulated by Ofgem for instance); and most of the
sector operates as private companies with the governmental signals as to its (and hence society’s)
desires for their actions are sent via a suite of price and other signals operating at arms-length.
Other countries have been less capitalist in their approach to ownership, regulation and incentives,
but in most cases these days even government owned entities attempt to operate as if they were
private sector companies and most governments attempt to pass on a majority of their signals via
incentive mechanisms designed to look like markets.
Hence when we look at the characteristics of trading systems and similar mechanisms we are
studying the approaches which governments, in service of society, take in order to incentivise the
deployment of private capital, through private agents, who would not otherwise receive that signal
as it is not naturally provided by the private market.
This brings us to our first need to correct much of the talk around “climate change finance” and that
is that in our headlong pursuit of a better world much of our basic macro-level accounting seems to
have gone awry. In the coming paragraphs I attempt to explain what climate change finance really
is. The first characteristic we look at is the basic balance sheet of climate change finance.
On Which Side of the Balance Sheet do Trading Systems Sit?
A fundamental instrument of finance and accounting is the balance sheet. The balance sheet simply
says that a company’s assets minus its liabilities must equal its equity. Assets are comprised of the
value today of the future cash inflows to the company and the liabilities are the value today of the
company’s future cash outflows (its commitments to pay). Now liabilities come in real and financial
form and so we will re-arrange the balance sheet a bit to say that it is actually in the following form.
Real Assets – Real Liabilities = Financial Liabilities + Equity
All this re-arrangement does is differentiate between those liabilities in the real economy and those
which are undertaken for financing purposes. The latter largely being debt. It is a fundamental
premise of financial theory that in a perfect market it is impossible to create value through
financing17 (i.e. on the right hand side of the balance sheet) and hence that all value is created in the
activities of a company in the real economy (expressed as the real net assets on the left hand side of
the balance sheet). The right hand side of a balance sheet (financing) is hence meant to be the
servant of the left (real economy) providing the finance required to sponsor value creating activity in
the real economy.
In a market where companies naturally received a signal to make clean energy and emissions
reductions investments and those investments were value creating in their own right then it would
look no different to that of any other company. However, that is not generally true in a world
without policy intervention. Hence it is well documented that there is an un-priced externality called
climate change which due to its global nature needs a policy intervention in order to prevent a
simple tragedy of the commons occurring to the whole planet (in the parlance of Essay One we are
actually failing to price the value of the non-human dominated world as a sink for the disorder
created by our imposition of our order on the world).
17
See the classic paper on this (Modigliani & Miller, 1958)
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This externality is given a price in a variety of ways. The best known in the climate arena are capand-trade schemes for emissions and green certificates (renewable portfolio standards) for
renewable energy and various other devices. These systems tend to reward activities in the real
economy which involve either the reduction of emissions or the creation of cleaner energy or
related products and hence send a signal to the agents of investment to deploy capital in low-carbon
investments rather than high carbon ones.
A carbon credit or green certificate in any of their forms is a real future flow of cash to the company
which is reducing its emissions or creating green energy. Hence these are real assets and hence
reside on the left hand side of the balance sheet. These assets are created by the future cash flows
being paid by energy consumers or tax-payers. In the case of the EU Emissions Trading Scheme (EU
ETS18) or the UK Renewables Obligation (RO)19 the costs are paid by the end consumer as they are
passed through into the costs they pay for their energy. Now a fundamental feature of accounting is
that all assets have a liability, the real asset that is the payment for emissions abatement for the
company engaged in the activity of saving the planet is a liability for the energy consumer who is
paying for the transition.
Hence the €30-40bn per year of value in the EU ETS or the £1-1.5bn or so of value each year in the
RO is not financing, it is not financing anything, instead it is the creation of new property rights
(European Union Allowances (EUAs) and Renewable Obligation Certificates (ROCs) or under the
Clean Development Mechanism of the Kyoto Protocol Certified Emissions Reductions (CERs)) which
provide economic incentives in the real economy for the purpose of stimulating investment in real
assets and internalising the externality which is the future detrimental effects on the planet of
dangerous climate change. This real asset having been created, it is then the financial community’s
job to actually finance those assets.
Hence we have shown that the things that are generally called “climate change finance” are not
finance at all, but instead are new property rights created in the real (left hand side) of the economy.
If it were finance it would get a financial return, which it doesn’t in most cases: EUAs, ROCs, CERs
are all just costs created to provide a real asset which private agents can use to finance low carbon
activities.
The area of climate change finance is one of great debate at present. Following the UNFCCC
meeting in Copenhagen in 2009 a High Level Panel was formed by the United Nations expressly with
the task of developing ideas for where $100bn per year of “climate change finance” for the
developing world will come from, from around the year 2020 onwards20.
The first problem with this confusion about the sector’s balance sheet is that I suspect that the
developing world thinks that this $100bn per year will be real economy cash flows, or in other
words, payments for taking a low carbon rather than a high carbon pathway in their development.
This clearly isn’t finance, it is a subsidy, or a signal for agents of investment to do things a different
way. If the $100bn per year is financing , then it will require a return, because then it would be on
18
See (Ellerman, Convery, & de Perthius, 2010), (Gallo, et al., 2009) and (Lararowicz, 2009) for reviews of the
various carbon trading markets including the EU ETS.
19
See (Kildegaard, 2008) for a review of the role of green certificate systems like the RO.
20
See their report in (UN, 2010).
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the right hand side of the balance sheet. In that case, we, in the developed world, would be looking
to give the developing world money to invest in an area where there might not be the real economy
signals to do so.
This distinction is really important in the debate about the role of private sector capital. Proper
climate change financing will come from the private sector and the financial community, however
the private sector is clearly not going to create the real assets which internalise the externality
because if they did (or could) it wouldn’t be a externality or market failure in the first place. Hence if
the $100bn per year is properly raised and distributed then the financial sector will provide the
investment capital needed to finance those newly created real assets, but they cannot create them
themselves. Hence if the $100bn per year is to create real property rights which send signals to
economic agents in the pursuit of a lower carbon way, then the private sector has no role (except
perhaps as a conduit for some of the money – like the cashier at the local petrol station collects your
fuel taxes).
I hope we have now established that there is an un-priced externality which in the process of being
appropriately priced will create new assets in the real economy which will be paid for by the
populous at large in some way; agents will react to the incentive to make low carbon investments
and then the finance sector will enter into the service of this endeavour by providing the financial
wherewithal for the right hand side of the balance sheet.
In the wake of the financial crisis of 2008-9 a strong narrative emerged around the need to intervene
anyway on the right hand side of the balance sheet, as the failure of capitalism was a signal that low
carbon investments would be impossible without such intervention. It is actually very hard to
construct a reasonable argument that for most of the emissions in the world that the economies in
which those emissions are released do not have reasonably good access to capital, them having
sponsored the build-out of existing (dirty) power systems, roads, telecommunications, and much
more. Hence there is no reason to assume that in the majority of cases they cannot fund the right
hand side of balance sheet which has a well constructed left hand side.
One reason people have for the creation of institutions designed to interfere with the right hand side
of the balance sheet is that the privately managed investment community is unprepared to take the
policy risk inherent in the real assets created by climate policy on the left hand side of the balance
sheet. As we shall see later, this may be true, but still doesn’t justify intervention. Firstly, it suggests
that a public body will be more risk seeking with the deployment of our taxes than a rational and
informed private sector agent is prepared to be with their capital, which is a little concerning.
Secondly, the idea that a public investment body is required to invest against public policy
instruments because said instruments have been too badly designed to promote private investment
is clearly the stuff of a Yes Minister21 sketch. Hence if the signal isn’t working, change the signal,
don’t intervene to be the agent.
21
For the benefit of international readers and young Britons without access to UK Gold (the TV channel) Yes
Minister is a very famous and funny situation comedy from the 1980s which poked fun at the ridiculousness of
government and the dysfunctional relationship between politicians and their officials. One can imagine Sir
Humphrey explaining to his Minister that they were announcing a policy to create an institution to invest
against the risks created by their last policy which there had turned out to be no other institutions to take.
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Also you will remember that at the start of this essay I highlighted the fact that the government is
simply another economic agent. Something that the desire of policy-makers to interfere with the
right hand side of the balance sheet often ignores is the absence of the right agents in the market to
react to the signals being sent by the property rights created to incentivise them. Hence if the
agents exist, fix the signal, and if the agents do not exist then maybe create the agent, but
government should not look to be the agent unless it is completely convinced that it has the skills
and capability.
Despite all the above, interference with the right hand side of the balance sheet is justified in some
circumstances and it is important to understand why institutions such as the World Bank, IFC, EIB
and various others do exist. The rule of law; the ability to identify distinct economic agents; and the
establishment of enforceable property rights are essential to the well-functioning system the
arguments above have relied upon. Without them then assets cannot be quantified because there is
not a legal system under which to assert the right to the future cash flows. Public bodies are often
used to leverage private finance where these things are poorly defined or hard to enforce. This
might be the case where countries have poorly defined legal systems or interestingly in the case of
climate change mitigation where property rights are poorly defined or difficult to exercise security
over. This latter case might occur in the case of energy efficiency investment, for instance, where it
can be hard to differentiate the cash flows of the energy efficiency intervention from those of the
host emitter.
To finally conclude this important point, where the property rights related to the act of emissions
abatement are well defined in law then the right hand side of the balance sheet should require no
intervention and in fact the need for such intervention almost certainly signals poor execution of the
policy in the real economy. We need to very clearly establish in the minds of climate policy makers
the distinction between the two sides of the balance sheet and that they should spend most of their
time worrying about the left hand side.
Essay Four will bring us back to the theme of accounting and the role of trading systems in the
creation of a global emissions accounting system. We will move on now to explore how the assets
on the left hand side of the balance sheet are defined and how this relates to the property rights
created in policy.
Asset Mismatch in Trading Systems
“A tonne is a tonne” is one of the battle cries of those who promote market solutions to the creation
of the incentives that create the real assets for emissions-reducing companies. It is a statement of
the physical fact that a tonne of CO2e (carbon dioxide equivalent) saved anywhere in the world has
the same physical impact in terms of reduced warming as one saved somewhere else.
However this has lead to the creation of market in emissions reductions which appear to be
mismatched in time with the investments required in order to reduce emissions. As we will see in
this section the application of financial theory to understanding investment behaviour is
fundamentally dependent on the definition of the asset which is being analysed and that asset’s
characteristics.
Markets in emissions reduction, clean energy investment, and indeed electricity itself are based on
rules made and signals sent by policy. The nature of the power system is such that the rules for
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trading and pricing power have to be made up in a way that they aren’t for other markets. The
power grid constrains physical arbitrage such that without such rules a functioning market would not
evolve (as we saw in Essay One, there has been a very significant role for information and
information technology in the development of these markets to date).
When systems of incentives and price discovery such as power markets or the EU ETS or the CDM or
the RO are defined then one of the key characteristics of these markets is the period over which the
market settles and hence price forms. In the case of the UK power market the market settles every
half hour, in that the supply and demand for power on the system must balance commercially every
half hour (actually the grid is kept in balance in real time during these 30 minutes period, but that is
detail22 for the purposes of this paper). The RO settles every year: That is that the demand for RO
Certificates (ROCs) is set every year and companies have to comply every year and hence a
settlement price is determined based on demand and supply for every year. For EU ETS, compliance
is at the end of a period, so while allowances are submitted and allocated every year, compliance
occurs at the end of that period, as is the case with the Kyoto Protocol. Those periods being from
2008 to 2012 for the current phase (Phase 2) of EU ETS.
You will note already that all of these markets settle over very short periods compared to the lives of
the large-scale emissions reduction investment that companies might make. For the purposes of
illustrating the point, please allow me to discuss a hypothetical idealised market for (say) carbon
credits which settles every year.
The real asset or new property right which has been created in such a system is a carbon credit
which is valid for one year and whose price is dependent on the supply and demand for such credits
in any given year. There is, of course, a market in subsequent years which again settles in those
years depending on supply and demand.
This is a perfectly good market for stimulating short term changes in carbon emissions. If there is
the capacity to change the carbon saving in the economy on an annual basis then there is an exact
match between the property right created in law and the economic benefit of the action of reducing
emissions. Within a power system where coal and gas stations are both present then a tonne of
emissions reduction can be created instantaneously by reducing coal-based generation by
approximately 2MWh and increasing gas-based production by the same 2MWh in order to keep the
system in balance23. It is easy to see here how the real asset created by policy matches the real
action which it stimulates in the real economy. Also the information (signal) which the trading of the
credit sends in that given year is exactly to reduce emissions (at a certain price) in that given year.
Now however, consider an investment in a wind farm or solar park or any other of the capital
intensive things which we described in Essay One. Being things, the investment being made is
substantially upfront and there is almost nothing that can be done to change the cost of the
investment over its lifetime (these are highly irreversible investments). Hence the cost of the asset
22
With apologies to all grid managers of the world for this glib approach to the thing that actually keeps the
lights on.
23
This by implication assumes an emissions intensity of gas-based generation of 0.5 tonnes CO 2e and for coalbased generation of 1.0 tonnes CO2e.
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being financed is defined at the point of investment decision and is whatever a wind farm or solar
park or other thing costs to build at that time.
The value of the asset (in our simple conceptual world) is the value of the future carbon credits from
which it benefits, causing there to be emissions reductions in the power sector. Hence the value of
the real asset is equal to the discounted sum of the carbon credits which represent the emissions
savings over the useful life of the investment24.
The actual asset being invested in and its value are clearly not directly related to the property right
which has been created in law in our conceptual carbon credit market. The value of the actual asset
being invested in is dependent on the value of N of the real assets created to internalise the
externality with these N real assets spread over an extended period of time (N years), whereas the
investment in our thing, is made substantially based on the cost of that investment at a specific
point in time (the start of its productive life).
This fundamental mismatch creates a number of issues.
Firstly, the rules of the carbon market may change over the lifetime of the investment which makes
dependency on those N future assets quite risky. Secondly, the year-by-year price formation
mechanism for carbon credits in this system may have no relation to that required to stimulate the
wind farm investment we postulated. If the marginal tonne of annual carbon abatement is from fuel
switching then its cost relies on the spread between gas and coal prices (as well as the relative
efficiencies of the two forms of production) and it is hard to assert how this is in any way related to
the costs of building a wind farm, solar farm or any of many other of the things we have described.
Similarly if in the UK power market the marginal unit of generation in any given year comes from an
existing coal or gas station it is not at all clear how this sets a meaningful price related to the cost of
potential future forms of power like nuclear power, wind or carbon capture and storage (CCS).
One way to bridge the mismatch is for forward markets to evolve in the newly created asset
classes25. For instance, there is a hope that there will be a forward market in carbon credits which
extends over the life of the actual physical assets involved and hence a forward market closes the
asset duration mismatch which we have identified above.
Unfortunately there are very few markets in the world which trade forward with any liquidity more
than a few years. Those that do, tend to do so because the asset can be stored and hence there is a
no-arbitrage relationship between the spot price of the asset and the forward price which is based
24
This can be expressed mathematically as:
where:
r
Carbon Credit Pricet
N
Cost of capital
Value of a carbon credit during any year in the future t
Life time of the asset
25
See (Blyth, Bunn, Kettunen, & Wilson, 2009) and (Bunn & Gianfreda, 2010) for discussions on forward pricing
in these markets.
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on the prevailing interest rate and something called the convenience yield. An important
misconception that many policy-makers have (and a few financiers too) is that the forward price
(where it exists) is an estimate of future price. It isn’t it is the no-arbitrage price based on the spot
price today and the interest rate and the convenience yield26.
This means that just because price is formed in a certain way today and it is possible to store the
asset doesn’t mean that price will be formed that way or at that level in the future.
Some assets created to internalise the climate change externality can be stored to some extent (i.e.
ROCs, EUA can be banked), but again there is still a mismatch between what forms the price on an
annual basis today and the price of the asset investment today and the likely price formation in the
future, and the simple truth is that due to uncertainty as to future policy and the capital required to
back trading positions, there is not substantial forward trading of most of the instruments we care
about in climate change incentives and such instruments are unlikely to ever join the very limited
ranks of the financial instruments which do trade forward many years in reliable volumes.
Some people like to make analogies between carbon credit and other policy-created property rights
and shares traded on the stock market. It is not uncommon to hear people talk about trading
carbon credits as being like trading shares. Carbon credits; EUA, CERs, ROC, and power are not like
shares, they are like dividends. The wind farm or solar farm or other such thing is equivalent to the
share. This is a really important distinction.
Shares (or bonds for that matter), which for many companies are traded quite liquidly on many
markets around the world, are in effect a right to receive cash-flows from a company (for a share in
the form of dividends) which are uncertain over time. Hence the value of that share today is equal
to the discounted estimates of the dividends over the remaining life of the company (for real
companies this is often taken as forever, for companies comprised solely of projects it might be
finite). Dividends are paid out every year and their value is unknown. Carbon credits and related
instruments are similarly created every year by an investment in an emissions reducing enterprise
and are of uncertain value, but holding the asset which creates the emissions reduction creates the
right of the holder to receive the credit (or ROC or EUA or CER etc). Hence carbon credits do not
trade like shares because they are like dividends and the analogous asset to a share is the wind farm,
solar farm or other emissions reducing enterprise.
26
For the mathematically minded amongst us:
where:
F
S
t
n
r
c
Forward price
Spot price
time today
time period in future
risk free rate (on a continuously compounded basis)
convenience yield (on a continuously compounded basis)
E
denotes an expectation at a given time t
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We have discovered that the real assets created as new property rights by policy in order to
incentivise investment in the things which we need in the low carbon energy sector, are generally
mismatched with the assets which they are meant to incentivise investment in. An instrument
which has annual (or even shorter) price formation and settlement, is clearly not matched to the
investment in a thing which has a long life, but whose investment cost dominates and hence is set at
the point of investment.
We will now move on to discuss this issue of high upfront costs of thing investments, and what this
means for the financial characteristics of investments and for the policy design of mechanisms
intended to create the incentive to make those investments.
Defining Average and Marginal Cost Investments
We have noted throughout this and the previous essay that a thing-based energy system is one in
which investments are made in capital intensive equipment which has most of its cost in the initial
investment. Most things then have a very low operating or marginal cost of production (the sun and
the wind are free, for instance). This leads to a need to understand how the investment
characteristics of a thing-based energy system might be different from a stuff-based one and how
we might therefore have to think about the incentive systems and signals which we need to send in
order for agents to make the required investments.
The average cost of energy generated from a given investment is generally calculated as the cost of
all the inputs required to create the energy including the initial capital investment with that capital
investment recovered at a reasonable cost of capital over the estimated useful lifetime of the asset.
The marginal cost is the avoidable cost of generating the next unit of energy, paying no attention to
any cost already incurred or cost which is not variable with the output of the plant.
Hence in the case of a stuff-based energy system we are used to thinking about the average cost of a
coal or gas-fired power station as being the estimated cost of fuel, operating and maintenance cost,
and the cost of the initial investment recovered at a reasonable cost of capital over the useful
lifetime of the station (or actually more correctly over the estimation of the number of units of
energy which the station is expected to produce over its lifetime). The marginal cost of the station is
usually thought of as the fuel cost and possibly some elements of the operating and maintenance
cost which vary with individual units of output.
Stuff-based energy generators therefore clearly have a high ratio of average cost to marginal cost,
whereas thing-based energy generators generally have very low marginal costs as their fuel is free
(sun and wind for instance) and they have a high upfront investment cost, and even their operating
costs are largely fixed (you will give the solar panel a wipe with a duster whether it produces the
next unit of electricity or not). This means that things have a much higher ratio of average to
marginal cost.
As mentioned in Essay One and as we will explore in great detail in Essay Three this means that there
is a greater capital burden, irreversibility and opportunity cost of investment for a thing-based
investment than a stuff-based investment.
If we are to incentivise investments in a thing-based energy system it therefore appears that we
need to provide them with payments which reflect this very different average to marginal cost ratio.
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The above section showed how we have a mismatch between the forms of many types of trading
system arrangement and the investments in assets that they are meant to incentivise. The other
thing about things in the energy system is that they cannot react to price signals, so in the case of
stuff-based generator, it can turn off or otherwise change its behaviour in the market, based on the
information content of a say annually or hourly settled instrument, however to an inflexible
generator with low marginal cost the information at this level of granularity is of no use; they cannot
act on it.
This issue is increasingly recognised in system design and hence we have systems of feed-in tariffs or
regulated returns in many markets which have low ratio of marginal to average cost in order to
ensure that there is proper capital recovery and hence a reason to invest.
Of course, this average and marginal cost problem and the mismatch highlighted in the previous
section leads some people to the view that government should simply pay for the capital for a thingbased system upfront. That way we can achieve perfect matching of the cash cost of the investment
and the payment for making the investment. This argument is rather unhelpfully reinforced by some
people’s views that governments can systematically access cheaper capital than the private sector
and hence it is cheaper for society if the government does all the financing. This latter point, of
course, isn’t true as by extension you get complete state domination of the economy, which didn’t
go well the last time we tried it.
The real reason why we should not have the government pay upfront is about incentives. If society
is to support the investment in a thing-based energy system then we need to make sure that
someone is suitably incentivised to keep the system operating at its full capacity over its lifetime.
The payment of the average cost of generation by performance (i.e. by units of electricity or
emissions reduction) has the benefit of giving the economic agent in charge the ongoing incentive to
ensure the performance of that capital investment over its life. In fact a pleasant side effect of the
ratio of marginal to average costs in the case of thing-based investments is that this incentive is very
high.
Therefore it is a good idea to remunerate thing-based investments based on their continued efficient
performance, but it is not a good thing for the price to vary substantially after the initial investment
has been made as this price variation creates no information or incentive which can be acted upon
by the agent and hence is only likely to add costs in to the system (see the next essay).
Another average and marginal cost issue in the design of our transition to a low-carbon economy is
that of the level of investment decisions incentivised on the market. In particular it matters what
size of transformation one is trying to make and hence in the language of finance what the size of
the trade is which policy-makers are trying to execute. This is best illustrated by a live example.
The rules for connections of new generators in the UK power system have historically been
deliberately designed to create an incentive to locate in areas where there is a deficit of generation
compared to demand. If the form of generation one is trying to incentivise is infinitely transportable
and doesn’t need much space then this makes a lot of sense, and also if the increases in the
generation stock required are small compared to the overall system then it makes sense to
incentivise investment where the marginal costs of the grid system absorbing that new power are
the lowest. However this system has caused no end of heart-ache for the UK wind industry as it has
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tended to “penalise” those who wish to locate their wind farms in windy places with low population
density like Scotland, which has seemed a bit perverse. The system is now under review and rightly
so, because the size of the trade the UK is trying to do has changed and so the marginal investment
has therefore changed.
In the days where renewable energy was a marginal industry and we might have occasionally
wanted to put the odd small wind farm on the system then the previous system made perfect sense.
From a system perspective we would want to accommodate such projects at the lowest marginal
investment cost and hence it would make more sense to squeeze them into a cheap bit of grid in
southern England than to re-wire the north of Scotland for the sake of a few Mega-Watts of windier
wind farm. However today the marginal investment that the UK is trying to make is sufficient to
power between a third and a half of it electricity system with renewable energy. Hence the size of
the trade in wind power which the UK is doing is much bigger and hence the marginal cost of that
trade is at a very different place on the overall cost curve for renewable energy investment. The
investment (trade) is now of national significance and the only way to realise such a scale is to make
substantial investments in the whole system. In this case it makes more sense to do this in a way
which accesses the greatest resource (Scottish and offshore wind for instance) than to penalise
those places.
We have seen in this section that a thing-based energy system has quite different financial
characteristics to a stuff-based one in particular with respect to the average and marginal costs of
the investment. Systems that pay by performance are essential in creating the incentive to realise
the value of the initial investment, but variations in price provide no information or incentive for an
inflexible asset the majority of whose costs were expended at the point of initial investment. Hence
we may need different approaches to incentivising these investments. We have also seen how the
size of the investment programme which we are trying to execute changes the marginal investment
cost of the activity and hence can again influence the rules under which we should incentivise and
signal those investment preferences.
In the debate about how to design these incentive or signalling systems one of the key and often
debated issues is that of whether price or quantity should be regulated. This is the final
characteristic of trading (incentive) systems which we will explore in the next section, before then
rounding off the essay with an attempt to bring these disparate issues together in some robust
conclusions.
Price versus Quantity
Most people who start to learn a bit of economics spend a lot of time drawing graphs of price versus
quantity. For most products supply curves slope up from the bottom left to the top right and
demand curves from the top left to the bottom right. The intersection of such curves gives you a
market equilibrium price and hence we assume that markets have the equilibrium position of price
and quantity.
If we are to invent a market-style arrangement whose job it is to incentivise investment or
alternative behaviours then clearly we have to decide how we create such a market in order to
provide for the prospect of it achieving an equilibrium which achieves our societal objective.
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It is hard to design an approach which allows both price and quantity to be free variables and then
have confidence in an equilibrium position being attained, hence the design of incentive or signalling
mechanisms in environmental property rights and emissions abatement has focussed on setting
either the price or quantity and letting the interaction of the agents of investment (the market)
cause the free variable (quantity or price) to be set. (There are some examples of setting neither
variable and hence both being free variables which we will discuss briefly at the end of this section).
Hence in most continental European systems of renewable energy incentives, price is fixed through a
fixed or formulaic feed-in tariff and then the quantity of investment and hence renewable energy
production is allowed to vary freely. In systems such as the European Emissions Trading Scheme
(and the design of most cap-and-trade schemes) then the quantity of allowable emissions (the cap)
is set and the price is allowed to find its own level.
The economic theory of deciding which approach to take involves the relative slopes of the damage
and emissions functions27. So, the theory goes, if the damage function is very steep and the
emissions curve is shall, then regulate quantity. For instance the costs of not emitting mercury into a
lake are small, but the damage of even small emissions of mercury into a lake are big, and hence
simply state that you can’t emit mercury into the lake and hence regulate quantity.
Similarly, if the damage function is shallow, and the cost of abatement is steep, set a price. So some
argue that the marginal impact of an extra tonne of carbon dioxide emitted into the atmosphere is
small, but the abatement cost could be very high and so we should set a price we are prepared to
pay and let the quantity of emissions vary. This is the main economic argument against the use of
cap-and-trade systems and for carbon taxes instead (a tax being a way of setting a price on
emissions but not the quantity).
Any cursory look at the actual application of these different approaches around the world leads to
two observations. Firstly, that the economic arguments are not followed. We have cap-and-trade
systems for instance, and secondly that no policy-maker ever seems happy setting one of price and
quantity and letting the other vary.
There is a good reason for this; that is that price times quantity equals money and it is the total cost
of any system which eventually policy-makers, consumers and tax-payers care about. Hence we
observe quantity regulation being put in place where we have price set (Spanish feed-in tariffs as
one example) and we have price setting being introduced in systems designed by setting quantity
(the UK’s plan for a floor price in the quantity-based emissions trading scheme, for instance).
One of the further issues which quantity-based systems have is the asset mismatch issue which we
highlighted earlier. In a price-based system one can say that a certain project gets a certain price for
a period, whereas a quantity-based scheme needs to settle, usually on a relatively short time-frame
or otherwise there is nothing to force price formation. One way to look at this is that the quantity in
the market is just the aggregate of all the investments taken based on the price in a price-based
system, but in a quantity-based system price has to form by some mechanism which causes the
whole market to come together at some point. This is the role of the settlement period and its
27
See (Hepburn, Regulation by Prices, Quantities or Both: A Review of Instrument Choice, 2006) for an
excellent review of the economic theory.
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procedures and hence if we are to have any visibility on payment, then quantity-based systems are
doomed to give short-term price signals because they must have short-term settlement periods.
Settlement and the setting of price is also a market wide signal in a way that quantity is not. Hence
quantity-based systems tend to have higher volatility, higher uncertainty, higher information
content, and hence higher ex-ante entropy than price-based systems. As noted above, high price
volatility, and hence high information content is actually not much use to thing-type investments
because of their low marginal costs and inability to react to the information. As we discussed in
Essay One, quantity-based systems have high entropy and high information content, but this is only
useful if the receipt of that information can cause a reduction in the entropy of the overall system.
Thing-based power generation has no such capacity28.
There are at least two examples of systems in the environmental arena where both price and
quantity are free variables. One was the original UK Renewables Obligation (actually now it is a
feed-in tariff by another name but it was once something different). The original RO set a quantity
of money to be spent in any given year on renewable energy in the UK and hence allowed price and
quantity to come to an equilibrium constrained by the market only containing a certain amount of
money. This has some advantages: it pragmatically recognises that all price-based systems seem to
need quantity control and vice versa. However, it does again require annual settlement in order to
create price formation across the market.
The other example is the CDM where a combination the UN Executive Board and the rules for offsets
in the various countries around the world control the volume, and a combination of the Chinese
government and the price mechanisms in those various countries set the price. Whether one can
consider this to be two free variables finding their place or two highly controlled variables would be
a long debate on which I would sit firmly on the side of the latter explanation.
Having explored one of the basic debates in the design of incentive or signalling systems in the
environmental area, the next and final section of this essay looks at drawing the concepts in
incentive design explored in this essay with those of the energy system we need to create which we
discussed in Essay One.
Stuff and Things, and Energy and Entropy
We have discussed the fact that when people say “climate change finance” they actually don’t mean
finance at all. In almost all cases the mechanisms that are put in place to “finance” the transition to
the low-carbon economy are actually incentive regimes which signal society’s desire for low-carbon
investments to the agents of investment in the energy sector.
In almost all cases they achieve this by the creation of a new property right (a carbon credit or a
renewable energy certificate etc.) which is a real asset, and hence a left hand side of the balance
sheet item. It is the job of government to create in law these new assets which it is then the job of
the financial markets to finance (the right hand side of the balance sheet). Climate change policymakers seem determined to confuse the two sides of the balance sheet, but it should be abundantly
clear to all that the private sector will not create the property rights required to signal society’s
28
See (Klessmann, Nabe, & Burges, 2008) for a review of the issues in exposing thing-based investments to
market signals
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desire for a low-carbon economy, and hence that must be government’s role. It is not clear that
government has anything but perhaps a light facilitating role on the right hand side of the balance
sheet.
In the drive from a stuff-based to a thing-based energy system, the nature of energy generation
investments will change to one of low absolute marginal costs and high ratio of average to marginal
costs. These things will create entropy in the energy system because of their inability to respond to
information which they might receive from, for instance, a price signal. Hence their inflexibility and
lack of ability to respond to information means that information rich incentive systems are wasted
on thing-based power generators.
It therefore seems appropriate that such thing-based investments be incentivised by price-based
(fixed price) incentives or signalling arrangements which recognise the fact that long-term price
certainty is more valuable than the information content on which the things cannot react. If climate
policy creates a price for a certain sort of investment in clean energy production then (assuming that
price endures over its useful life) that price creates both the incentive for the investment to be made
and for the owner of that investment to keep it operating effectively over the life of the asset (as
there is a high margin due to the low marginal cost).
We have said that thing-based systems require price-based incentives; that those incentives need to
endure over the life of the asset, not in a single shorter settlement period common in trading
systems; but that these things will create disorder in our energy system which they are incapable of
dealing with. We also noted in Essay One that this thing-based energy system needed wider
bandwidth for information (not less) in order to project this disorder (entropy, information) through
the system in a way that networks, storage and control systems can use it to reduce the entropy of
the energy system and hence create useful work.
This therefore all seems very contradictory. Thing-based investments have little use for information
but a thing-based energy system needs high information content in order to create useful work.
It isn’t contradictory.
Simply put, we need horses for courses. If a thing in our new clean energy system cannot use
information usefully then it is wasteful to expose it to that information (we will see really how
wasteful in the next essay), and hence price-based incentives with matching asset lives makes the
most sense.
However within this thing-based energy system we need the information on which we can act to
reduce the entropy of the system on a much shorter term basis (minutes, hours, days, weeks, years)
and in such a system (assuming a market-style approach) we need that information to be
transmitted through price. The formation of a price over a settlement period requires the bringing
together of all the quantities in the market over that given period (or more precisely at a relevant
point in time). Hence it is only in a quantity-based system, with a settlement period relevant to the
system’s need to process information, that the system is brought together to embody the
aggregation of the diverse information (entropy) into a price which might then provide a signal
against which the agents capable of reducing the entropy of the system can then react.
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Hence where information is crucial we need it provided (formed) in periods which are relevant and
this will lead to relatively short settlement period, quantity-based systems, and where information is
not relevant (or potentially even wasteful) then it makes sense to have price-based systems which
match the asset lives of the investments involved.
Put another way energy capture and usage devices need price-based, low information and hence
low-entropy systems of incentives, and entropy reduction needs quantity-based, information rich,
high-entropy systems.
There is currently quite a debate raging about the relative benefits of price versus quantity-based
incentive systems. The reader will note many articles on the subject which state somewhere that a
carbon tax (price-based system) would be preferable to cap-and-trade for instance. This debate has
many issues, but actually the debate simply shouldn’t exist. The fact is that the debate only exists
between people who have been brought up using an energy system where you get your energy in a
low entropy state (ready made by those pre-historic organisms). An energy system that has to
manage down its entropy very actively, rather than wastefully expelling disorder into the planet’s
wider energy systems, needs a system for managing energy capture and usage, and entropy
reduction, and hence has a role for price and quantity-based systems. The important issue is to
apply them in the right way and for the right tasks.
All of this is about the left hand side of the balance sheet. Almost nothing in this essay has been
about financing, instead it has been about how we design the economic ecosystem of incentives
which best fits the investments that we need economic agents to make in the development of a lowcarbon energy system.
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Why cap-and-trade systems don’t lead to investment decisions
Essay Three: Why cap-and-trade systems don’t lead to investment
decisions
From Essay Two it might seem quite simple to assert that cap-and-trade systems (quantity-based
incentive arrangements) don’t lead to investments in energy capture (or saving) technologies.
However the issue deserves a degree of formal treatment and hence this essay will seek to explore
how information, or the potential for receipt of future information, causes delays in investment and
increases in the observed costs of those investments. It will also allow us to start to formally
understand that information has a real price, and this will be extremely useful for the essays which
follow.
I have resolved to keep the amount of mathematics in these essays to a minimum and to put all
equations and calculation in other essays either in footnotes or appendices. This essay is the only
exception where I do perform a number of calculations. I trust the reader will find them simple and
instructive and there is an extensive appendix which deals with a number of the formal
mathematical issues.
As noted in earlier essays, climate change is a capital problem and more importantly, it is more of a
capital problem than our existing energy system. This capital intensity and its associated
irreversibility alone are sufficient for us to want to spend some time looking at the decisions which
are used to deploy that capital in investments. However, also, as anyone in the climate change
arena will tell you, delay is the scourge of the climate change debate and hence it is important to
understand what causes these delays and how they can be avoided (when it is rational to do so).
Delay is created by the possibility of waiting, or put the other way around, by the opportunity cost of
investing being greater than the value of investing at any given point in time. This trade-off of
investment now and in the future is analysed through the medium of option theory, and is created
by the prospect of future information. Hence we will show how the higher the information potential
of a system, the higher the value of delay, and the higher the cost of investment.
We will also see that while the investments in the low-carbon economy themselves are obviously
valuable, the actions of companies and individuals making investments also provides us with
observable action and hence information which is vital in understanding effective climate policy
design and in mobilising capital in the pursuit of a low-carbon economy.
Derivatives
Before we get into it too deeply, a few words on derivative theory. I find much of the literature on
this subject very hard to penetrate. There seems to be a desire on the part of authors to construct
massive amounts of numerical and theoretical analysis when the beauty of derivatives in my view is
the clear insights that they give you into information flows, decision making and the relationship
between economic agents29.
29
Having said this, the two best texts for those learning and applying derivatives I would say are (Hull, 2003)
and (Dixit & Pindyck, 1994) and these essays draw substantially on each.
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When looking at derivatives it is important to differentiate the three main components of any such
analysis. Behind the famous Black-Scholes-Merton30 formula, for instance, and other derivatives
models are three things. Firstly, the general structure and properties of the derivative itself.
Secondly, some assumptions about how the world works today. In the case of Black-Scholes-Merton
these assumptions include the ability to trade the underlying security continuously in any quantum
and without cost. Thirdly, they make assumptions as to how the underlying securities behave in the
future: in the case of Black-Scholes-Merton they assume that stock prices obey geometric Brownian
motion, for instance.
Both elegant formulas such as the Black-Scholes-Merton formula and less elegant numerical
analyses created by vast numbers of computer simulations rely very heavily on certain, often
unrealistic and arbitrary assumptions that fall in the second and third of these categories. Many
texts on derivatives therefore spend inordinate amounts of time explaining things like stochastic
calculus to the reader in order to lay the groundwork for the elegance of the final solution. It is this
that makes thinking about things as derivatives so inaccessible to the majority of sane humanbeings31. The Mathematical Appendix to this essay has a lot of this, but in the main text I am going
to attempt to stick to relatively simple mathematical formulations and I am also going to try to make
it quite clear what assumptions I am making and when. I am also going to use numerical examples
as I think people find it easier to relate to them. I have roughly referenced my sources and they are
vaguely realistic as at the time of writing, but I have obviously manipulated the individual numerical
examples in order to get the answer I am looking for. The formal and general proof of the answers
can be found in the Mathematical Appendix.
NewClear investment decisions
For the purposes of analysing an investment decision and illustrating the various affects of
information on that decision to deploy capital we are going to take as an example the replacement
of existing traditional light bulbs with energy efficient ones. I am going to construct an artificial
example in order for the analysis not to be clouded by too many facts so please don’t shout at the
check-out girl in B&Q32 if your light bulbs don’t cost what I am about to say they do. Also, I am going
to treat the light-bulb purely as an energy usage investment and I am going to pay no attention to its
lack of capacity for entropy reduction in the energy system, and in fact I am going to attribute no
cost to the increase in disorder in the energy system which investments in lighting (or any other
form of passive energy usage) create.
Let’s say that there is a new form of energy efficient light bulb which in order to garner kudos with
the early-adopter green-consumer segment of the marketplace has been branded a NewClear light
bulb (investments in NewClear are a major issue in the drive to mitigate emissions and are
particularly pertinent in the UK energy market at the moment, of course). As we noted earlier, they
tend to use less stuff and replace it with more of a thing, and hence have a high average to marginal
cost ratio and they are only of use as a light bulb and so have a high degree of irreversibility as an
investment.
Let’s take the following set of parameters for the NewClear investment.
30
See (Black & Scholes, 1973).
And see (Dunbar, 2000) to see how it can all go so wrong
32
This is a well-known UK hardware chain for the international readers among you.
31
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
Parameter
Average UK domestic energy usage33
Lighting as a percentage of energy usage34
Claimed savings for energy efficient light bulbs over life of the
bulb35
Number of bulbs in an average house36
Price of power today37
Cost of a new conventional light bulb38
Cost of a new energy efficient light bulb39
Energy saving from using an energy efficient bulb
Bulb lifetime40
Assumed Value
4,196kWh / year
19%
£45-60
25
15p/kWh
£1
£20
80%
10 years
I am further going to assume that the appropriate cost of capital for my investment in NewClear is
10% and that the risk free rate in the relevant economy for me is 3% (more on this later).
Using the above we can deduce that the average traditional bulb in my average house uses about
31.9kWh/year41 of energy and that the equivalent energy efficient bulb would use 20% of that or
6.4kWh/year42 or so. This means that the energy saving from using a NewClear bulb instead of a
traditional bulb is 25.5kWh/year (31.9 minus 6.4).
Now let’s assume that one of my traditional bulbs has failed and it is in the downstairs loo where not
having light in the future is not a viable option and so I have to replace the bulb43. In order to decide
which bulb to invest in I can do a simple net present value (NPV) calculation of the two alternative
ways of providing my bathroom with light. For the purposes of making the discounting simple and
intuitive for the reader we will assume that the light has failed the moment following the payment of
my last electricity bill which was issued to me and paid by me instantaneously at the end of the
period to which it pertains44. I will also assume that the investment can be made instantaneously45.
33
(DECC, 2010)
(Carbon Independent, 2010)
35
(EST, 2010)
36
I made this up – sounds about right and a lot less than I have, I notice.
37
What my bill currently says I pay to my supplier (mid 2010).
38
Less if it is a simple bulb, but I have lots of fancy types of bulbs and I will assume others do too.
39
Ditto, I know that very standard ones are <£10 these days but I am currently replacing the spotlights in my
house (the most common bulb in my house is a spotlight) and the good ones of those are costing me £35 each.
40
Blasphemy! Energy efficient light bulbs last forever apparently. Well if you had been using them for years
you would know that they don’t (I am on at least my second set in my current house and I suspect the ones I
had installed in my college in 1993 are not still there) and anyway it is what I think and then put in my
calculation that matters and I am going to assume I get 10 good years out of one.
41
4,196kWh / year of consumption times 19% divided by 25 bulbs.
42
20% of 31.9 kWh / year
43
Members of the UK’s new Coalition Government will be pleased to see that my downstairs loo requires no
explicit subsidy.
44
This statement seems a little laboured but the timing of cash flows is really important in these kinds of
analysis and all too often forgotten when such analyses are explained.
45
Not a bad assumption for a light bulb (takes me about an 30 minutes to get to B&Q and back, traffic
permitting).
34
Ian Temperton
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2011
Why cap-and-trade systems don’t lead to investment decisions
The table below shows the total cost of light provision for my bathroom using a traditional bulb.
Element of lighting cost
Calculation
Cost of energy usage over Present value at 10% of the energy usage
lifetime
of 31.9kWh/year at 15p/kWh over 10
years46
Cost of light bulb
Traditional light bulb
Total cost of lighting
Sum of above
Cost
£29.39
£1.00
£30.39
The table below gives the same calculation for an investment in NewClear light bulb.
Element of lighting cost
Calculation
Cost of energy usage over Present value at 10% of the energy usage
lifetime
of 6.4kWh/year at 15p/kWh over 10 years
Cost of light bulb
NewClear light bulb investment cost
Total cost of lighting
Sum of above
Cost
£5.88
£20.00
£25.88
I now have two sets of cash flows and their discounted values and I must choose one of them and
hence I make the decision which yields me a positive net present value which in this case is the
NewClear investment as this provides for a net present value of £4.51 (£30.39 - £25.88). The above
two tables represent the present value or asset value of the stream of cash flows associated with
initial investment and lifetime energy usage, and the difference between them is the asset in which I
am really investing with this decision. The underlying asset of the light bulb investment is the
difference between the energy cost of the traditional and NewClear light bulb.
Note again my tortuously careful choice of words. Finance is full of people who believe they are
taking net present values when in fact they are not. You can only truly take a net present value of
two sets of numbers because a net present value is used to decide to do one thing or another as
noted above. This is really important. As we will see throughout this essay no decision is in itself a
decision, it is a decision (usually) to delay.
You will also note in the above example that the ratio of stuff (energy usage over the life of the
investment) to things (the light bulbs) are very different for the traditional light bulb and the energy
efficient NewClear investment (29x for the traditional light bulb versus 0.29x for the NewClear
bulb47).
The above analysis implicitly assumes that I have as easy an access to £20 as I have to £1, or in other
words that I am perfectly and costlessly integrated into a financial market which permits me limitless
access to capital for rational decisions.
Now moving to a more complex example, let’s assume that my bathroom light is working perfectly
well but I am a caring environmentally conscious consumer who doesn’t want to get caught out with
46
This is a simple annuity calculation with a 10% discount rate for 10 year or
11+10%10
47
.
Based on the ratio of NPV of energy usage to NPV of initial capital investment
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
the wrong kind of light bulb in his loo having published a paper on climate change finance. I have a
decision to make and that is whether to replace the traditional light bulb with a new one despite the
old one working perfectly well. I must redo my calculations.
The table below shows the total cost of continued light provision for my bathroom using a
traditional bulb.
Element of lighting cost
Calculation
Cost of energy usage over Present value at 10% of the energy usage
lifetime
of 31.9kWh/year at 15p/kWh over 10
years48
Cost of light bulb
Traditional light bulb (which I already
have)
Total cost of lighting
Sum of above
Cost
£29.39
£0.00
£29.39
The table below gives the same calculation for an investment in NewClear light bulb.
Element of lighting cost
Calculation
Cost of energy usage over Present value at 10% of the energy usage
lifetime
of 6.4kWh/year at 15p/kWh over 10 years
Cost of light bulb
NewClear light bulb investment cost
Total cost of lighting
Sum of above
Cost
£5.88
£20.00
£25.88
As you can see the net present value of the decision to replace the old light bulb with a NewClear
one is still positive with a value of £3.51 (£29.39 – £25.88, or for the quick-witted it was clearly
always going to be £4.52: £1.00 being the cost of the traditional light bulb49) and I can rest assured
that I can feel both environmentally and financially self-righteous.
So far I have used no derivative analysis and instead I have simply used the kind of net present value
analysis which appears to be prevalent in all investment decision making in business and on which
policy-makers often rely for their decisions on policy frameworks in climate change investment and
finance. However, I have implicitly assumed, in the last example, that I have no capacity to delay the
investment, which as I have a perfectly well functioning light in my loo is clearly wrong, and I have
also assumed that I am not aware of the prospect of any future information which might affect my
decision making today. This again is clearly wrong, and hence is where the options start to come
into play.
NewClear Options
Now let’s assume that I have just read an article in an environmental magazine which assures me
that NewClear investments will halve in value in a year’s time (to £10 rather than the £20 that they
cost today). This is obviously great news for the planet and for my finances. Let’s assume that I
treat this claim as being absolutely certain and what’s more, I am certain about everything else in my
investment. What will this do to my investment decision?
48
Note the implicit assumption that my change in light bulb is to occur instantaneously after I just fitted a
traditional one. Doh!
49
Please forgive a penny of rounding
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
If I make an investment in NewClear today I make £3.51 in net present value compared to doing
nothing as we saw above.
The table below shows the value of investing one year’s time.
Cost / benefit
Energy saving
Calculation rationale
25.5kWh/year at 15p / kWh
saved discounted at 10% for a
10 year investment life
NewClear light bulb
Cost of investment in one
year’s time
Payment of one year’s 25.5kWh/year times 15p/kWh
electricity
as payment for difference in
energy
usage
between
NewClear and traditional bulb50
Present
value
of
bulb Sum of the above
replacement in one year’s time
Present value discounted to Note that this is done at the
today
risk free rate not 10% as we
said we were certain we knew
the future51
Value in one year
£23.51
(£10.00)
(£3.83)
£9.68
£9.40
So the present value today of an investment in a year’s time is £9.40 and the present value of an
investment today is £3.51, and so the net present value of the decision to delay my investment for a
year is £5.89 (£9.40 - £5.89) and hence that is what I should rationally do.
The table below shows the sources of value in waiting for a year compared to investing now.
Part of investment
decision
Value today
for investment
in a year
£9.71
Difference
Investment cost
Value for
investment
today
£20.00
Energy savings
£23.51
£22.83
(£0.68)
NA
£3.72
(£3.72)
£3.51
£9.40
£5.89
Payment
for
inefficient energy
Total
£10.29
Source of difference
Reduced cost of bulb
and delayed outlay of
investment cost
Delay in achieving
energy savings
Have to pay for
inefficient energy while
waiting to change the
bulb (discounted)
50
i.e. if you don’t replace the bulb then you have to keep paying for the old amount of energy usage. This is
like the dividend yield foregone on the underlying energy saving asset, for those who can’t wait for me to get
to that bit later. I assume that the bill for this is payable in exactly one year’s time.
51
Without writing a treatise on the cost of capital it is important to note this point. If something is completely
certain then you discount it at the risk-free rate. In the case of the cost of the light bulbs or the saved /
consumed electricity in the case of the above calculations our 10% cost of capital assumes that there is some
degree of what finance theory refers to as systematic risk in the cost of electricity, energy usage and of the
bulbs. My decision to use 10% and not say 8% or 12% is, or course, in this case, entirely arbitrary.
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
Hence the information that this investment will become cheaper in the future, causes the
investment decision to be delayed even in the case where we have no uncertainty at all, and where
the investment today has a positive present value.
Being a pioneer does you no good.
Now often cost reductions are dependent upon volume sales and hence there is a possibility that the
decision to delay will influence the future cost reduction. This is a major issue in incentive design
especially when learning curves and learning-by-doing are important supposed benefits of that
incentive scheme.
In the above example we have introduced the possibility of delay in the investment in new lighting in
my loo, but we have not introduced any uncertainty (or entropy) into the calculations yet. We have
simply said that we have certain information about the future and that we have the potential to
delay the investment.
Now we can finally introduce some uncertainty into the analysis. The Temperton household is
debating whether replacing the light in the loo is rational given what might happen to future
electricity prices. One half of the household believes that Europe will stick rigidly to its climate
change related commitments and that given the expensive nature of renewable, nuclear and carbon
capture and storage technologies (never mind that they have no idea how to reduce their entropy)
that come next year domestic energy prices could have risen to 25p/kWh. The other half of the
household believes that the discovery of unconventional gas reserves will create 250 years of
relatively clean and cheap energy supply and that decarbonisation costs will not be able to be
sustained in an era of natural gas found easily around the world at $4 / mmBtu and while the world’s
economies remain in a state of long-term fragility. Hence they believe that domestic electricity
prices will have fallen to 5p/kWh by next year.
The halves of the household, while disagreeing, have decided that they are equally likely to be
right52, but also that no outcome other than the two described above will come to pass. Hence they
have agreed that each of these scenarios has a probability of 50%.
This progression of the power price is illustrated below.
Today
Power Price
52
One year’s time
25p/kWh
Probability
50%
5p/kWh
50%
15p/kWh
Possibly my least realistic assumption, I know.
Ian Temperton
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2011
Why cap-and-trade systems don’t lead to investment decisions
Using the same calculations for energy saving as we have done previously then we can illustrate the
uncertainty in the value of the energy savings which come from replacing the light bulb in a similar
way.
Today
Present value of
energy savings
One year’s time
£39.1953
Probability
50%
£7.8455
50%
£23.5154
You will note in the above that in the case of a movement to low energy prices a NewClear
investment clearly does not make sense anymore (£7.84 of present value of savings is less than £20
investment cost) and so in the case where we wait a year to see who in the Temperton household is
right then if the low energy price case is right then no investment will be made. Hence we can
illustrate the value of making a NewClear investment in each scenario in a similar format to the
above (note we are back to assuming the cost of the NewClear bulb is £20 forever).
Today
Present value of
investment in
NewClear
One year’s time
£19.1956
Probability
50%
£0.0057
50%
£3.51
You will see that the above is simply the application of the formula (max[NPV Savings – Investment,
0]) or in other words: only make the NewClear investment if it makes sense at the time you make it.
From the above we can now calculate the value of waiting for a year to make the investment
decision. In one year’s time we will have an investment worth £19.19 with a probability of 50% or
one worth zero with the same probability and hence this is worth £9.59 in a year (£19.19 x 50% plus
zero x 50%) or £9.32 (discounted at the risk-free rate) today. We will have to have paid for another
year of inefficient energy which we know from the previous analysis has a present value of £3.72
and hence the net present value of waiting for a year to invest is £5.60 (£9.32 minus £3.72).
Given that the present value of an investment today is £3.51 then the net present value of the
decision to wait a year is clearly positive and has a value of £2.09. Hence the uncertainty of the
future energy price causes us to delay the decision to invest in the light bulb, again despite the fact
that the present value of the investment is clearly positive today.
53
The same 10 year annuity we have calculated throughout but using a 25p/kWh power price (the quickwitted will spot that this should be 23.51 x 25/15 and it is).
54
As in the previous calculation
55
The same 10 year annuity we have calculated throughout but using a 5p/kWh power price (again the quickwitted will spot that this should be 23.51 x 5/15 and it is)
56
£39.19-£20.00
57
Because we would not make the investment in this case as £7.84 present value of savings is less than the
£20 investment cost of the NewClear light bulb
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
The table below again highlights the sources of the differences between the case of investing today
and deciding to delay for one year.
Part of investment
decision
Value today
for investment
in a year
(£19.42)
Difference
Investment cost
Value for
investment
today
(£20.00)
Energy savings
£23.51
£22.83
(£0.68)
Payment
for
inefficient energy
NA
(£3.72)
(£3.72)
Value of resolving
uncertainty / value
of information
Total
NA
£5.90
£5.90
£3.51
£5.60
£2.09
£0.58
Source of difference
Delayed outlay of
investment cost
Delay in achieving
energy savings
Have to pay for
inefficient energy while
waiting to change the
bulb (discounted)
Ability to avoid
investment in low price
case
What we can see from the above table is that the delay in investing means that future costs and
future benefits are delayed (the first two lines above) that costs are incurred in the intervening
period (the third line) but that uncertainty is resolved (the fourth line) and in the above example the
value of the uncertainty exceeds the loss in value of benefit foregone and interim costs incurred.
In other words future uncertainty has caused us to delay an investment decision despite the fact
that the investment has a positive net present value today (£3.51 in this case) and the fact that
therefore not investing causes us to lose the time value of that benefit (in this case £0.1058). This is
because delaying the decision in order to achieve resolution of the uncertainty has a benefit of
£5.90.
In the language of information, we would be making the decision today in a state of high entropy.
Uncertainty is basically the knowledge of the information that the investment parameters might
change in the future. At present, in the above example, there is a wide range of known future
parameters, and information arrives in the future which reduces that uncertainty and hence reduces
the entropy of the environment in which the decision is made. In our example, the value of that
future information, in fact the value of that information in as much as it reduces the entropy at the
point of decision, exceeds the other costs of delaying the investment.
58
£0.68 minus £0.58 in the above table for those who didn’t spot it.
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
So going back to the more established language of derivatives: the option to invest has a value in
excess of the investment today; or the opportunity cost of investment exceeds the value of
investment today. We can express the value of an option generally in the following way.
Option Value = Intrinsic Value + Time Value of Delay + Information Value59 + Real Cost of Delay60
Hence it is possible to re-present the above table in a way which his more relevant to option theory
and which shows the true value of the option to invest.
Option Value
Component
Intrinsic Value
Previous Presentation
Calculation
Value
Value of investment if
made today
£3.51
Time Value of Delay
Delay in savings and
delay in investment
Real Value of Delay
Payment for inefficient
energy
Information Value
Value of resolving
uncertainty
Value of savings today
minus investment cosy
£23.51-£20.00
Delay in achieving
savings minus delay in
having to invest money
Discounted value of
payment for inefficient
energy
Avoided downside
investments
Option Value
(£0.10)
(£3.72)
£5.90
£5.60
Note that the option to invest is worth £5.60. The intrinsic value is £3.51 and hence the net present
value of the decision to wait is the difference between these which is £2.09. Note also that in the
case of an option with a positive intrinsic value whether one invests today or delays appears from
the above to be a fight between the Time Value, the Dividend Value and the Information Value. In
our case the Information Value exceeds the Time Value loss and Dividend Value loss by £2.09.
We have used NewClear investments as a case study in the properties of the investment decision
and the impacts which various parameters have on it. We have observed through this example that:




Where the investment must be made (no light in the loo) and hence there is no possibility of
delay then a simple net present value comparison of the two options is appropriate;
Waiting can create a positive net present value in the case where everything is certain but
we have certain information that the investment costs will fall in the future;
Uncertainty (the prospect of information which resolves uncertainty in the future) as to
outcomes creates option value which again can cause there to be a net present value
associated with waiting;
The decision to invest today or wait appears to be a fight between the time value of delay,
the real value of delay and the value of future information (or the potential for an
investment based on a lower entropy state created by the receipt of that information).
59
Options geeks will probably more commonly see this referred to as uncertainty value or even option value
Options geeks will understand this better as the dividend yield on the underlying asset which in this case is
clearly the cost of inefficient energy use during the delay
60
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
The Mathematical Appendix to this essay deals with much of the formal mathematical development
of option theory both to prove the above characteristics in generality and to develop some more
concepts and solutions that for the purposes of the rest of the body of the essay will simply be
asserted.
Further Option Insights
We have seen from the above examples that the battle as to whether to invest today or in the future
is a fight between the costs and benefits of delay. The most substantial benefit of delay being the
value of future information and hence the reduction in uncertainty (entropy) under which the
investment is made.
In the above examples we have implicitly assumed that the only times at which we can make the
investment are today or in a year’s time. In reality of course, for light bulb replacement, an
investment in a wind farm, solar farm, wall insulation or many other things in the energy system, we
have a running indefinite option to make the investment decision or not. Hence in reality what I
should have done in the above example is assess again in a year’s time what the uncertainties as to
investment might be and again evaluate the trade-off between investment in a year’s time and
investment at a future date. In fact I should have done that for every point in time in the future, in
order to determine exactly when in the future the benefits of investment exceeded the benefits of
delay. This is where the maths gets a little complex and hence here we shall simply assert the point
that it is entirely possible to have an investment with a positive net present value which is never
made because uncertainties about the future create value in waiting which exceed the value of
investment at any point in time.
There are two other ways to look at the option value (the positive value in delay).
Firstly, one can see it as the amount by which the value of the investment today must exceed the
calculated present value in order to incentivise investment today over delay. That is to say that in
order to incentivise investment in the presence of uncertainty, then the net present value of the
investment decision must exceed that which would be calculated based on a simple discounted
present value analysis. Another way of saying this (very much less rigorously from a finance theory
perspective) is that the returns on investments must exceed their true cost of capital by a certain
amount in order to provide an incentive to invest rather than delay in the presence of uncertainty.
Secondly, one can look upon this value as the cost of information on whether agents will make
investments in certain technologies under the prevailing uncertainty. We cannot observe a net
present value of an investment in the market; instead we can only observe companies and
individuals making investments. Hence if we observe an economic agent making an investment that
tells us something about the parameters under which they will invest rather than delay. In order to
make the investment the value of that investment must have exceeded the value of delay and hence
we can see the premium of the net present value of the investment today as being a cost of the
information or the cost of observing the investment decision61.
61
See (Dixit A. , Entry and Exit Decisions Under Uncertainty, 1989), (Dixit A. , Analytical Approximations in
Models of Hysteresis, 1991) and (Lin & Huang, 2010) for more formal treatment of exit and entry issues and
some examples.
Ian Temperton
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Why cap-and-trade systems don’t lead to investment decisions
Hence we can see that in the presence of uncertainty about the future (a lack of information or the
knowledge that information will arrive in the future) then the cost of incentivising and observing
investments today goes up.
There are three more insights into option theory which we will now discuss which again affect the
costs and designs of incentive arrangements.
The first is the problem of future cost reductions which we observed in one of the earlier NewClear
light-bulb examples. Simply knowing with certainty that prices of investments will fall leads to a
disincentive to make the investment today. Often in the climate change arena policy-makers are
convinced to support new technologies with very high initial costs on the basis that there are large
potentials for costs to fall as the industry achieves certain volumes of production. This has been the
case in wind and solar power, as well as in some forms of conventional power generation such as
natural gas turbines and so it is an approach not without foundation. However, our option insights
show us clearly that this promise can be self-defeating unless those who make the investment today
are in some way insulated from the future price falls, or more correctly, unless the benefits of future
price falls are reflected in lower remuneration in the future. There is also clearly an inherent
problem with convincing people to go first with investments on the basis that this will create
“learning-by-doing” as is often claimed. While the market overall and certainly policy-makers may
wish to see the “learning” it is not entirely clear what is ever in it for those doing the “doing”.
Secondly, if we extend our analysis to industries then we can gain some insight into the costs of
incentivising new players to enter a market. If a company is already in a market and has, for
instance, operating plant or a division which does a certain thing, then it can be considered to hold a
running option to abandon this particular business activity. Similarly any company not in a certain
sector might be considered to have an option to enter the market under certain conditions. In the
latter case, from our previous analysis, it will be clear that the value of being in the business will
need to exceed the net present value as calculated at the cost of capital or otherwise in the
presence of uncertainty then the value of the option to invest will clearly exceed that of investing
itself. Similarly however the company already in the business with the option to abandon will have
to yield the option to be active or idle in the market if it decides to exit completely. This actually
means that the value of being in the business, in the presence of future uncertainty, might have to
fall substantially below the net present value at the cost of capital in order for it to make the
decision to exit62.
This basically means that in the presence of uncertainty things have to get much worse than a simple
net present value calculation might suggest for a company to exit a market, and that similarly things
have to be a lot better than a simple net present value calculation might suggest in order to new
companies to enter new markets.
Applied to energy companies, then considering that power generation companies set off in coalfired power because most of them do set off as substantially coal-based in their generation base
because of history, the additional costs which need to be put on coal-fired power and the extra
62
There are, of course, also transaction costs which further increase costs of entry and exit, but I have ignored
these simply to ensure that the reader gets the point that simply the presence of uncertainty creates the
issue.
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Why cap-and-trade systems don’t lead to investment decisions
incentives which need to be put on say wind or solar or nuclear power need to exceed those simply
required to equalise the costs of the dirty and clean technologies. Also the greater the uncertainty
in those instruments used to close the gap in the costs between these technologies then the wider
the gap that must be closed in order to incentivise such companies to abandon polluting
technologies and begin a business focussed on clean technologies.
The third insight into option theory requires us to look again at the trade-offs which make an
economic agent decide whether to make an investment or not. Investments in new projects are call
options, that is they bestow the right but not the obligation to invest on the agent involved and as
such they are left with making the decision as to whether they invest today or in the future. If we
look at the components of option value again below we have the following:
Option Value = Intrinsic Value + Time Value of Delay + Information Value + Real Cost of Delay
Observe that the Intrinsic Value (the value of the investment today) is the first term in the
calculation and hence simply increasing the value of the investment today does not cause the
decision to invest today to prevail over waiting. In the case of a call option without dividends (real
cost of delay) it is actually true that there is always a value in waiting unless exercise of the option is
forced on the agent holding the option.
Hence the investment decision will only be made when the Real Cost of Delay and Time Value of
Delay exceed the Information Value of the option. In other words, the benefits forgone from not
making the investment and hence owning the asset in question, must exceed the Information or
Uncertainty Value of the option in order for the decision to invest to be made.
The mathematics of this are quite complex, but the importance of the short-term returns to the
underlying assets (the inefficient use of energy during the investment delay in our light bulb
example) is worth emphasising due to the very long build times of many low-carbon assets. If one is
building a nuclear power station, for instance, the first cash flows foregone by a delay in investment
might be five or six years after the decision to invest and yet they are crucially important in making
the decision to invest rather than delay.
This analysis all seems very complex and it is certainly true that I have no experience of a company
making investment decisions in the clean energy sector using complex option theory, so is this
analysis valid for the real world?
Insights from Real Life63
It is true, I suspect, that there has never been a Board of Directors which has sat in front of an option
calculation and decided to make and investment because the Real and Time cost of delay exceed the
Information benefit of delay.
The investment decision however can be expressed in very simple terms. People invest when greed
exceeds fear. In other words, our equations above are easily re-expressed as the greed associated
with the prospect of lost value of the investment today (time and real cost of delay) and the fear of
63
For a range of applications of option theory to investment decisions in the climate and energy arena see
(Albers & Goldbach, 2000), (Blyth, Yang, & Bradley, Climate Policy Uncertainty and Investment Risk, 2007),
(Camacho & Menzes, 2009), (Xepapadeas, 1999) and (Yang, Blyth, Bradley, Bunn, Clarke, & Wilson, 2008)
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making the wrong decision (the value of future information). Hence any decision maker in business
will now very readily observe the option valuation playing a key role in the way in which every
investment decision is made in business. It is always the task of those sponsoring the investment to
make the perceived risk (uncertainty / future information) of the investment as low as possible, and
the immediate benefits of investment as high as possible. Indeed companies quite deliberately
invest in the process of design and assessment of investment decisions in order to reduce the
uncertainty (future information) associated with them. This is what decision-makers probably see as
the risk of the investment at the point at which they make the investment decision.
When decision makers in business refer to the risk and return of an investment people often think
they are referring to the cost of capital of the investment versus its return, and of course they are,
but they shouldn’t be, because nothing about the cost of capital of the underlying investment is
going to change in the event of delay, and actually relatively little of the effort of exploring an
investment decision in the corporate environment involves a rigorous analysis of what the
appropriate cost of capital actually is. In fact when a decision maker says that they are balancing risk
and reward they are really referring to is the information value of delay versus the rewards of
immediate action. Of course, they will undoubtedly be formally using the tool of net present value
to do this which is clearly wrong, but I am discussing here what is really going on in their minds, not
what is on the presentation in front of them.
One slightly awkward potential corollary of the option analysis presented above is that investment
decision are only made when the value of the underlying exceeds the NPV value and therefore it
appears that all investment decisions should be inherently value creating. There are one or two
examples in the corporate world where investment decisions are not value creating and so does this
not disprove the above? No, firstly even in competitive markets, this analysis holds64. Secondly, and
most importantly, it is not the outcome that matters, it is the basis on which the decision is actually
made. Hence the case presented in all investment decisions, at the time of decision, will always
show greed exceeding fear, even if that turns out not to be the case ex-post.
In daily life we can observe myriad examples of attempts to frame in our minds the idea that a
decision must be made today. “Offer must end”, “last day of sale” etc are examples in the normal
retail world where we are constantly bombarded with messages that our investment decision must
be made today or we will lose out. Calls to arms in the climate arena, and in fact in all politics, are
similarly framed to attempt to make people feel a need to act (we shall look at this in more detail in
Essay Five). I have a good friend and former colleague for whom the next three months have been
critical in climate policy for the close to a decade that I have known her.
Such messages are trying to frame in the mind of the decision maker the idea that an option to
invest may expire or that the time and real cost of delay far exceed the uncertainty as to whether,
for instance, you really need another pair of shoes or not.
If you take a little time to observe those all around you who try to make you make decisions, you will
observe them doing three things: making you feel like the investment option will soon expire;
making you feel very certain about future events; and making you feel like the short term pay-off
(the time and real cost of delay in other words) to owning the asset is as high as possible.
64
See (Pindyck, A Note on Competitive Investment under Uncertainty, 1991) for a more formal treatment.
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Why cap-and-trade schemes don’t lead to investment decisions
The higher the level of uncertainty the greater the value of delay in investment today. This can be
proved rigorously, but should also be broadly intuitive and consistent with the above examples.
Hence the greater the entropy today, and the greater the amount of information resolution which is
possible in the future then the greater the cost of incentivising (and hence observing) agents
investing today rather than waiting. Hence it is clear why cap-and-trade schemes don’t incentivise
investment to the degree that policy-makers have historically hoped that they would.
In terms of investment decisions it is the very richness and breadth of the potential future
information which a cap-and-trade scheme can provide which causes the uncertainty and delay
today.
Should we then forget these high entropy systems in favour of more certain regimes?
Essay Four explores the reasons why this would be a disastrous course of action.
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Essay Four: Observation, accounting, communication and climate
disagreements
So trading systems such as cap-and-trade systems are completely useless it seems.
No.
They do not perform the functions that many people want them to, but they are an absolutely vital
part of the architecture of the financing of the low-carbon economy. In this essay we will explore
the key features and benefits of cap-and-trade systems and their vitally important role. The essay
explores four distinct issues: observation, accounting, communication, and finally how trading
schemes are essential parts of our ability to achieve what I have playfully characterised as
international climate disagreements.
What is very clear from our previous analysis is that the prevailing narrative in the climate policy
community about carbon trading schemes is wrong. To reprise, this narrative is that there is a need
for a global carbon price which rises to such a level that it makes the NPV of clean investment
greater than or equal to that of a dirty investment and then the clean investments will occur instead
of the dirty ones. Also that price needs to be global, as to the planet, a tonne of carbon dioxide is
the same wherever it is emitted and hence a global carbon price will drive rational investment
agents to make investments in the technologies and geographies that are the most cost efficient
given this all encompassing price signal.
In rigorously analysing why this is wrong, I believe that we can similarly rationally explain the great
importance of cap-and-trade schemes as components of the financial and informational
infrastructure needed to ensure a migration to a low-carbon economy.
Observation
Essay Three has taught us that investments do not occur simply because they have a positive NPV.
The prospect of future information causes there to be an opportunity cost of investment today
which must be overcome in order for rational agents to invest today rather than delay. Hence the
price we have to pay for investments in clean energy is not the NPV, it is the price required to
overcome the uncertainty (which is the other word we use to describe our knowledge that
information may arrive in the future).
The uncertainty in a cap-and-trade scheme however is clearly of the scheme’s own making, we have
designed a scheme, in the EU ETS for instance, where price is variable and dependent on future
market and policy developments. Hence we have proved that this is simply a silly way to incentivise
investment and that our costs of supporting clean energy investments would be much better served
with a price-based system. If the price is fixed then we will clearly minimise the cost of uncertainty
and the spread between the NPV of an investment and the value at which a rational agent will
undertake the investment will be minimised and hence the cost to the energy consumer and taxpayer of funding the migration to the low-carbon economy will be similarly minimised.
Simple. All we need to do is set the price.
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This is where the problems start, in order to set the price of a carbon tax, feed-in tariff, or other
price-certain mechanism, we need information on what investments in the appropriate technologies
cost. In fact, we need the information as to what the most cost effective technologies are and then
how much those technologies cost.
If there has been no investment in those technologies then there will be no such information and we
will not have had the opportunity to observe the circumstances in which agents in the market are
prepared to make those investments. Hence we clearly need a system with a variable price which
will in some way cause the market to reveal to us the price at which said rational agents are
prepared to make investments and in what technologies they are prepared to invest.
However if we have a system of incentives where the price is variable we know very well from Essay
Three that we will not observe agents making investments at the NPV of the investment, but instead
we will observe them making investments at a price above the NPV value because of the uncertainty
in the price they will receive in the future.
As an aside it is worth noting at this point that even if one sets a price, if one does it in the absence
of any good quality information then the market will know that you are guessing and will assume the
fixed price will change in the future and so simply fixing the price is not the answer.
We are now at the crux of the matter. Quite simply, it is impossible to observe, and hence to know,
the NPV of an investment. The observable phenomenon is the decision by an agent to deploy capital
in a certain way, for instance making an investment. Hence an observer of the market cannot say
that an observed investment decision reveals the NPV of that decision, they can only observe that
the decision was made and the circumstances in which that decision was made.
The price at which the observed investment is made is dependent on the system of market and
incentives which was put in place to incentivise and observe that investment. If it is a highly volatile
quantity-based system such as a cap-and-trade scheme then the observed price at which the
investment is made will be higher than the true NPV and will reflect the volatility and uncertainty
(the potential for future information) inherent in such a system.
What we observe and therefore the information which the actions of agents communicate to us is
therefore crucially dependent on the characteristics of the systems which we put in place in order to
incentivise the investment action and elicit the information as to the circumstances in which agents
will make the investment.
Those with a cursory or better knowledge of physics will recognise that we have a conundrum
similar to the famous uncertainty principle of quantum mechanics discovered by Werner
Heisenberg65. Put in very simple terms this principle states what you measure depends on how you
measure it, and that if you want to measure one characteristic, of for instance sub-atomic particles,
very precisely then you will create greater uncertainty in the measurement of another characteristic.
There is no way of knowing both characteristics precisely, that is simply not allowed, according to
the uncertainty principle.
65
See (Heisenberg, Physics and Philosophy, 1958), (Heisenberg, The Physical Principles of Quantum Theory,
1949) and (Lindley, 2007) for treatments of varying degrees of difficulty.
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We have uncovered a similar contradiction in the observation of the cost of investment. If we wish
to have a broad scope of geographic and technological diversity covered by a given market or
incentive scheme, and if we want that scheme to hence provide to us information across a wide
population of potential investment decisions then we will inherently create a system which has a
highly volatile price. Such as scheme, as we have seen, will be very poor at allowing us to observe
the actual NPV of the investment.
The trade-off in observing information on investments is therefore one of scope versus precision.
The broader the scope of the observed universe the less precisely the observed investment decisions
tell us the actual NPV of the investment undertaken by the agents we are observing.
You will remember that the scope of potential outcomes of a channel in information theory is its
entropy, and hence we can see again that the higher the entropy of the system we use to observe
investments, the greater the information content of the observations of agents making investments
with respect to geographies, technologies etc. (because we have the potential to observe low
probability events which have a high information content), but the less precisely we measure the
actual NPV of the underlying investment and also, importantly, the more that observation
(information) has cost because the greater the premium that will have to have been paid over and
above the actual underlying NPV.
If we start to understand these trade-offs then we can begin to understand some of the conundrums
in designing a financial system capable of encouraging the migration to a low-carbon economy. In
the terminology of thermodynamics and information theory, a high-entropy system (such as a capand-trade or quantity-based system) has a very high potential information content, but that
information is costly.
This analysis explains at least in part one of the issues which often baffles policy-makers in the
climate change arena. In order to establish that they are making economically rational decisions and
prioritising low-cost investments in emission mitigation first, policy-makers have become quite
dependent on a form of analysis called an abatement curve66. An abatement curve is basically the
calculated NPV-equivalent carbon price of all the potential investments in carbon dioxide emission
mitigation in a given economy or even in the world. These calculations are then ranked in order of
the price shown on the vertical axis with their emissions abatement potential shown on the
horizontal axis. The idea being that the area below the curve is the NPV cost of mitigating all
emissions in the economy and hence the cost to the economy of migrating to a low-carbon
economy.
There are numerous authors of such abatement curves and they clearly have numerous issues in the
calculations which we won’t debate here, but it is also very clear that in most cases the quality of
real information used in the analysis is relatively poor, as you would expect as there are not many
investments going on in the world to provide the data.
We however now know that, even if the data behind the NPV analysis were perfect, such curves
would still not tell us the price of action, because the price of action is dependent in the way we
incentivise it and hence the way in which we make the observations and secure the information
66
See (McKinsey, 2009) for one good example.
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which ought to be the basis for the analysis which creates the analysis behind the curve in the first
place.
Policy-makers often look at the latest abatement curves which might be in fashion at any given time,
and then look at the market and struggle to understand why there is such a mismatch between the
theoretical abatement curve and activities observed in the market. An abatement curve might
suggest that there is a vast potential for low cost or even negative cost investments in energy
efficiency for instance, but then a policy-maker will observe little investment actually occurring in
that arena. The answer, we now know, is that the actions observed in the market are dependent on
the system (market design) which we put in place to make those observations.
A global abatement curve is therefore clearly completely self-defeating. If we are to put all potential
abatement action on the same graph and measure them by the same metric, say the famous single
global carbon price, then in order to observe the curve in reality we would need to implement the
broadest possible carbon trading scheme covering every sector of every economy on the planet.
This would clearly be a very high-entropy system with an enormous cost associated with these
observations given the uncertainty created by the potential for the arrival of future information.
Hence if all the parts of the abatement curve are exposed to exactly the same uncertainty then the
level of the curve for actual observed abatement actions will be considerably higher than that of the
theoretical NPVs (even if those who constructed the theoretical NPVs had exactly the right
information on which to make their NPV analyses).
If however different parts of the curves (different emissions mitigation investment classes) are
exposed to different types of markets, for instance some of it is subject to feed-in tariffs, some to
emissions trading schemes, some to mechanisms like the clean development mechanism, then,
(leaving aside the obvious point that they therefore clearly shouldn’t all be shown on the same curve
anyway) the order of the different assets classes on the curve could change radically. Asset classes
where we have good information and hence actions in those asset classes are observed through a
low-entropy channel (a fixed or low volatility price-based incentive for instance) will have an
observed price much closer to its theoretical NPV value, whereas those observed through a highentropy channel (a highly volatile emissions trading scheme for instance) will have an observed price
substantially above the theoretical NPV value. Hence asset classes could move relative positions on
the abatement curve simply as a function of the way in which those asset classes are observed.
So this is meant to be an essay about the important benefits of cap-and-trade (quantity-based)
systems and so far all we appear to have done is uncover a rather confusing conundrum in how they
operate.
The point of this section of this essay is two-fold. The first is to highlight the conundrum, or more
correctly the trade-off, between the breadth of information and the cost of that information. It is
very important that policy-makers and climate change financiers understand it, and stop pursuing
the frankly silly narrative that there will be investment at the NPV of the next piece of global
marginal abatement as the global carbon price increases. This is all based on a simple but dangerous
misunderstanding of the nature of such a system. Understanding the properties of a trading scheme
would be a very important first achievement.
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The second point is that in the absence of good quality information about investments then we have
to discover that information in as efficient a way as possible. We cannot observe (or calculate) an
NPV in the absence of the information required to incentivise action, if our level of information
deficit is high then we have to create a channel for observation which is similarly wide, as otherwise
we might not garner the required information. However in doing so we will influence the
information we receive because of the entropy of the very channel used for observation. This
knowledge allows us to understand the quality and potential cost of information created by
observing the world in certain ways and to hence make rational trade-offs between the scope of the
channel (entropy) and the cost of that information.
To maintain our references to information theory and thermodynamics: in thermodynamics we
know we need to use energy in order to reduce the entropy of a system. In observing investment
decisions, if we create a wide, high-entropy channel (market structure) through which to observe
investments then the information observed through that channel will cause a substantial reduction
in the entropy for the observer of that information, but it will come at a financial cost which is
analogous to the energy expended in reducing the entropy of a physical system.
So trading systems are important in that price is variable and hence they can be used to enable us to
observe useful information which might assist policy-makers and investors. However that
information comes at a cost which efficient policy-making should seek to minimise, provided that
the loss of information associated with reducing that cost is a risk worth taking.
Another way which, in the financial world, we attempt to observe the entities is through reports and
accounts. We now move on to see how trading systems might be essential parts of the accounting
system of the low carbon economy.
Accounting
In the previous section we looked implicitly at two forms of observation. Firstly, and most prevalent
in the above, was the observation of economic agents making investment decisions. Secondly, and
more implicitly in the previous analysis, was the idea of the economic agent making an investment
decision observing the price in the market and from that making said investment decision.
Price is formed in markets, at least more efficient ones, by the bringing together of the positions of
all parties in a way which creates the ability of those participants to then observe a resultant price
coming from their interactions.
It has long been recognised that the periodic observation of companies and other economic entities
by third parties who have an economic interest in them is a good idea. Simply observing the actions
of a company does not provide sufficient information for investors, creditors, regulators, employees,
managers etc. Hence it became practice and then law and regulation to keep sets of accounts and
then to periodically bring together the full status of the company in a formal set of reports and
accounts.
This has not been, is not, and will not be an easy process67. There are still many controversies in the
way accounts for companies are put together and we continue to have scandals where the apparent
67
For some histories of accounting and accountants see (Brown, 2004), (King, 2006) and (Hawkins, 1904)
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state of a company according to its accounts turns out to not to be the truth. The scope of
accounting disagreements range from the fraudulent production of the accounting information,
through over aggressive application of certain principles, to real and genuine matters of judgements
as to how accounts can be produced which provide stakeholders with information on the state of
the company. The recent financial crisis has even exposed, in some cases, the fact that the accounts
of countries, even democratic ones, sometimes turn out to not be what they appear.
The examples are myriad and well-known to those with a basic understanding of the business world;
hence I will not reprise them all here.
As well as the continued evolution of standards and practices, the development of accounting has
another characteristic which is pertinent to our analysis here. Generally the development of
accounting systems has been ex-post. In other words, the late medieval and early renaissance
merchants of Italy68 who first applied double-entry book-keeping several hundred years ago did not
invent a method of accounting (double-entry was indeed it) before they started to trade with each
other and with the outside world. Instead it was the need to keep track of their ever more complex
businesses which brought them to the understanding that they needed to develop a reliable system.
These internal reasons for developing a system of accounting in order to control a business are, or
course, an example of the reduction of entropy within the economic system that is the enterprise
involved. The gathering and collation of information allows control of the system and reduces
disparate and voluminous information into a condensed and understandable form which hence
reduces the level of uncertainty of those receiving that information. The process of creating
accounts within an economic enterprise therefore performs the same process of entropy reduction
which we saw is required within the electricity system in Essay One.
This ability of the process of measurement and information collation to reduce the entropy of a
business system is important for the other major driver for the development of accounting which is
the communication of the state of an enterprise to those third party stakeholders who are a part of
that businesses network. In particular, for instance, in the second half of the nineteenth century
much of the early formation of US accounting systems was driven by the need for the massive and
growing railway companies to communicate with investors (largely in the UK somewhat ironically) in
order to provide those investors with the confidence to invest.
As we have discussed at length in Essay Three the greater the degree of uncertainty and entropy
which the investor has to tolerate in the investment decision process, the more likely they are to
delay the decision. In the example of the US railroads an industry hungry for capital to invest in the
ever-growing opportunity needed to find a way to reduce the uncertainties to which the distant and
ill-informed investors were exposed in order to overcome the opportunity cost of investment and
hence provide the much needed funding. Collating the state of a vast and complex railroad business
into a concise and understandable set of accounts was how they did this, and the rest is history, and
applies to all companies in the vast majority of countries.
You will notice that in the above paragraphs I have tended to avoid the use of the word “firm” when
referring to the entities for which accounts are produced and there is a reason for this. The concept
68
See (Geijsbeek & Sellsbeek, 1914)
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of a firm is relatively recent in human history and is still relatively poorly defined in many countries;
despite how much we in the western world take the implicit characteristics of a firm for granted. A
firm, or other economic entity for which accounts might be produced, are, in a thermodynamic
sense, a system. They are also defined by laws which enshrine certain property rights and the
characteristics of those property rights. (The definition of a firm itself and the related concept of
limited liability being important examples of properties which we inherently take for granted)69.
Hence, alongside the development of accounting was also the definition of the characterisation of
economic entities which allowed the system to be well-defined by its accounts. What we now take
for granted in terms of the definition of the firm; its separate status and standing from its owners
and employees; the limitations on what it can do, but also the rights it has and the obligations it
must fulfil, were hardly defined some two hundred years ago and have evolved, as with accounting,
with a time lag to the actual physical economic activity which made policy-makers and enterprises
themselves realise that such concepts were required.
Our potted history of accounting has taught us that: it has been an ex-post process; it reduces the
entropy of economic systems; it develops alongside the development of property rights (or in
thermodynamics terms the definition of the economic system involved); and the process of the
development of the rules and protocols is not, and probably never will be, complete.
But what does this have to do with climate change finance or cap-and-trade systems? Consider for a
moment this example.
Imagine a new system of information put in place in order to measure economic activity. All goes
well for a while, but then when it comes to the first period where results are audited it transpires
that previous data has been exaggerated and that therefore people have been operating on
something of a false pretence. Now imagine that such a system interacts in unpredictable ways with
the tax system, and that again people operate and make economic decisions on poor information.
We also then find that in some parts of the world assets are counted twice and there is a growing
controversy where some people believe that certain assets should not count in the system in the
way they have historically done, or that people have mis-stated past numbers in order to gain
favourable treatment within the new rules and protocols of this new system. Our imaginary system
therefore has a great deal of controversy about how it will operate in the future, and it is not at all
clear that one unified system will prevail and in fact it seems most likely that observers of the system
will be faced with having to compare different versions of a similar system in different jurisdictions
in the future.
This could, as we have seen, be an anecdote relating to accounting or at least to some accounting
rules, and it could certainly be valid for a number of forms of accounting rules today (not to mention
of course the accounting of and management of capital ratios in the banking sector, which after
several hundred years of banking we still appear not to have right).
However, it is, of course, a rough description of the development of emissions trading (carbon credit
trading) during the last decade.
69
See (Hart, 1995) for a discussion on the structure of firms and their relationships to each other.
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Over the period of ten years or so as the clean development mechanism and the EU Emissions
Trading Scheme, we have seen no end of controversies and disagreement and we probably have
more now, at the time of writing this essay, than we have ever had.
There was the massive crash in Phase One allowance price under the EU ETS due to the apparent
overstatement of historical emissions and lack of real information among market players until the
first real “accounting data” for EU emissions were announced in 2006.
There is the perennial problem of leakage, or emissions escaping from the coverage of the system of
emissions trading due to a move in sector or geography. This would be moving liabilities “off
balance sheet” if it were accounting.
There have been tax controversies. There was the incident of UN emissions credits apparently being
used twice in one eastern European country. Double counting is the scourge of accounting.
The analogy can be made at many levels and the truth is that it is not an analogy. Cap-and-trade
schemes are, first and foremost, in my opinion, the accounting system for emissions and therefore
emissions reductions.
Cap-and-trade schemes create the economic incentive and the regulatory necessity for the accurate,
verifiable and consistent measurement of emissions, and they do that by creating the need, at
certain points in time, to deliver data to the market in a way which forms a price.
Such schemes have clearly developed ex-post to the emissions they measure, but they are also in
reality ex-post measures of the effectiveness of emission reduction activities. Data is provided in an
analogous way in that the data is generally provided on the basis of property rights which are
evolving at the same time as the accounting system itself and the data provided by the entity
concerned is often verified by an auditor who has the same function (and issues) as an accounting
auditor.
As with accounting systems, cap-and-trade systems provide the incentive to produce the data which
the wider stakeholders of the economic entity require in order for it to maintain its licence to
operate and to provide a basis on which they can monitor and verify that it is doing as it says it will.
Some will object to the idea that the major function of cap-and-trade schemes is accounting on the
basis of cost. Surely, people will say, the cost of the EU ETS is vastly disproportionate to the cost of
simply measuring and reporting emissions (say the cost is 2bn tonnes CO2 per year times €13 / tonne
or €26bn per year).
As we have observed in this suite of essays, information is inherently very expensive, and hence it
should be unsurprising that it costs so much to extract the information from the current economic
system. One should also observe the vast industry of auditing which exists in the mainstream
accounting sector and how, despite this, there are still issues, scandals, restatements and massive
losses to investors on a relatively regular basis within the general economic system. If we add up all
the direct costs of our continued need to account for the economic system, and the indirect costs of
our continued inability to achieve this, then the costs of emissions information as procured via capand-trade schemes will perhaps come into perspective.
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Some will say that data collection should simply be regulated into existence. This doesn’t work.
There is very clear evidence that the quality of data provided where there is an economic incentive
to provide it is vastly greater than that which is required by regulation. The allocations for Phase
One of EU ETS were made based on the apparent technical measurement and estimation of the data
for the EU’s emissions and clearly when the economic system of trading required the restatement of
the same data in 2006 the reality turned out to be quite different.
If we come to terms with the fact that cap-and-trade schemes are the essential accounting system of
the climate change financing world then we can perhaps more easily come to terms with some of
the apparent weaknesses in cap-and-trade schemes which have been observed from an investment
perspective in recent times.
Firstly, we must come to terms with the fact that we have to embark on a never-ending process of
the development, expansion and refinement of cap-and-trade schemes, exactly as accounting has
done since the early renaissance, and we will have to live with the inevitable controversies, errors,
and changes of direction which this brings.
Secondly, cap-and-trade schemes are therefore inherently about ex-post measurement, not about
ex-ante incentives. Our schemes will also develop in parallel to the development of the property
rights which are reported against and hence we will also see an evolution in the definition of the
systems which we are measuring with our emissions accounting system.
Thirdly, information costs a lot of money, and as money is the proxy for effort expended somewhere
in the economy then we have to recognise that this is a simple thermodynamic fact which we should
not fight against.
Finally, this explains the fundamental contradiction in cap-and-trade schemes. They are not
incentives for investment because they have inherently high ex-ante entropy. The possibilities of
outcome which might be communicated through the system in the future are vast and this creates a
state of uncertainty which, as we have seen, discourages investment. However, it is essential that
the sectoral and geographic scope of our climate accounting system expands as much as possible as
we must eventually have all emissions accounted for, before we ever have a chance to completely
eradicate them. Hence cap-and-trade schemes must continue to increase the capacity of the
information channel that they represent and will therefore inherently have a state of entropy which
makes investment very expensive, and hence they are no good as an ex-ante signal for investment.
Accounting and cap-and-trade schemes do of course reduce the observer’s entropy at each point of
settlement or reporting. At this point they reduce the uncertainty of the observer as to the state of
the recent past quite substantially (if not completely) and hence create useful near-term information
for stakeholders, as accounts do for companies. Our next section looks closely at the purpose of this
within the climate change context.
Communication
One of the key issues in international climate change negotiations is what has become known in
recent times as MRV or monitoring, reporting and verification. This is basically the process by which
people check up on each other to see if they are keeping up their part of the bargain. In other
contexts of international arrangements such as arms control obviously the verification that arms
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don’t exist or that they have been safely destroyed or put beyond use, without letting your potential
enemy crawl all over your military secrets, was and is a key issue to be overcome.
In the climate change arena we have the analogous issue. Firstly, people don’t trust each other to
keep their end of the bargain up and so they want to be able to monitor, report and verify what
people say they are doing, but also people don’t trust their major competitor nations enough to
allow them to crawl all over their key industries on the premise of checking their emissions. As we
have seen in the above discussion, it turns out that even in very well-developed and well-regulated
countries information can be a very costly thing to extract, and a number of the economies which
are key to the future of any international climate deal have been historically quite closed in the first
place, making this a much more difficult issue.
The above section on the role of cap-and-trade systems as the accounting system of the climate
obviously goes some way to addressing this issue. If economies have cap-and-trade schemes then
they will also have created information on their emissions and emissions reductions which is useful
and which should be at the centre of “MRV” efforts. Hence the first part of MRV we have answered
and it is again an example of the climate change policy fraternity getting their ex-post and ex-ante
the wrong way around. People often talk of the need to establish systems of MRV in order to then
have cap-and-trade schemes which provides investment incentives. This is clearly not the point.
The cap-and-trade scheme is the MRV system, as it is the accounting system.
So then we have fixed everything: China can send the US a copy of the annual report for its cap-andtrade scheme and everyone will be happy.
This is not quite the case. As we have seen previously, the quality of information creation is vastly
improved if there is an economic incentive to produce it and the quality of the information which is
transmitted to other stakeholders in the system is much greater if it is part of an economic
transaction (in the case of a firm for instance, say lending the firm money, or being prepared to do
business with them on certain credit terms based on their accounts).
Hence we come to the next crucial role of cap-and-trade systems: That is to facilitate the economic
communication between the parties involved in the reduction of emissions in different parts of the
world. By trading with each other, parties to any agreement have direct economic interactions with
the actions which are being taken elsewhere in the world and have a window through which to
observe the results of those actions taken.
Cap-and-trade schemes, or more importantly the connections between them, should also therefore
be considered communication channels between different parties to the deal on climate change.
The wider these channels are the more information can be transmitted across them and hence the
greater the uncertainty which is resolved by each interaction between the parties over that channel.
The downside, as we have discussed above, is that means again that the communication between
cap-and-trade schemes is likely to have high-entropy ex-ante and hence makes the cap-and-trade
less of an incentive for investment.
Trading between systems or between parties to a deal therefore is a mechanism for building trust
between the parties. It provides for an exchange of information and hence the observation of what
the other parties to any global climate deal are doing.
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The trade will involve a transfer of funds between the parties and while, of course, theoretically this
could go either way, our expectation would be that funds are likely to flow from the developed
world to the developing world through this information channel. This is the case both because the
emissions abatement options are likely to be cheaper in the developing world than in the developed
but also because their accounting standards (the rules of the cap-and-trade game) are likely to be
more lax, at least to begin with.
This wealth transfer has always been a part of the overall climate deal and has been justified in many
perfectly valid ways and in particular under the heading of common but differentiated responsibility
which is the principle under which, while climate change is a global problem and physically a tonne
of carbon dioxide emitted has the same effect wherever it is emitted, rich countries should bear a
disproportionate burden of the cost of emissions abatement both because they can afford it and
because they have benefited from their disproportionate share of historical emissions. The transfer
is justified economically in the developed world as it is seen as cheaper to abate in the developing
world than in the developed and hence the developed world’s part of the trade is the ability to delay
expensive abatement by doing cheaper abatement elsewhere. This is also the essence of the clean
development mechanism.
In reality what the developed world is paying for through these trades and their associated transfers
of wealth is information. We are providing an economic incentive for the development of the
accounting system that we have described above, which will allow us to monitor, report and verify
the emissions in the developing world (and other countries for that matter); which will allow us to
observe the cost of emissions abatement in those countries; and which will allow us to establish
greater and greater degrees of trust between the various parties to the deal through the constant
trading which will occur between them.
One of the great sticking points in climate negotiation is whether the developed world can and
should pay sufficient funds and resources in order to decarbonise the developing world. The answer
is probably not. However, if we ask ourselves if the developed world can dedicate the resources to
develop the information systems of global climate deal then the answer might well be yes.
There are two related concepts in information theory and thermodynamics which merit discussion in
the context of trading systems as a mechanism for the transfer of information between parties to
the climate deal. They are mutual information and phase transitions – they are, or course, related.
Mutual information as you might suspect is the concept of shared information between two entities,
and tells us what information about one entity can tell us about the other. Hence in the context of
communications via trading of emissions, mutual information would be in some way a measure of
what the trading price in one scheme told us about the cost of abatement in another scheme.
Climate change, as we all know, is in part a collective action problem and, as we will discuss at length
in Essay Five, the relative starting points of the parts of the global collective. To the extent that
trading and communication between parties increases the mutual information in the climate
accounting systems then there is the possibility that it will be possible to move forward globally.
This is what happens in a phase transition. A phase transition is what happens when water freezes,
or boils, it changes state or phase and without any change in temperature the whole of the system in
question changes from one state to the other. At these points there is a high degree of mutual
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information between the particles in the fluid because it is clear that they are all becoming ice or
steam and observing one in this state tells you the vast majority of what you need to know about the
state of all the others.
There is a vast literature on phase transitions in lots of different sorts of systems and again the
overlap of information theory and thermodynamics run through all of them. A phase transition, is,
of course, what we are trying to achieve in the global economy. That phase transition is that all
economies develop ways of maintaining the order of the human sub-system of the planet without
the need to draw on the Earth’s reserves of capacity for useful work and hence without increasing
the entropy of the wider planetary system. For those who believe that we need that phase
transition soon then achieving high degree of mutual information within the economics of our
energy and emissions systems is clearly crucial.
We are a long way from that today and the next and final of the four sections in this essay now looks
at how cap-and-trade systems assist in facilitating us embarking on that journey.
Climate disagreements
The irony of the EU’s support for cap-and-trade systems is well documented70. To reprise, in the mid1990s in the run up to the Kyoto Protocol the EU’s position was completely against such things and
in favour of what we would all probably much more usually associate with Europe which was a tax
on carbon. Cap-and-trade was driven up the political agenda by two things: firstly the complete
inability of the European nations to ever agree a common tax, or to yield the power to set one to
Brussels; and secondly the insistence of a form of trading in the Kyoto Protocol by the US as a
condition of them signing up to a treaty that they then never ratified. Hence the EU became
reluctantly the main proponents of cap-and-trade schemes pretty much by accident.
A corporate financier would probably look at the situation which lead to the Kyoto Protocol in a
slightly different way and this brings us to the fourth of our important characteristics of cap-andtrade schemes which are not so often talked about.
The Kyoto Protocol, or frankly any past or future global deal for tackling climate change, involves a
large number of parties signing up to a future commitment to reduce emissions. They do that in the
full knowledge that should they get this commitment wrong relative to their key trading partners
then they risk eroding the comparative advantages of their economy. They also do this in the
absence of full information, in fact probably in the absence of almost any information as to the real
costs of achieving the decarbonisation of their economy which they are committing to.
This is clearly a very scary place to be and therefore it is somewhat unsurprising that there haven’t
been very many such deals, and that the one there has been has only really been ratified by the EU
and Japan if one only counts those for whom there is a risk the deal might be a cost not a benefit
and who might just about stick to the deal.
In corporate finance where deals are done in the absence of full or sufficient information and where
there is a high risk of ex-post regret on the part of one party or another, then there are some
70
See (Grubb, Vrolik, & Brack, 1999) and (Ellerman, Convery, & de Perthius, 2010) for histories of the Kyoto
Protocol and the EU Emissions Trading Scheme.
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relatively well established mechanisms for making the deal happen and managing the level of expost regret. This is where derivatives come in again.
In essence when trying to make a deal between parties who have limited information and hence
high potential ex-post regret, mechanisms can be designed which redistribute the spoils of the deal
ex-post based on pay-outs derived from future information, or more correctly the resolution of the
information deficit (uncertainty) which prevails at the time at which the deal is done. So for instance
let’s say that a corporate financier is trying to broker a deal between two pharmaceuticals
companies and the deal makes perfect sense, but there is a real prospect that one of the companies
will get approval for an amazing new drug. Everyone agrees that the deal is a 50:50 merger in the
absence of the new drug approval, but that it should be a 70:30 split in the case where the drug is
approved. Both sides want to do the deal but neither is prepared to risk the ex-post regret in the
presence of the uncertainty before them (this should sound a lot like the issues addressed in Essay
Three). The options are for the deal to be delayed, but there are other benefits to both sides which
would be lost from delay, or to structure a derivative instrument for the shareholders of the
company with the prospects of the new drug which basically gives them 50% of the company if there
is no drug approval and 70% if there is. Said derivative instrument (because that is what it is)
manages the ex-post regret of one side and overcomes the opportunity cost of making the decision
today. In the context of our analyses in Essay Three the new derivative in the deal acts to negate the
value of the option to wait by putting in place a derivative which replicates the future pay-offs in the
possible future states. Hence the derivative allows you to invest now in the knowledge that the
economics of the deal will be put right later.
This is what emissions trading schemes between parties to a global agreement also do. They
manage the ex-post regret of the parties in terms of the potential future impact on their
comparative advantage. If a deal is struck with fixed emissions reductions targets for the parties
involved, but with the capacity for those parties to trade between each other, then if it transpires
that Country A has done a bad deal and it discovers ex-post that it has a high cost of emissions
abatement relative to its key trading partner Country B then if it can buy emissions credits from
Country B instead of undertaking high cost abatement then its ex-post regret is managed.
The cap-and-trade schemes and more importantly the links between them, act as a derivative
applied to the deal at the point of signing. This derivative has the effect of providing the opposing
pay-outs to those which the countries are fearful will occur if they get the decision wrong. The
presence of such a derivative counteracts the uncertainty and fear of ex-post regret in the same way
as it does in the pharmaceutical merger example described above.
This is what the concepts of emissions trading; the clean development mechanism and joint
implementation actually did in the Kyoto Protocol. They made the deal possible, and I am sure that
instruments which manage ex-post regret will be needed again in order to make any such similar
deal happen.
You will notice again that this is the cap-and-trade schemes acting as ex-post measures in the global
climate change financial eco-system.
This is why this section is cheekily entitled “Climate Disagreements”. Quite simply this is all we can
ever hope to achieve. Deals between countries on emissions reduction have been and always will be
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entered into in a state where it is entirely unclear where the true burden will fall and where there is
persistent disagreement about how and, most importantly, where the reductions will be achieved.
Achieving new climate disagreements will require us to manage the ex-post regret countries
potentially have in signing up and that means that there is a crucial role for cap-and-trade schemes,
and the links between them, to act as derivatives which manage the ex-post distribution of cost
amongst the parties.
You may also notice another irony. We explored in Essay Three how the uncertainty (high entropy)
state of emissions trading schemes was a disincentive for private capital to invest in emissions
abatement as the opportunity cost of investment was too high. We used the science of derivatives
in order to analyse this. We now see that such instruments are an essential part of encouraging
countries to make emissions reductions commitments. This is because the disincentive to do a deal
comes from the possibility of future information leading to regret on the part of one or more parties,
however if a derivative is introduced which produces (at least in part) the opposite pay-offs for the
parties in the future regret state then the uncertainties as to the pay-offs to each party are
substantially reduced and hence their opportunity cost of deciding to sign the deal is drastically
reduced.
Hence cap-and-trade schemes and in particular the links between them increase the opportunity
cost of investment for private capital in specific emissions reducing projects, but they increase the
possibility of achieving a deal between countries on the reduction in global emissions.
Observation, accounting, communication and climate disagreements
In this essay we have discussed the four main characteristics of cap-and-trade systems and you will
note that none of these is stimulating large-scale investment in low-carbon energy systems. In fact
the very nature of the system in achieving the four objectives set out for it in this essay make
stimulating that investment cost effectively almost impossible.
Observation must have a broad scope; accounting must capture all eventualities; our
communication should be as frequent and unconstrained as possible; and if we are to achieve
climate disagreements then we must put in place derivative structures between nations which have
pay-offs which are opposite to those that people fear at the point they enter into the deal.
This means that cap-and-trade systems, and their linkages, need to have high bandwidth, should
capture low probability events, and hence have the potential to be information rich. This means
that ex-ante (before reporting or decision making) and on into the future these systems have
inherent uncertainty and hence create a high opportunity cost of investment. This, as we have seen,
is a disincentive for large-scale, capital-intensive investment.
As noted in earlier essays such quantity-based systems are appropriate for high entropy situations
such as the ones we describe above, but not for situations where the information they yield is
worthless to the decision or operation in question.
Hence we have uncovered one of the key problems with climate change finance discussions to date.
The faith put in cap-and-trade systems and other forms of credit trading was extreme. The attempt
to create a global carbon market and global carbon market was underpinned by a desire to establish
a robust and reliable price for carbon emissions on which long-term investment decisions could be
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made. Since this attempt has come to be seen largely as a failure in recent times then it appears
that the talk of cap-and-trade has largely been sidelined in favour of more price-based, ex-ante,
lower entropy systems of incentives.
This is clearly a disaster, as it is impossible to design a low-entropy (price-based) incentive
mechanism without the information on which to base it, and this can only come from observation. It
is also impossible to properly understand the effects of those measures without proper accounting
systems, and it is impossible to tell whether others are doing their part of the bargain without
communicating with them. Furthermore, there is a risk that no-one will do anything of substance
faced with the high risk of ex-post regret that comes with making commitments for emissions
reductions today.
Cap-and-trade schemes are however a route to very high cost abatement if they are the only
instrument, and hence as such systems yield information then applying that information to the
setting of lower-entropy, price-based incentives is essential.
Cap-and-trade schemes substantially reduce the entropy and hence uncertainty of all observers at
the point of reporting, or trading, or settlement. Hence they are an essential source of information
for all parties, and for well-designed systems the entropy of the observer is substantially reduced at
the point of trading, settlement or reporting, but this is all about the observation of the past not the
future, which is what matters for an investment decision.
There is another key issue about high-entropy systems as incentives for investment, and that is that
they have the same affect on low-carbon investment decisions as they do on high-carbon ones. In
the parlance of those who have proposed cap-and-trade schemes as a means to incentivise lowcarbon investment and to dis-incentivise high-carbon investment, the NPV of a low carbon
investment is increased relative to that of a high-carbon one and hence people will make low carbon
investments in preference to high-carbon ones. The problem here is that both investments, low and
high-carbon, are exposed to the future uncertainty of say, the carbon price, or whatever instrument
is put in place. As we saw in Essay Three, the future uncertainty or entropy of a system delays
investment due to the opportunity cost of investment which it creates. This phenomenon is true for
both high-carbon and low-carbon investments. In other words, the impact of volatility on the value
of the option to wait and the value of new future information on the investment decision has no
respect for the sign which the uncertain phenomenon has in the NPV analysis of the investment.
Therefore, while it is true to say that the NPV of a low-carbon investment is increased relative to a
high-carbon one, NPVs are not that important in the decision to invest or not (as we saw in Essay
Three). Hence cap-and-trade schemes, or more importantly any uncertain or high-entropy scheme
of incentives, delays all the investments which they affect, whether they increase or decrease their
NPVs.
Before concluding, it is perhaps worth a few sentences on the impact this has on incentive systems
within the low-carbon energy system itself. As we discussed in Essay One, we are going to have to
get used to our energy coming from high-entropy sources rather than the low-entropy ones which
we have got so used to. In order to manage such a system then the mechanisms for trading power
are going to have to become higher in entropy in order to accommodate the much greater
informational possibilities in a system driven by natural forces (for energy capture) and human
activity (for energy demand). Such a system is clearly no good for incentivising the high capital cost
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and high-entropy investments that a low-carbon system needs, but it is essential if we are to be able
to garner the information required in order to implement the measures to reduce the overall
entropy of the system in a way that makes the energy it captures able to reduce the entropy of the
human inhabited sub-system of the planet.
Our low-carbon energy system needs a high ex-ante entropy system of observation, accounting and
communication which is capable of providing the information basis on which such a system can be
managed to the use and convenience of humankind, but this will not be the system which most costeffectively incentivises investment in low-carbon energy capture and use.
It seems almost then that we may have to think about one system to manage the entropy of the
energy system, and another to ensure we have sufficient energy and use it efficiently.
Back briefly to the bigger picture. The failure to establish a global carbon price, or any short-term
prospect of one, and the failure of anyone to observe major investment decisions based on what
carbon prices do exist has made many give up on the whole idea of carbon pricing. As noted above,
this would be a disaster. However, it has also caused some to say that carbon pricing or cap-andtrade schemes are necessary but not sufficient conditions for low-carbon investment at scale. I
suspect that for the moment, this is a politically expedient position which has no economic thought
behind it but it is actually completely true.
There is a whole field of thought which this suite of essays has been crying out to reference which is
known as ecological economics. This field looks at the similarities of the economic system to the
natural system and treats markets, not as the all-knowing guide of economic activity towards a point
of equilibrium, but instead as the environment in which forms of new economic species (firms for
instance) must exist and against which they either flourish or die out in the way that a natural
species does. Viewed in this way, the environment (the markets) may never be in equilibrium and it
is not clear at all that the most optimum solution will prevail. Also and most importantly, markets
do not create new forms of economic activity, they simply determine whether they succeed or fail.
So, for instance, no market pulled through the development of the iPod, someone in Apple simply
thought it was a good idea, and the market environment was such that it flourished. This means
that those who design cap-and-trade schemes with a view to pulling through new innovations in
clean technology may well be disappointed. However what they do do, is create a market
environment which favours those low-carbon technologies.
It will come as no surprise that this field of economics has strong ties to thermodynamics and
information theory, none of which we will explore here71. However, it does explain what people
might mean when they say that cap-and-trade systems are necessary but not sufficient for lowcarbon investment.
We need to create an economic ecosystem which rewards low-carbon investments and against
which they can be observed, accounted for, and their effects communicated. Such schemes are not
ex-ante creators of low-carbon endeavour, but they are an essential part of the ecosystem which
promotes the evolution of that endeavour, and they are a fundamental part of the creation of the
information basis which will see (some of) them prosper.
71
For a good exposition of this and much else in economics see (Beinhocker, 2007)
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Essay Five: Risk Management for the Planet
Four elements of climate change analysis
Large capital intensive investment decisions, as we have seen, have a high opportunity cost of
investment compared to delay in the absence of certainty about the future (or the prospect of
future information arriving). If we leave aside for the moment the problems associated with
collective action then this lack of certainty about the future may seem to be the greatest
impediment to the world deciding to embark on a programme of decarbonisation. In essence if we
look at saving the planet from dangerous climate change as an option which the human race has
then they will take that decision (leaving aside collective action issues) when the prospect of future
regret is outweighed by the perceived time and real costs of delay (we will come back to this
approach later but bear with me for now).
Implicitly this has long been recognised and hence the climate change community, as all sponsors of
major investment decisions do, has attempted to both reduce the uncertainty associated with the
decision to decarbonise and increase the perceived cost of delay (the time and real cost of delay).
The primary instrument for this two pronged approach to achieving an investment decision on global
decarbonisation has been the science of climate change. Bodies such as the Intergovernmental
Panel on Climate Change (IPCC)72 have been tasked with analysing the science of our climate and in
producing reports which both explain the degree of certainty we have about the future effects of
climate change on the planet and what the short-term impacts might be if it is not addressed
quickly. As we know from our analysis of option-based decision making these two focuses of
scientific investigation clearly address the fundamental trade-off in the process of decision making
under uncertainty: that of future uncertainty and the time and real costs of delay.
It should therefore come as absolutely no surprise to anyone that the key areas for debate and
controversy around the work of people like the IPCC have been the degree to which they do or do
not present the level of uncertainty associated with predictions of the effects of future climate
change, and the extent to which they portray events in the short-term as being the results of climate
change. The former being the value of future information and hence the benefit of delay, and the
latter being the real costs of delay.
For anyone wishing to generate a decision to decarbonise the energy system of the planet there is
every reason to try to find ways to present the future effects as certain and the costs of inaction as
high. When this incentive is taken out of the steadying influence of the peer-reviewed scientific
realm and portrayed in the media and to the wider public it is unsurprising that, as with most
advertising campaigns for goods and services, the factors which contribute to the short-term cost of
delay has the greatest prevalence73.
Interestingly, what the science of climate change is very good at is reducing the uncertainty as to the
fact that climate change is a problem and that bad things will happen. This is widely accepted
science in my view. What it is bad at is predicting the short-term costs of delay; however it is these
72
See (IPCC, 2007)
You may note that the latest Climate Change Committee report in the UK makes a particular point of
attempting to quantify the costs of delaying taking or not taking its advice. See (CCC, 2010)
73
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short-term costs of delay which perhaps have the greatest impact on people, at least as portrayed
through the media. In other words our prime lever is that of the short-term greed of keeping a
habitable planet, not the long-term fear of choosing the wrong energy system. Obviously, as this is
where the science is the weakest and hence the easiest to attack, it is not surprising that where
short-term claims have been made as to the cost of delay in decarbonisation and have captured the
public imagination, then the science has left itself most open to attack.
This, one could argue, is another fundamental misuse of the science of thermodynamics. Climate is
analogous to a thermodynamic system, despite the many variations within the system, we can
characterise that system using a small number of variables. Going back to the basic origins of
thermodynamics, while we cannot practically explain the position and motion of every particle in a
given volume of gas, we can characterise the gas as a system using a small number of variables
(pressure, volume and temperature for an ideal gas). Climate is the word we use to embody the
state of the atmosphere and oceans and all that affects them74. Predicting climate is not predicting
the weather, and attributing a specific weather event to climate change is like implying the state
variables of an ideal gas from the motion of one particle in that gas. No thermodynamicist would
taken that approach to characterising a gas, but we can see that the science (note not the
psychology, simply the maths) of decision making under uncertainty makes us reach for information
in events in a way which is not appropriate.
The second instrument used to justify action on the development of a low-carbon energy system is
economics or more correctly welfare economics or cost-benefit analysis. As any sponsor of an
investment decision would, the climate policy community has attempted to create an NPV analysis
of the investment in that new energy system which is positive. Such an analysis is tasked with
proving that it is economically rational to invest in emissions abatement given what the science tells
us about the costs of abatement and the consequences of climate change. The idea is also that this
analysis may also tell us the rational rate of investment in that new energy system75.
This form of economic analysis is most famously the basis for the Stern Review76 which was
published by the UK Government in 2007.
As with any NPV analysis there are three main components required for this analysis. The first is the
cash flow associated with “business as usual” or the state of the world without any action on climate
change. Embedded within this is often what is termed a “damage function” which is the economic
impacts associated with the impacts of climate change. Second, is the cash flow associated with an
alternative future in which action is taken on climate change, at some investment cost compared to
the business as usual scenario, and where there is higher long-term economic benefit from the fact
that climate change is averted. At a macro-economic level these first two input variables are often
measured in the gross domestic product (GDP) associated with the two pathways, with the implicit
assumption that climate change damages GDP (if for no other reason than we have to spend a lot of
resource adapting to the new climate, but potentially also because climate change negatively
74
(Hulme, 2009) is excellent at exploring what climate really means in all its forms and meanings to human
beings
75
See (Dreze & Stern, Policy Reform, Shadow Prices, and Market Prices, 1990) and (Dreze & Stern, The Theory
of Cost-Benefit Analysis, 1987) for introductions to cost-benefit analysis
76
See (Stern, The Economics of Climate Change, 2007)
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impacts economic activity generally), but that some of our resources will need to be diverted to
climate change mitigation in the short-term hence potentially constraining short-term growth. As in
all good NPV analysis the difference between these two pathways provides for a cash-flow profile
which we can discount to see if the NPV is positive and hence, theoretically that investment in
climate change mitigation is rational. This, of course, means we need the third component of
analysis which is the appropriate discount rate for the cash flows.
Let’s leave aside for the moment the fact that one of the main purposes of this series of essays has
been to question the validity of NPV analysis, and let’s discuss the analysis.
One of the major controversies surrounding the Stern Review and similar analyses has been the
choice of discount rate. Critics have suggested that Stern’s choice was too low and that given the
long-dated nature of the difference between the two cash flows being discounted then a small
change in the discount rate can change the conclusions of the NPV analysis radically (the sensitivity
of the NPV of a set of cash flows to the discount rate is known, slightly confusingly, as the duration,
which is actually the first moment in time of the discounted cash flows rather than how long they go
on for which is what it sounds like duration ought to mean). Stern and other welfare economists’
argument is an ethical one which basically says that the only reason why future generations should
be able to bear the costs of climate change better than us is because they might be richer than we
are and hence the right discount rate is close to the assumed level of growth in GDP77. Critics argue
that this is all very well but climate change is a capital problem (as we have noted earlier) and capital
cannot be mobilised at scale at these rates of interest, and hence even if this is ethically right it is
practically unhelpful78. They also observe that in other areas the human race perhaps does not act
as if it values the future in quite this way79.
Of equal debate are the two GDP pathways. These pathways need to contain information on future
climate change, its costs to the economy, the costs to the economy of leaving it unabated, and on
putting the mitigation actions in place to prevent it. These pathways extend for hundreds of years in
some analyses and hence have immense uncertainties. One of the main premises of this set of
essays is that we do not have the information basis on which to understand the costs of mitigating
and adapting to climate change and we will not do so for some time, if ever. It is clear to anyone
that predictions of costs to the economy which go out decades or even centuries are highly
speculative and have substantial potential errors in both directions. Studies like the Stern review do
attempt to embody this in their analysis by taking a risk-based approach. This in effect involves
stating that a certain scenario has a certain percentage chance of being exceeded and hence is not a
precise forecast but a bound to the probability of the scenario occurring.
77
I wonder if we shouldn’t view GDP as some form of measure of the imposition of the human-ordered system
on the planet and hence it is interesting to think that if this is the case then it surely has a thermodynamic
limit, when adjusted for inflation at least.
78
For discussion on this see (Atkinson, Dietz, Helgeson, Hepburn, & Saelen, 2009) and (Beckerman & Hepburn,
2007)
79
For other analyses and conclusions see (Nordhaus W. D., A Review of the Stern Review on the Economics of
Climate Change, 2007), (Nordaus, 2008), (Nordhaus W. D., The ghosts of climates past and the specters of
climate change future, 1995), (Nordhaus W. , 1993), (Nordhaus W. D., 1991) , (Weitzman M. L., 2007) and
(Sterner & Persson, 2007)
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So far we have looked at the world as one entity deciding whether or not to abate emissions and
hence prevent the dangers of climate change. We have assumed that one omnipotent body can
make the decision based on the science or on an NPV. Unfortunately this not the world we live in
and hence we come to the third main factor in the decisions we make about climate change: that
they are global collective decisions.
You will remember that in Essay One we talked of the challenges of optimising an energy system in
space and time. We discussed the fact that the inherently low entropy of fossil fuels means that
they can be transported and stored and that hence we are currently saved much of the heartache
that goes with managing an energy system in space and time in the way we will have to in the
future. There is another issue in space and time which occupies climate change policy-makers and
that is the distribution of the benefits and burden of decarbonising the energy system and of
adapting to climate change. There is a very broad discipline which has evolved into the ethics of
climate change80.
Put very simply the issue is how we distribute the benefits and burdens of decarbonising the energy
system and adapting to climate change across different countries and different people within those
countries (space), and how we determine the fair distribution of the burden across generations
(time). This is an ethical argument about how the costs and benefits of mitigating and adapting to
climate change should be shared between people on Earth today who have different abilities to pay,
different priorities, and different historical levels of benefit from the emissions which have already
entered the atmosphere over the last 250 years of so. It is also an argument about how much of the
burden it is fair for us to take today when the benefit of these actions will accrue to future
generations who may anyway have a higher standard of living and ability to pay.
The distribution of the burden in time is the crux of the debate about the discount rate which we
described above with respect to the NPV analysis of climate change mitigation. The distribution of
the burden in space has historically been dealt with through principles such as common but
differentiated responsibility which embodied, in effect, the principle that the rich have an historical
debt to the planet which means they should take a greater burden associated with mitigating and
adapting to the consequences of these historical actions. The current generation some-how taking
responsibility for the action of past generations who happen to have had the same nationality is
ethically troublesome in its own right of course. This is further compounded by the fact that no-one
can realistically claim that past generations had any idea of what they might be doing to the planet
before the 1970s or 1980s at the earliest, and perhaps they could not have done anything about it
even if they had known. However what the principle is in effect saying is that those who appear at
the moment to have benefitted most from the increase in entropy into the non-human system of
the planet, in other words, those who live in a more ordered society at the cost of disorder in the
planet’s systems, should bear more of the burden of reducing emissions and hence creating a more
ordered human system for themselves and the rest of the world, without the increase in entropy of
the wider planetary systems.
Some authors have attempted to look at the climate change problem as an option. They tend to
analyse the action to mitigate emissions as a call option in much the same way as we did in Essay
80
See the following for a range of discussion on the ethics of climate change (Hulme, 2009), (Northcott, 2007),
(Page E. A., 2006), (Posner & Weisbach, 2010), (Harris, 2010) and (Gardiner, Caney, Jamieson, & Shue, 2010)
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Three. As we know, in such an analysis one invests in the action when the costs of delay are greater
than the benefits. This means that investment occurs when the real and time costs of delay exceed
the value of future information (resolution of uncertainty)81.
Dispassionately and scientifically observed the costs of delay in emissions mitigation often seem low
because one more year of delay doesn’t affect the climate that much and, as we noted earlier,
science finds predicting the short-term costs of climate change quite hard, and there are a wide
range of long-term uncertainties about the outcomes for the planet. This, you may remember, is one
of the arguments used by economists to set a tax (setting price and letting quantity vary) for carbon
emissions, because the marginal damage for a marginal tonne of carbon dioxide emitted to the
atmosphere is apparently small. It will be very clear therefore, without calculation, that if the
outcomes appear highly uncertain and the short-term costs of delay are low then an options-based
approach is likely to lead to a decision to delay. The short-term costs of delay are low and the value
of future information in a highly uncertain world will be high and hence we should wait, expend the
short-term costs of delay, in the hope of achieving the certainty we need in the future about climate
change.
To summarise, we have seen that the scientific study of the climate is tasked with providing the
informational basis on which mankind can make decisions about the migration to a low-carbon
economy; we have seen that economists have recently attempted to employ NPV-style analysis to
analyse the decision to invest in that low carbon economy; we have seen that we have a severe
problem with the ethics of making that decision in both space and time; and we have seen that a call
option based approach to the analysis is almost certainly going to give us “delay” as the answer.
Risk Management for the Planet
None of this looks very good if you are a believer in the dangers of climate change, so let’s now pick
apart a number of these issues using the tools of thermodynamics, information and derivatives
which we have used throughout these essays.
First things, first; for the avoidance of doubt we are destined for thermal death. Our friend the
second law of thermodynamics tells us that the universe is marching inexorably to its highest state
of disorder (entropy) and hence boring, useless, nothingness. This is many billions of years away, so
we will discount it (even at the Stern Review’s discount rate), but it is the truth. It is also true that
many other factors have in the past and probably will again cause the major changes in the Earth’s
systems which have seen ice ages and other highly destructive phenomena. These factors are
volcanic activity, meteorite strikes and perturbations and cycles in the Earth’s proximity to the sun.
Hence the human race, even if it does not destroy itself, will be destroyed at some point in the
future, as may the rest of life on Earth (or large parts of it).
On these fronts, for the moment, we look alright and hence we are clearly in the business of
extending the period of human existence and increasing the capacity of the planet to serve
humankind’s needs for as long as possible, and with the minimum disruption for humankind in the
fight it has to maintain order in its own sphere against the disorder of the non-human systems of the
planet.
81
See (Pindyck, Irreversibilities and the timing of environmental policy, 2000) for an example of this form of
analysis.
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In geological time the periods of human civilisation and post-industrial human civilisation are both so
extremely short as to be considered almost instantaneous events. Hence to you and me, hundreds
or thousands of years might seem like amazing lengths of time, but we are thinking about an instant
in geological time.
Hence if we fear that the instant in time when our successors might comfortably inhabit the planet
might be shortened by climate change then it is perfectly alright to try to prevent that, but, to be
clear, we will be done for at some point. It is perhaps an interesting experiment to reveal people’s
true perceived discount rate to see how they respond to the thought of the extinction of the human
race in a hundred, a thousand, a million or a billion years.
It is perhaps amusing to think of the human race as one of a series of organic instruments of climate
change. We have discussed the inorganic instruments of major changes in our climate system
(meteorites, volcanoes, the orbit around the sun etc.), but we should not forget the organic ones,
such as the forests and small sea creatures of prehistoric times which so effectively reduced the
carbon dioxide levels in the atmosphere and sequestered our now famous low-entropy and highenergy sources in the Earth’s crust82. The human race can be considered another organic
colonisation of the planet which is releasing that carbon dioxide back into the atmosphere in a very
short period of time and hence changing again the Earth’s climate systems and setting off another
cycle of events.
A geologist on an alien probe passing Earth in a billion years time might stop off, drill a few ice or
deep-ocean sediment cores, and impute that among the many other varied events in the geological
history of this particular planet there must have been organic species which sequestered carbon
from the atmosphere, followed, a while after in geological time, by either some form of natural
disaster which released that carbon or another organic species capable of releasing that carbon back
into the atmosphere. It will be hard for the alien geologist to tell the difference between a truly
instantaneous event and one that took several hundred years to complete.
Back to how we decide whether to do something about climate change.
The science of climate change, as we have discussed, is extremely good at providing an
understanding of the impacts of carbon emissions to the climate system, but may always be bad at
attributing and quantifying the short-term impacts of delay. It is also true to say that the potential
range of outcomes and their timings are also hard to quantify. This makes the decision to exercise
the option to invest in a low-carbon economy much harder because looking at climate as a system
doesn’t provide one with easily attributable short-term costs. There is another difficult problem
with the science and that it is that is trying to predict the future affects of today’s actions. As the
release of greenhouse gases into the atmosphere retains more heat, increases the temperature of
the system, and causes increased disorder in the climatic system, then the observable impacts of
that take time. Ice caps and glaciers take time to melt; the seas take time to warm and expand, etc.
etc.
82
By way of example, oxygen occurs in the atmosphere because photosynthesising organisms put it there
originally when the Earth was quite young, so the air we breathe as well as the hydrocarbons we burn are gifts
from organic colonisations of the planet in distant times.
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In normal option analysis, when we exercise an option we know the return we will receive from it at
the time we make the decision to exercise. However in the case of our climate the actions we do or
do not take today could easily have impacts in the future which are unavoidable, but still uncertain
today. This means that we do not have certainty of the pay-off to exercising the option to
decarbonise even when we exercise it. The maths of options gets even more hair-raising in this case
and so I suggest we avoid it, as the point, I trust, is intuitive. There is at least some probability that
we have already created sufficient disorder into the planet’s systems that processes are in train that
are irreversible and catastrophic for human habitation of the planet, but we will not be able to
observe the actual impacts of those processes until it is too late83.
Giddens84 has introduced his own paradox which he applies in a political sense with respect to
climate change and that is that by the time we have mobilised collective action then it will be too
late. This can also be seen as a simple function of the rate at which we can viably expect to have
observable information on the effects we are already having on the climate. If you like, the
information related to the impact of our actions today on the planet may not be available until long
after the fact and, most importantly, long after the irreversible destructive processes have been put
in train. Giddens tends to look at his paradox as a function of our political system’s inability to
mobilise collective action, and he is probably right, but we can also apply his paradox on a much
more basic level. By the time we have the information we need to make the decision to decarbonise
our energy systems, then we may already be doomed, even in the case where we can orchestrate
the required collective action and political will based on that information.
This collection of essays has consistently tried to expose the flaws in NPV analysis in investment
decision making processes, and the same goes for NPV analysis of the climate change issue, in my
opinion. While analyses such as the Stern Review and related critics and supporters has
undoubtedly moved the debate on intellectually and perhaps most importantly in the public eye, it is
clear that there are many problems associated with the use of NPV analysis for decision making.
As we have seen previously, even in the presence of good estimates as to the appropriate discount
rate, damage function and abatement curves today, if there is substantial uncertainty within any of
those important variables, and hence new information which we believe we will receive in the future
then even if the NPV of the decision is positive there is a high chance of delay, especially in a world
where we do not experience immediate short-term costs associated with that delay.
There is then the simple fact of the enormous uncertainties associated with the three key variables
in the NPV analysis. As I write this in 2010, three years on from the Stern Review, I can tell you that
the cost of deploying wind power onshore in northern Europe has gone up by nearly 50%; the cost of
deploying it offshore had gone up by more than that; and the cost of solar panels has more than
halved, but are still very expensive85. I could go on. There is a growing literature from all sides of the
energy debate and all lobbies within the energy market which points out quite simply that estimates
of the future tend to be very, very wrong most of the time. This, of course, is as much a problem for
the critics of the Stern Review as for the original analysis itself. There are those who claim to
83
See (Hansen, 2009) if you want to get really worried.
(Giddens, 2009)
85
For good reading on how we aren’t very good at predicting things see (Taleb, Fooled by Randomness, 2004),
(Taleb, The Black Swan, Penguin) and (Mandelbrot & Hudson, 2008)
84
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secretly know what it will cost to eradicate disease and poverty in Africa for instance, and hence
suggest that as the NPV of that is in excess of the NPV of abating climate change that we should
divert our resources to that instead86.
One might observe that those who know the secrets of the future costs of solving (and of not
solving) the world’s great problems really ought to be made to tell the rest of us, as if the
information is robust, it would clearly prove very useful.
Of course, with clear, unquestionable and robust information the decisions would be easy (easier
perhaps). The real challenge is to make the trade-offs and compromises in the absence of that
information.
In fairness, those who pursue NPV analysis of future climate issues do know that they are making
estimates of the future, and hence often talk about taking a risk-based approach given the range of
viable scenarios. The Stern Review takes this risk-based approach. As we noted in Essay Three, this
is probably the state of the art in corporate investment decision making. Most investment decisions
are presented with ranges of scenarios and sensitivities. Generally, the Goldilocks approach is used,
where there are scenarios where the investment turns out to be really hot; scenarios where it could
be really quite cold; and usually a “base case” (often implicitly presented as it is in the Stern Review
as the scenario that is 50% of the way between hot and cold) where the investment turns out to be
“just right”87.
This form of approach exposes the risks of the decision (or not making the decision) through the
analysis, but it has two main flaws. Firstly, as we have seen throughout these essays, even if the risk
adjusted NPV is positive given all the scenarios, the inherent uncertainty in those scenarios may well
lead to a decision to delay. Secondly, there is no risk management in this approach, in that it tells
you that it could be good and it could be bad and on average it will be alright, but there isn’t much
you can do about it.
As we discussed in Essay Three, very few negative NPV decisions are taken to Board of Directors or
Investment Committees, and so NPV analysis tends to not, in reality, contribute much to the actual
tendency to make decisions. Instead there is the need for greed (opportunity cost of delay) to
exceed fear (future uncertainty), and there is also the need on the part of smart decision makers to
have managed the identified risks to the highest degree possible.
The inherent problem with NPV analysis of this kind is that while it may identify future ups and
downs, identifying them isn’t risk management, action to mitigate those risks however is. Hence
the problem with the use of NPV analysis to justify climate change mitigation actions if that in the
presence of some pretty poor information different analysts will get different numbers and hence
their averages will be different and hence they will recommend an entirely different binary and
irreversible decision at a given point in time. This isn’t risk management, however many scenarios
and probabilities one creates.
86
See (Lomborg, 2010) for example.
Some friends I have in the British civil service tell me that there is a famous “Yes, Minister” sketch which
exposes this exact approach from civil servants in recommending actions to Ministers. I have not
independently validated the existence of such an episode, but I am prepared to believe it.
87
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At first look it also appears unlikely that our friends derivatives are going to help us, but let’s look at
how we should view risk management for the planet.
Firstly, let us simply take from the science what is most certain. I am going to allow myself to believe
the following things. Carbon dioxide and the other recognised greenhouse gases do trap more of
the re-radiated energy of the sun as their concentrations in the atmosphere increase. Throughout
the history of the planet changes in atmospheric composition have been associated with major
changes in the global climate. We are currently in the process of reversing a reduction in the
entropy of the planet’s systems which was performed by the flora and fauna of prehistoric times,
and hence we are increasing the entropy of the non-human world in pursuit of the creation of order
and utility in the human-dominated systems of the planet. There are identifiable positive feedback
loops in the climate system, such as the potential release of stored methane as the Earth warms; the
reduction in the sun’s energy reflected out to space due to the loss of ice mass; as well as others.
The timing and actual impact of these changes is highly uncertain and major catastrophic events
such as the loss of the Greenland or West Antarctic ice shelves are similarly highly uncertain.
Note that in the above I have made some pretty certain statements about the climate system, but
have retained a high degree of uncertainty in statements about specific events. In essence I am
saying that we know the state of the thermodynamic system, but we will always be uncertain as to
what we will observe by looking at a small part of that system at a specific point in time.
One can look at this as a scenario where there may be gradual change in the climate system and
there are some identifiable catastrophic events which have the capacity to substantially truncate the
period of human habitation of planet Earth in its current form, or at least on its current development
trajectory.
One problem with using standard call option derivative theory to look at the decision to invest in the
low-carbon economy is that the option is likely to expire prior to us having the information required
to exercise it. That is, that by the time we know with some degree of certainty that we are losing the
Greenland ice shelf (solely by way of example) then we probably no longer have the option to invest
to mitigate that. Back to the version of Gidden’s paradox which we described earlier.
This problem is further exacerbated by the lag in the time for action, so again, by the time you have
the information to act it is probably too late and then it will, of course, take some time to mobilise
the required actions.
What this all really means is that a simple form of call option analysis of the decarbonisation decision
is flawed because in such an analysis one makes the implicit assumption that it is possible to put the
planet back to the state which we would like it to be in at the time at which we receive the
information which tells us to do so. We simply cannot assume this with climate change.
Taking a simple example, if you are visiting a place or performing an act where you might catch a
disease which is definitely fatal if you catch it, but there is only a certain probability of catching it,
then, given that a vaccine is available, it makes sense to take the vaccine ahead of time. If you were
to wait for the information as to whether you are infected or not, and assuming that there is no
antidote despite there being a vaccine, then you have no capacity to act on the information which
will then be certain. The vaccine is a hedge, which likely costs you some money and discomfort,
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which means that you are safe in the case where you both catch the disease (or are in a situation
where you would have caught it without the vaccine) and the situation where you don’t catch the
disease. You will have invested in the hedge due to the probability of a bad event and in the
presence of substantial uncertainty about the event occurring, but in doing so you will have ensured
your survival in all future states of exposure to the disease.
This is risk management.
It is in effect the purchase of a physical insurance policy which maintains a certain level of utility in
the case of both good and bad outcomes.
The insurance policy is analogous to a put option. This is an option that pays off to the holder in the
event of bad outcomes (low prices for most commodities or stocks on which the option might be
written in financial markets). The investment today by the buyer of the option is made in order to
avoid low pay-offs in the future. For instance a farmer growing a certain crop might buy such an
option in order to ensure that he at least covers his costs and can feed his family, even in the event
of a very low price come harvest time. He (she) will pay for that derivative, in the way that we all
pay for insurance policies of one kind or another.
Understanding that climate change mitigation is a put option (insurance policy) not a call option (like
many other investment decisions) has some interesting implications. Firstly, future uncertainty
makes you want it more, and hence makes you more prepared to pay for it today, indeed the
greater the volatility of future outcomes then the greater the value of the put option (insurance
policy) today.
Hence, what the science tells us, which is that there are some pretty horrid outcomes for humans on
planet Earth which are uncertain, makes us want to buy the insurance more. It is also important to
note that as the potential disease victim above is definitely dead if they catch the disease
unvaccinated, then as there is no way to get nine billion people off of planet Earth then the
insurance policy that we buy has to be one which genuinely rectifies the affects of the uncertain
future states in which we might end up.
We buy our insurance of course by moving to a low-carbon economy. There is no market in trading
the entropy of our planet’s systems and so the only way to hedge is to prevent that entropy reaching
critical states which the scientists tell us could be very bad.
This still, of course, does not tell us how much we ought to be prepared to pay for the option, or
what it will cost. We have used derivative concepts to deal with a couple of issues however. Even if
outcomes are uncertain, we are prepared to insure against them, and we have to fully insure against
those outcomes because there is no getting off the planet so the mitigation actions need to be a full
hedge to the bad outcomes.
The price we have to pay for the insurance policy is determined by the cost of mitigation and the
speed with which we need to act in order to provide for a full hedge in the cases of bad future states
of the planet.
We have discussed at length in these essays that we need to discover the cost of mitigation
investments through the observation of actual investment decisions.
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The speed of required action for a complete hedge is still dependent on the science telling us how
much headroom we have for increasing the entropy of the planet’s non-human systems without
causing bad future states for our existence. The key insight here though is that it must be a
complete hedge to at least catastrophic climate change and that uncertainty is not a reason for
delay, in fact quite the opposite.
We will make the decision to invest in the transition to a low-carbon economy in the absence
therefore of complete information as to the affects we have already had on the planet, never mind
what affects we may have in the future. However it is this very lack of knowledge about the future
which should make us want to invest more.
In the above analysis I have of course made enormous ethical judgements, and somewhat glossed
over the issue of action in time. It may be that we decide that we don’t care if there is catastrophic
climate change events in a couple of hundred years time and hence the human habitation of Earth
(as we know it) is truncated by a substantial period, but I have assumed that we do care, and hence
that we are willing to invest today to avert catastrophe for future generations. Note however that I
have solved the time question in a different way to the NPV analysis. I have said that we must have
a full hedge, because we have no other means of mitigation of bad future states of the planet.
Hence the action taken to mitigate climate change is determined by our view of the action
requirement to achieve a full hedge against the more troubling potential outcomes of climate
change88.
I suspect a full hedge is going to require a pretty abrupt purchase of an insurance policy (put option).
Interestingly, if we have determined from applying the simple principles of derivative theory that we
need to preserve the planet in all its future states, then we have solved the discount rate problem.
The answer is the risk-free rate. Put simply, we know that if we are certain about the outcome in all
future states of the economy then we know that we are in risk-neutral space which is that easy place
in option analysis where everything is discounted at the risk-free rate. Using any other rate implies
that we are seriously contemplating future states of the world in which human existence as we know
it, pretty much ends, and as far as I am concerned you can discount that at whatever number you
like. Of course, we don’t know the cost of the insurance policy until probably after we have
implemented it, which is a bit of a shame, but at least the discount rate is sorted out.
The final issue in risk management for the planet is how the costs and benefits of mitigation are
distributed in space (i.e. across people and across nations). This is the collective action problem
which throws up many ethical issues of distribution and the rights and wrongs of historical and
future actions and distribution of responsibilities. The final essay in this series will attempt to bring
some of the thoughts explored in these essays together in a way which tries to provide answers to
this question.
It would perhaps not be unkind to say that our conclusions here on what to do are not that far away
from where the international climate change community currently is, and I would agree. I hope
88
I appreciate that this sounds quite a lot like the precautionary principle which some authors, (Giddens, 2009)
for instance, are starting to say doesn’t really help. The basis of the argument is that taking precautions
doesn’t get anyone excited about a subject. I appreciate this, but I think the above argument stands.
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however that this review and critique of some of the ways we look at things has helped put a new
light on the way we look at these things in climate policy.
To reprise.
Viewed as an investment decision just like any other it is tempting to try to reduce the uncertainty in
future outcomes and increase the apparent short-term opportunity cost of delay. This clearly plays
against the strengths of climate science. Climate is best looked at as a system, not as its component
parts, and there are some pretty robust things one can say about it as a system both through its
history and into its future.
Large variability of outcomes in the future makes us want to insure the viability of human existence
on planet Earth. Hence we should not be afraid of uncertainty as we often are in normal investment
decisions. This is a decision to insure, not a decision to invest. It is protection for the investments
we have already made in developing human civilisation.
NPV analysis will always be open to argument given the enormous uncertainties in the three main
input variables in the analysis.
Viewed as risk management, and knowing that we currently have no viable option of leaving the
planet, then the hedge we put in place must be defined by its completeness, hence the speed of
action is conditioned by the need to deliver a full hedge rather than burdens allocated in time
through a discount rate.
This assumes that we are prepared to change our trajectory today in order to extend the length of
viable human habitation of Earth despite the full knowledge that there is nothing we can do to
prevent the eventual thermal death of the universe and eventual naturally occurring radical changes
to the climate which will threaten the existence of humankind.
The physical time lags in the climate systems, combined with the inevitable lags in mobilising action
mean that we will always take mitigation actions in the climate change arena in the absence of
robust information.
The final point to make in our critique of NPV analysis is the reliance it then places on carbon prices.
We have seen in previous essays that cap-and-trade schemes are really ex-post mechanisms which
perform many crucial functions in the financing of climate change mitigation, however stimulating
large-scales investment in mitigation actions is the least important of those functions and actually in
complete contradiction to a number of the other more important functions. The problem with
believing in the certainty of the assumptions of an NPV analysis is that out of that analysis can
naturally come an idealised carbon price for a certain emissions pathway. Said carbon price being
the value which makes the investment and emissions pathway of a given analysis NPV positive. This
is unhelpful on lots of levels. As we have discussed, carbon pricing through emissions trading
schemes is important, but not for large-scale investments. Secondly, we see a new source of
volatility in the carbon price as economists are likely to change their views on their NPV analysis and
hence where the right level of carbon price ought to be. Third, and finally, in doing this people are
again mixing the ex-ante and ex-post. We simply don’t have the information to know what the costs
of many required investments are, and as we have seen, the accuracy of inputs to many NPV
analyses (even when qualified by probability) cannot be sustained even over short periods and
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certainly not over the lifetime of most climate mitigation investments, or, as they are indeed often
used, over the lifetime of a global emissions pathway.
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Essay Six: Information and Climate Change
Thermodynamics is the science of transformations89 and the science of systems.
We are concerned here with a number of systems: that which has been created by human-kind on
Earth which provides us (most of us) with a substantially greater length and quality of existence than
we would otherwise have; the energy system which powers the development and maintenance of
that human system on Earth; the financial system of money and information flows which powers the
development of that physical energy system; and the wider planetary system in which we exist (of
which our biosphere, atmosphere and oceans are the major part).
We are also concerned with a number of transformations of those systems. Our existence on Earth
is the result of a number of accidents in geological time which have lead to the Earth’s systems being
amenable to human development and habitation within this particular inter-glacial period. While
operating in the full knowledge that meteorite impacts, long-period oscillations around the sun,
volcanic activity or the eventual expiry of the sun will one day lead to the extinction of the human
race on Earth, we are concerned with preserving our current state of civilisation and its generally
positive trajectory for as long as possible. This being our deeply felt ethical obligation to the
generations which come after us (actually it is probably a genetic predisposition). It is also true to
say that the events which will otherwise destroy us currently seem likely to happen only on a
timescale which is orders of magnitude greater than known human civilisation and hence
substantially beyond our ability to comprehend.
The only known prospect of the Earth’s wider systems being transformed in a way which threatens
the human-dominated system and the abrupt end to the current benign state of that system is the
result of the almost instantaneous (in geological time) release of substantial quantities of gases with
enhanced warming characteristics into the atmosphere.
We fear a transformation of the Earth’s system which is consistent with those which have happened
previously in geological time, where a dramatic and abrupt change in the composition of its
atmosphere has caused major changes to its sea level, glaciations levels, temperature, and weather
patterns. We fear the destruction of the Greenland and Antarctic Ice shelves; we fear sea level rise;
we fear the deglaciation of the Himalayas; and major changes in our weather systems. Such
transformations, when they have occurred in periods where life existed on Earth, have created mass
extinctions and hence massive changes in the biological systems of the planet.
We fear these transformations, not necessarily for their own sake, but for the impact they have on
the human systems in which we have invested so much historical resource and on which we crucially
depend. Our human system, while apparently dominant on the planet, is both critically wedded to
the wider planetary systems and in a constant battle for survival against them90.
89
This is a quotation taken from Enrico Fermi the Nobel Prize winning physicist, but I think it is also a general
statement. See (Fermi, 1936)
90
See (Lovelock, 2006) perhaps.
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Amongst the many ironies of climate change is the fact that the transformation we fear is the result
of the most productive transformation in human history, which was, itself, the product of a great
transformation of the planet’s system by its interaction with biological life.
We owe much to the organisms of prehistoric times which contributed to the transformation of the
Earth’s system into one habitable by human civilisation through the extraction and sequestration of
carbon in the Earth in the form of hydrocarbons such as coal, oil and gas. This pre-historic
transformation, in part, provided us with the benign atmospheric situation which we inhabit today.
The ability of the human race to impose itself so dominantly on the planet in the last 250 years or so
has involved the reversal of that pre-historic transformation. The creation of the great order and
capacity for useful work within the human-dominated system of the planet has enhanced human life
and caused an exponential growth in almost every measure of human existence (including and
especially population).
The second law of thermodynamics tells us that disorder must always increase (and hence capacity
for useful work decrease), and hence as we have increased the order and capacity for useful work in
the human systems of the Earth we have increased the disorder and reduced the capacity for useful
work of the rest of the systems in the universe. With the whole universe as our sink for disorder
then this should not be a concern. However, it is not. The consequence of the release of greenhouse
gases into the atmosphere is that our planet becomes a more thermally closed system, and hence it
can only expel sufficient heat to the wider universe to balance the sun’s incident energy by being at
a higher temperature. One consequence of our current transformation is that we are closing
ourselves off, thermally, from the wider universe and in the process retaining greater disorder in the
planet’s systems as we increase the order and capacity for useful work of the human-dominated
systems of the planet.
Our challenge now is to transform the energy system on which the human dominated systems of the
planet rely into one which is no longer dependent on the use of stored hydrocarbons and hence
which does not increase the state of disorder in the wider planetary systems. We have, if you like,
the thermodynamic definition of sustainable development, and that is development of the human
systems of planet Earth without the creation of disorder in the wider planetary systems.
How come our transformation of our human system has been so dependent on hydrocarbons?
Some would say that this is obvious, and is a simple consequence of the cheap and abundant nature
of hydrocarbons as an energy source. This may be true, but I do not believe it is as obvious as it
seems. Hydrocarbons are abundant, and in some parts of the world cheap to extract, but no-one
should under-estimate the scale of the investment which has been required over the last 250 years
to access that energy. The entrepreneurial endeavour, capital deployment and political turmoil
which have surrounded the development of our hydrocarbon energy system have been immense. In
no way did investments in coal mining in eighteenth century England look the sure thing that they
may now appear in hindsight for instance.
Surely the sun and wind and other renewable resources were equally apparent to our forebears and
so was it really a simple matter of cost which saw hydrocarbons win out? I do not believe so. There
is one renewable energy resource which required large amounts of capital and the taking of major
risks in order to exploit, but which was pretty much exploited to the full in all practical instances and
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that is hydropower. Hydroelectric power is an example of a renewable energy resource which was
harnessed at least contemporaneously with much hydrocarbon development. So was it cost? And
why were the so much more obvious sources of energy such as sun and wind ignored? Standing
back, and removing our historical prejudices for a moment, it seems very strange to imagine a
eighteenth or nineteenth century entrepreneur walking in the hills of England on a sunny day with
the wind buffeting him as he walked and him thinking to himself: “I know what, I will dig a mile
underground and see if I can find a store of low-entropy energy”91.
Of course, hydroelectric power is not the only example of humans looking to harness renewable
resources. Long distance transport (in the form of sea travel) was dominated by the wind until only
150 years ago, and wind and water mills ground corn for centuries. So it must just have been that
hydrocarbons turned out to be a lot cheaper. Right?
Wrong. I frankly don’t know whether hydrocarbon energy is, has ever, or will ever really be cheaper
than clean forms of energy. However, I am completely certain of one thing and that is that
hydrocarbons deliver us that energy in a much lower state of entropy than that in which we can
harness most clean energy resources. Hydroelectric dams are the renewable energy exception
because they have inherent storage capacity and hence the ability to move energy in time, and
therefore it is no accident that they were developed at scale at least contemporaneously with
hydrocarbons.
The transformation that has occurred in the world’s energy systems from 1750 or so onwards is not
one of the discovery of new energy sources. It is the discovery of low-entropy sources.
So the transformation we need to make in our energy system is not about energy at all, it is about
entropy. It is about no longer increasing the entropy of the planet’s systems through the release of
stored energy in the Earth, but instead harnessing the sun’s incident energy in all its disparate forms
and delivering it in space and time for the use and convenience of humankind.
The reliance we need to wean humankind off is not as often quoted, the reliance on cheap polluting
energy, but it is the reliance on low-entropy sources of energy, and the ease with which they allow
useful work to be done at the place and time of our convenience. This means the transformation we
need to create in our energy system is the ability to instantaneously reduce the entropy of that
system at any given place and time such that it can provide the same level of useful work as the
current hydrocarbon energy system does.
Throughout this final essay I will highlight areas where I believe that the current mantra of the
environmental movement is self-defeating. The first, of course, is that we do not have an energy
crisis, we have an entropy crisis. Unless we understand this, we will never understand how we got
to the system we have today and we will also never understand how we create the transformation
which we wish to see in our energy systems. It is the entropy problem which is hard to solve and the
reliance on low-entropy energy sources which is so hard to break, not the energy itself.
Second is that our choice of energy system to date has been completely logical and based on the
low-entropy state of hydrocarbon fuels and the additional convenience that we can generate from
91
I appreciate that early mines probably were not a mile deep and that entropy wasn’t discovered until late in
the nineteenth century. Allow me the occasional bit of artistic licence if you will.
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such fuels. It is the replacement of this low-entropy system which is the most daunting task. The
hydrocarbon economy, I am afraid, is not maintained by a conspiracy of hydrocarbon company
executives, western politicians and middle-eastern autocrats92. It is maintained by its inherently low
entropy state: pure and simple.
This leads to the third failing of the environmental movement and that is that they have a habit of
saying that we have all the technologies we need to migrate to a low-carbon energy system. We do.
But that simply isn’t the point. What we do not have is all the technologies that we need to
transform our energy systems to a low-carbon one while maintaining its current low state of entropy
and hence its ability to deliver useful work in space and time. I do believe however that we now
have the potential to create such technologies, from the knowledge we have available to us today93.
The mechanism for the reduction of the entropy of the energy system is the use of information.
Information, which we know to be equivalent to entropy in a thermodynamic and information
theory sense, is the crucial component of the low-carbon energy system. It is not sun and wind
which will replace oil, coal and gas, it is information. Only information has the capacity to transform
the high-entropy captured incident energy of the low-carbon system and turn it into useful work in
space and time.
Storage and interconnection are crucial new components of the energy system, as they allow us to
act on information. Both of these new components of the energy system, you will note, consume
energy, and hence my fourth gripe in almost as many paragraphs. Thermodynamically, the
reduction of entropy in a defined system requires energy to be expended. Given that today we get
our energy in a low-entropy state for free then it is clear that a low-carbon energy system of the
future will use more energy, not less, even if we ignore all the increased demands we expect on the
energy system. Hence while I agree that energy efficiency investments are important,
environmentalists need to stop saying that the answer is using less energy. Thermodynamically this
simply isn’t true. Using more energy is the answer to our low-carbon energy dreams.
So it is indeed true that if we transform our energy system to include clean energy and energy
efficiency investments, we will create a system which creates less disorder in the wider planetary
systems, but we will also create chaos in the human energy system and the reduction in the
convenience provided to humankind by the energy system will not be tolerated by the wider
populous.
Information therefore has a role crucial in both the energy system itself and in the financial system
that directs capital to the investments required in that energy system. The low-carbon and lowentropy energy system of the future will be vastly more capital intensive than the energy system we
have today. This means that the systems of climate change finance must cause the efficient
deployment of vastly more capital than has been deployed in today’s hydrocarbon-based system.
This is evident from all we see in the market, but it is also close to a thermodynamic fact given that
we have been getting our energy in a low-entropy state for free (or more correctly at the expense of
the planet and hence of future generations). The scale of this capital deployment and the fact that
92
As noted on another topic in an earlier essay, anyone who does actually believe this is has either never met
anyone from these three categories of individual, or has been one a little too long.
93
This makes for an interesting reflection on many of the ethical issues in climate change, but that is for
another time.
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we have an entirely new challenge of developing a low-entropy energy system in the absence of
hydrocarbons are perhaps the two things about climate change which are the most daunting, given
the time we potentially have to solve them.
Let us deal first however with the role of information in the low-carbon and low-entropy system of
the future. Information systems in many applications allow for the increase in the utilisation of
systems through their intelligent and efficient use and hence the delivery of greater utility from the
same capital investment. Outside the energy sphere one can think about the utilisation of
communications infrastructure and within the energy system one can think about the shared use of
grid and other infrastructure. Information therefore is crucial in reducing the required amount of
physical energy capture, use, transmission and storage investments which are required in the lowcarbon and low-entropy energy system. It is also crucial in optimising that system on a minute by
minute basis.
Because information can therefore lead to a less capital intensive system, it appears that as well as
being equivalent to entropy, information is also equivalent to capital in the energy system, in that
there is some trade-off between further capital investment in the low-carbon energy system, and
the enhanced use of information.
The low-carbon and low-entropy energy system of the future will need to manage vast quantities of
information on the available energy resources of the system (is the sun shining on the solar panels,
can we turn the nuclear power station on quickly, is the wind blowing etc?), the energy needs of the
human uses of the energy system (bath time in an hour, granny is cold this winter, I need the car
tomorrow afternoon etc.), and of the energy stored and available for use. This requires a massive
increase in the bandwidth of information in the energy system, and it will require that information
to be digested and processed in a way which allocates the available energy resources to the needs
and preferences of the users of the system.
If we assume that this system will be a form of market then this information will be brought together
by that market (or collection of markets) and that allocation of resources will be substantially
arbitrated between the myriad of agents in that market by price. In information theory terms we
will need a high bandwidth market which will therefore be of inherently higher entropy because exante there will be a very wide range of uncertain outcomes, and it is absolutely essential to the
stability of the overall system that it is capable of receiving low probability, but then high
information content, messages.
Markets then reduce the entropy of the system at the point of settlement. In information theory
while the communication channel may be one of high entropy, and hence the receiver is in a state of
high uncertainty before the message arrives, the entropy of the receiver is reduced by the receipt of
the message. Similarly the low-carbon energy system has high entropy and has a state of high
uncertainty before the market clears, but the market clearing allocates the resources appropriately
and reduces the entropy of the system for the users of energy.
Information is therefore what turns a high-entropy system of energy capture and use, into a system
of low entropy for the users of the energy system as they are delivered their required utility from
the energy system in space and time. A consequence of the high- entropy information system is that
the allocations will be made by a price which must be inherently more volatile and have a greater
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range than we are used to. Again this is close to a thermodynamic fact. If we are to replace our
“free” low-entropy energy sources with high-entropy sources, then the information system which
bridges the gap between those high-entropy sources and the desires of users must be able to absorb
a much wider range of information and must have much greater ability to allocate resources based
on a wider range of uncertain price.
There is an increasing trend in energy market design to “create certainty” of price. This is in some
respects well meaning as we will see in the rest of this essay, but it is also completely misguided, if
misapplied. As we have shown, the energy system of the future will need to have a system of
allocation of resources which has much more volatile and widely ranging prices at least in the shortterm or we simply will not be able to have the informational ability to reduce the entropy of the
energy system to a useful state for its users.
Numerous of the remaining gripes about the environmental movement and the energy market
intelligentsia will be about their apparent desire to destroy both information and the ability of
economic agents to communicate with each other. If there is a recurring sin of the environmental
movement it is certainly the desire to destroy information and its associated communication.
This trend for the introduction of certainty into energy markets is the first of these. If regulatory
systems are established which prevent the transmission of sufficient information between agents in
the low-carbon energy system via the price or other mechanism then it will simply be impossible to
create a system which reduces the entropy of the energy system to a state equivalent to that we
have inherently in the hydrocarbon-based system.
Increasing short term energy price volatility is an essential part of saving the planet.
The reason for this trend in the development of price certain mechanisms, as noted above, is well
meaning (if somewhat misguided and infuriating), and it derives from a rudimentary understanding
of the next issue in the use of information in the low-carbon energy system and that is in the
direction of capital to low-carbon investments. Policy-makers have recognised that ex-ante price
uncertainty, that essential feature of a low-carbon, low-entropy energy system, can create an
incentive to delay investment, or put another way, increase the opportunity cost of investment
above the level of the NPV of the investment.
This is completely true and is further exaggerated in the case of low-carbon investments such as
clean energy and energy efficiency as they have a high degree of capital intensity and a high ratio of
average to marginal cost. The investment decisions that agents make are therefore highly
irreversible (another concept borrowed from thermodynamics, you may notice) and hence the
prospect of new information in the future in the form, for instance, of price volatility, causes there to
be a substantial opportunity cost associated with investment today compared to delay.
The simple fact is that most energy capture and usage (reduced usage) investments in a low-carbon
energy system have very little use for information in the future and hence it is completely true that
future uncertainty at the point of investment simply puts the cost of investment up above the cost
of the real NPV of the investment and hence causes the investment to be more costly than it
otherwise would be. This premium to NPV which is due to the value in delay can be seen as a cost of
information. In other words it is the cost of being able to observe an agent making an investment
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decision in the presence of uncertainty in the future. You don’t get to observe the NPV of the
investment but you do get to observe the circumstances under which the agent will invest.
The premium paid above the NPV of the investment is created by the value of waiting to see future
uncertainty resolved and hence the value of receiving future information before the investment
decision is made. Hence when we pay this premium we can see it as the price we have to pay to
create action today in the presence of uncertainty, or the value to us of observing investment today
compared to the investment agent observing information in the future.
Hence it is not that price certainty is inherently good, but it is true that in the presence of price
certainty, price certainty is good.
To unpack this. Price certainty is good for two reasons. Firstly, if the investment itself cannot react
to the future price signals then the information contained in those price signals is clearly useless to it
(for instance a wind farm is going to produce energy when the wind blows whatever the price is in
the market). Secondly, the reason for price uncertainty to exist in the incentive mechanism for
investment in low-carbon energy is to account for the fact that those setting the parameters of the
mechanism might not know what the price actually is. In this case price discovery is a good thing,
but we have done enough thermodynamics now to know that nothing is ever free, and so the
observed price discovery will come at a certain cost. Information has a cost and that cost is the
premium over NPV created by the inherent price uncertainty at the point of investment.
Hence it is possible only to observe the price at which an investment is made; it is not possible to
observe the NPV of an investment. The simple paradox is that in order to observe an act of
uncertain value today, a premium must be paid above the real cost of that investment, and that
premium itself is created (at least in part) by the fact that we have to create a system with price
uncertainty in order to observe uncertain prices.
Taking the first form of price certainty first. If the investment being made has no use for the
information in the market over its asset life, which is the case for most capture and use investments
in the low carbon energy system, then there is little point in exposing them to that price uncertainty
at the point of investment. To do so simply creates deadweight cost in the system, as investment
agents wait, or require to be remunerated with the opportunity cost of waiting in order to invest,
due to future information on which it cannot act anyway.
Hence there is little point in exposing a wind farm, solar farm, or home insulation investment to our
ever more volatile short-term energy price because they have no capacity to act on the information
they will receive. Such investments are the creators of disorder in the energy system. They create
information but they cannot use it.
Hence the “price certainty” people have something of a point in this regard as there is no point in
exposing investments made today to future price uncertainty to which they cannot react, but which
will cause an information cost to be reflected in the initial investment cost (the deadweight cost).
This is what we referred to as “asset matching” in Essay Two. However such investments must be
allowed to communicate their information into the energy system to the fullest extent, as someone
else has to use that information to reduce the entropy of that system such that the energy captured
or used can be done so usefully.
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In the presence of certainty about the price of investments therefore those who advocate price
certainty win, with the qualification that they are right that the investment in question should not be
required to be the receivers of information, but they must not be prevented from transmitting their
information into the wider energy system. If you like, the difference between many low-carbon
energy investments like say a solar farm, and a hydrocarbon based one, say a coal-fired power
station, is that the former can only transmit information, it cannot usefully receive it. A coal-fired
power station can both transmit and receive information in the market (more correctly it can react
to receiving information). This difference in their capacity to participate in the information flows of
the energy system is a function of the starting state of entropy of their energy sources (the sun being
high, and the coal being low). Again we have an information equivalence of entropy, inherent in the
design of our energy system.
We are not certain, however, of the cost of investment of the majority of the investments which are
to be made in order to transform our energy system. Hence it is less obvious that price certainty is a
good thing in the second regard which is observing the true cost of investment in low-carbon energy
systems.
If we are uncertain as to the NPV of an investment then we can set a certain price at that certain
NPV and hence stimulate investment at the lowest deadweight cost to society, because we will not
be paying for future uncertainty or suffering delay in investment due to that uncertainty. However
in a world where we are not certain as to the true investment cost then we must establish a system
that has inherent price uncertainty in order to discover the price at which people will invest. We
will, as a consequence of this, suffer information costs, because that price discovery is not going to
be free.
This is another fundamental failing of the environmental movement and that is its inherent aversion
to anyone making a profit, or heaven-forbid, a super-profit.
Well it is a simple fact of the need to stimulate investment in things which have uncertain costs that
it will require the value of the investment to be above the NPV, because the information deficit
which is inherent in doing something new and hence of uncertain cost means that we have to pay
for the information resolution. Another example of the environmental policy community destroying
its very life-blood, information, is the constant attack on any environmental investment which
appears to be making profit above its NPV. This profit embodies the very information which the
environmental movement needs in order to manage the transition to the low-carbon economy.
Having said this, it is responsible policy-making to limit the level of uncertainty and hence
information cost (super-profit) in order to properly manage the limited resources we have to deal
with the transformation of the energy system. Hence we should look hard at the degree of
uncertainty we put into the systems which we design in order to discover the information as to the
cost of making economic agents invest.
This basically involves managing the ex-ante entropy of the information channel used to discover the
price of investment, and there is an inherent trade-off between designing a system which can
capture all low-probability outcomes and one which minimises the costs of obtaining that
information.
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As an aside, but an important aside, for the most part in these essays I have been describing
genuinely unknown costs of investment, rather than information asymmetries between investors
and policy-makers. There is a whole issue of information asymmetry in policy-making, of course, but
industry and the investment community have proven themselves to be pretty poor at predicting the
real cost of wind, solar, nuclear and various other forms of low-carbon investment over very recent
times and so I see the information deficit we face as being inherent rather than the product of
different levels of information between different actors in the market.
So, for instance, if you are a UK policy-maker then you can be pretty certain that in order to achieve
a high level of production of renewable energy in your energy system you are going to have to
harness offshore wind power at scale. The cost of offshore wind power is uncertain, but there are
some data points of relatively limited statistical relevance, but they exist all the same and (today) are
at the level of around £3m / MW of investment cost. Costs have been £1.5m / MW in the not too
distant past and there are people in the market saying costs could more than halve again, and there
are those who say they could need to be £4m / MW to make some of the deeper water applications
sufficiently attractive.
Given this (not particularly good) information and knowing that the higher the ex-ante entropy of
the incentive system then the greater the cost of observed information (in the form of investment
decisions) at all levels then as a UK policy-maker you probably would not devise an incentive scheme
that had the potential for the value of an offshore wind farm to be zero to £10m / MW. If the
system embodied uncertainty in this range then the cost of observing investment and hence the cost
of information would be very high, and, of course, the observed cost would be quite far from the
true NPV value, and hence there would be a high cost associated with a relatively low quality of
information.
If you fix it at £3m / MW however, given the relatively recent uncertainty in price then you stand a
high chance of being wrong, and hence seeing no investment or stimulating a large amount of
investment without the opportunity to observe any indication of the obviously truly lower cost.
Hopefully these essays have well and truly buried the idea of a single global carbon price as a
stimulant for large-scale investment in low-carbon energy generation, but just in case we can play
the argument through this example of offshore wind in the UK.
We have shown that for investment in entities incapable of the receipt of information then price
signals which change over the life of the asset simply create deadweight cost. Hence a carbon price
which is formed on an annual (or even more frequent) basis provides information which is only
creating deadweight in the investment in offshore wind in the UK.
Furthermore, a global carbon price has to have the ex-ante entropy required to capture the cost of
observing investment in every form of low-carbon investment in every country and in every carbonsaving technology throughout the world. Hence it has an inherent uncertainty, due to the high
potential information content, which would cause investments in UK offshore wind to suffer an
unnecessarily high cost of information given that we simply know that in the UK we have to harness
the offshore wind resource and that it has recently cost around £3m / MW (give or take a bit this is
around a €250 / tonne CO2e carbon price by the way for those who think I am mixing my units).
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This clearly makes no sense.
Instead, in such circumstances, it is better to implement a system which attempts to discover
investment cost, but then does not expose the investments in question to price volatility over their
lifetime.
The question then becomes: how can policy-makers discover investment cost?
We are in the fortunate position with most low-carbon investments, that they are inherently capital
intensive and hence most of the cost is incurred at the point of investment. This increases the
potential for ex-post regret on the part of the investor but it also means that policy for investment
cost discovery can be focussed on costs today, while retaining flexibility for the future.
The approaches taken to investment cost price discovery to date have been two-fold. Either people
have continued down the misguided route of relying on quantity-based instruments with high
inherent volatility and hence high information costs and they have observed only the highest
possible margin investments taking place; or they have adopted what a British person would call the
“suck it and see” approach.
So we know the first approach has failed. The second however has a varied history. In the case of
the feed-in tariff regimes of Europe, for instance, governments have tended to set a price which is
fixed over the life of the asset (hence getting the asset matching bit right) and then waited to see
what would happen. As the price is fixed, then one of two things happen, of course, either people
invest or they don’t. Now fortunately non-financial issues like local democracy’s effect on the
planning consent rate and the availability of grid connections have meant that in the cases where
investments have occurred the quantity has been constrained and hence the binary outcome has
not been too harmful.
However there are well-documented examples where setting price and seeing what happens has
lead to an excess of quantity over what policy-makers had intended (the situation in the Spanish
solar market being the best known example in the investment community94).
This is basically because, while systems that set price have many advantages in terms of asset
matching and the reduction of informational deadweight cost, there is no mechanism in a pricebased incentive for taking the market through some sort of clearing and settlement process. This
means that unlike a quantity-based market (such as a cap-and-trade or carbon pricing system) where
the market mechanism brings the whole market together regularly to determine a clearing price, a
price-based system can let quantity grow unconstrained, with little information flow to the policymaker (or anyone else). This means that in such price-based systems, quantity can get out of
control.
94
In 2008 the Spanish energy market saw some 2,000MW or more of investments in solar PV power stations
based on a price-certain tariff which was only ever intended to stimulate 300-400MW of investment. Given
the high cost of PV systems at that time, the 2008 Spanish solar investments are likely to rank amongst the
highest cost power generation that has ever or will ever be built on planet Earth. The reaction to this,
particularly given the general economic deterioration since 2008, has created no shortage of angst in the
relationship between Spanish policy-makers and the investment community.
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In many, but not all, cases the combination of a price-based system, with a “suck it and see”
approach, constrained inadvertently by other factors such as grid and planning, has lead to policymakers being able to reduce or increase the prices for future investments in line with the observed
success or otherwise of the current tariff level. The truth however, is that this has been ad-hoc and
certainly not part of a concerted strategy on the part of policy-makers to embody their observed
information in future policy-making. It is also true that a successful fixed price incentive system
simply tells the policy-maker that they can probably make the price a bit lower next time, but it does
not tell them by how much.
There are other approaches to the same problem, and some governments have created implicit or
explicit quantity criteria along-side their price-based systems. The implicit ones being often based
around a time limit which, when factors such as planning, grid and the availability of resources are
taken into account, defines a quantity limit. The UK’s Renewable Obligation system had the
potential to set a financial limit on the combination of price and quantity, but it was, in effect,
converted into a feed-in tariff relatively early in its life95.
What policy-makers have generally failed to do is to be explicit about their strategy for information
management within their incentive arrangements. Policies should be set to expose the required
range of information at an acceptable cost, and should then have the inherent flexibility to react to
that information in setting the next set of incentives.
For large-scale investments therefore the market is in reality defined by the interaction between
policy-makers and the agents of investment. There is a periodic exchange of information which it is
the policy-makers job to manage the cost of, but to be clear, it will have a cost which will show up as
super-profit for well-managed investments. In this exchange, it is the policy-maker who makes the
first move in setting a price, or a price range, defined by what is likely to be relatively poor quality
information (not to mention biased given where most of it will come from). The job of the policymaker is to make an intelligent observation of the effects of this shot in the dark and to harvest
better quality information on which to make a more considered (but never perfect) judgement as to
the parameters for investment incentives in the next phase. Any intelligent policy-maker is likely to
build inherent risk management into such a system in order to limit or credibly observe the quantity
of investment taking place under the price-based system.
The most important design consideration in this interaction is the creation and productive use of
information with respect to investment decisions, and to ensure that the investments which are
created can transmit their information into the energy market in such a way that allows for the
reduction of entropy of the overall energy system. The interaction between the agents of
investment and policy-makers should be aimed at reducing the entropy of that interaction over time
through the exchange of ever higher quality information.
95
In 2003 some bright spark suggested that the UK’s Renewable Obligation should be modified to give price
variability over a certain short period of investment (a “vintage”) and then this would be systematically
converted into a certain price for assets of that vintage, while the rules for the next vintage could be set on the
basis of the information received. Instead they basically turned it into a feed-in tariff without asset-matching
for the investments, and with regular pricing reviews, or about the worst of all worlds in other words. No-one
ever listens to him and he is not bitter. See (Temperton, 2003)
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One of the key aspects of this interaction is that the set of exchanges is initiated by policy-makers
making a wild stab in the dark in the pursuit of an overall climate change objective. This is the
inherent nature of markets, and is a key factor which is ignored by those who believe that we can
analyse our way to a solution to the climate change problem.
Markets tend not to tell you what to do. They tell you if what you are doing or what you have done
is good or not. The economic ecosystem rewards certain species of economic activity and causes
other to become extinct. If you like, the back-drop of the markets in which we operate is causing
our endeavours to be constantly observed and those that fit well in the current eco-system tend to
succeed and those that do not, do not. No inventor, innovator, entrepreneur or the like, ever really
does a rational analysis of the right thing to do before they do it: they simply believe in the right
course of action and, the good ones, react to, and adapt to, the interactions they have with the
wider economic ecosystem. However, despite all the money spent on analysing markets in the
world, the first act, is always a wild stab in the dark, based primarily on belief.
Hence if we are to transform our financial system such that it creates the signals which direct capital
to investments in the low-carbon and low-entropy energy system which we need for the future, we
also need to create a system which observes and rewards activities which contribute to the
development of that new energy system.
Such a system will be rich in information and will create mutually reinforcing communication
between the actors in the market (both governments and private economic agents). Such a system
will also help create the global collective action which is clearly required in order to deal with the
global collective action problem that is climate change.
We have seen how the information exchange between policy-makers and investors on large, capital
intensive projects can be created through the management of information, observation and
intelligent change in policy over time to reflect valuable information where it can viably be used. We
have also seen however that in this interaction no market really forms price; that is left to the
interactions of the policy-makers and the investment agents, and as such the ex-ante entropy is low
and the potential information content of the communication channel is similarly low. Inherently in
this exchange we have decided to make the compromise of a somewhat awkward system of market
settlement and observation based on quantity in a trade-off for the reduced costs of information
that comes with asset-matching and low ex-ante uncertainty for investors. We do this based on the
information the policy-maker has as to its physical investment options and its (imperfect) knowledge
of current investment costs.
While this is the right trade-off for specific cases, nothing in the above paragraph allows for
observation outside of the narrow communication channel of that policy interaction and nothing
allows for wider communication and economic interaction with those outside a specific country or
technology.
This is where quantity-based systems such as cap-and-trade systems are essential. All the things
which make such systems inherently bad at stimulating large-scale, capital-intensive investments in
low-carbon energy production make them an essential part of the overall eco-system of climate
change finance.
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Quantity-based systems, such as cap-and-trade, involve a wide range of countries and sectors and
hence have the potential to include a wide range of national and industrial solutions to mitigating
carbon emissions. Their scope makes them inherently uncertain as to price ex-ante and their
settlement on a (say) annual basis, does not match the lifetime of any large-scale investment
project. However, in bringing together all the parties in the system and enforcing settlement at a
point in time such systems cause the creation of information on the progress of the transformation
of the energy system, and hence reduce the entropy for all observers.
Such schemes are the accounting systems of the low-carbon economy. It is only through the
provision of an economic incentive to produce high-quality and accurate information that we will
even begin to understand the real quantity and sources of emissions in the world economy. This is
the essential information basis from which we can start to target solutions and it quite simply does
not exist today. It will be created by the development of schemes which pay people to create that
information through the creation of economic benefit simply in the delivery of accurate information
at the time of settlement96. This is why in the majority of credits in such schemes are given away to
those who pollute in the first instance. This creates a cost to the consumer and a benefit to the
majority of those who pollute in the short-term, but in exchange for that economic rent, we receive
information as to the emissions of the polluter involved.
In the case of cap-and-trade systems in developed countries such as the EU ETS the development of
this information basis has been paid for substantially by the consumer via the mechanism described
above. In the case of the developing world, if we are to create the information basis which we so
desperately need, then it is likely to be the case that the developed world consumer or taxpayer will
also pay for the establishment of that information set (as they do in part through the CDM at the
moment).
This brings us again to some truths which the environmental sector simply has to get used to. We
have no idea how much people really pollute and we won’t unless we pay them for the information,
and the best way to achieve this is through carbon trading systems. This will mean that those who
currently pollute the atmosphere and create climate change will initially profit from the
development of the very schemes which we implement to attempt to avert dangerous climate
change. This is a simple consequence of such polluters holding the most valuable commodity we
need in that fight against climate change and that is information. To get that information we are
going to have to pay them. Monitoring, reporting and verification (the famous MRV beloved of
climate negotiators) is a consequence of participation in global carbon trading schemes, not a prerequisite for joining. If it is a prerequisite we will simply never establish a scheme with sufficiently
rich information content.
Carbon trading is the accounting systems of the planet and yes, there will be scandals, as there have
been in accounting systems for as long as they have existed, and which there certainly have been in
the development of carbon trading schemes in the developed countries in the world who have
implemented them to date.
96
This we could call the “pay the polluter” principle rather than the “polluter pays” principle. Think it will
catch on?
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This doesn’t matter97. It would matter if we were reliant on global carbon trading to stimulate
investment in large-scale, capital-intensive clean energy infrastructure, because then the volatility
which would be created by the scandals and mis-information would cause delay and unnecessary
excess return in such investments. However, as we have seen, we are not reliant on carbon trading
for those investments and we should not be.
Once we unshackle carbon pricing from the unrealistic expectation of providing a single global (or
even regional or national for that matter) investment signal to all clean energy investment then it is
able to do its real tasks so much more effectively.
Firstly, we want to use carbon trading to lay down the information basis of emissions in the world,
and as such we want it to be as broad a system as possible, encompassing as many countries and
industries as practical98 and settling on a regular basis. Hence we want as wide a communication
channel as possible and the highest possible state of ex-ante entropy in the system, which is a level
of uncertainty which is resolved to all observers at settlement of the market. It doesn’t matter if we
initially grandfather polluters’ rights to pollute, as we are not expecting this to be any major
incentive for them to invest in non-polluting technologies, and we know that information costs
money, and so if we don’t pay them somehow we simply won’t get the information. It also doesn’t
matter if the price of credits turns out to be low for the same reasons. In fact, we probably want the
price of credits to be low because there is no point in paying more than we have to, to those who
pollute, for information. This therefore means that we don’t really mind what the cap is to begin
with, we just care that there is one. We are also more concerned that people (countries and
industries) participate than that investments are created and hence the starting point for
participation in any scheme can be determined solely by the need to manage parties’ ex-post regret
at entering into such a scheme. Hence we should focus on getting the deal which brings the most
participation, as quickly as possible.
Secondly, carbon trading provides for some limited ex-post reward for those who do invest in low
carbon investments. This helps create an economic environment which rewards low-carbon actions
ex-post in a way that the general economic system tends to reward good ideas. This will send
something of a signal to economic agents that the economic environment is being tilted towards
rewarding those who take low-carbon actions. Ex-ante, of course, the uncertainty in the level of
carbon pricing will create delay for both polluting and non-polluting investments, as option value is
determined by volatility not NPV, and volatility is no respecter of sign. We should not however,
belittle the impact of ex-post reward in a world where the major actions on climate change will need
to begin as wild stabs into the informational darkness.
Thirdly, carbon trading has a major role to play in the facilitation of collective action. Such schemes
allow for the regular exchange of information between economic agents through trading and
between economic agents and governments through both trading and the regular settlement
process. That information allows the mutual observation of action and the costs of action with
respect to climate change mitigation in different countries and difference sectors. In order to
achieve a phase transition in the global energy system we need all parties in the energy system to
97
OK, it matters, in the specific case, but not at a macro level. No-one suggests that we all stop doing audits of
companies because that might lead to accounting scandals in the future.
98
Transaction costs (real transaction costs not information costs) probably limit the realistic coverage.
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experience mutually reinforcing economic exchanges with each other which will build up to a
transformation of the energy economy globally.
So we can see that where specific national actions are logical and reasonably well defined then that
information exchange is best managed based on a price-based system between policy-makers and
investment agents.
However, this means countries and industries taking individual actions in the absence of knowledge
of what others are doing, which is unlikely to lead to continued action as it does not pay to be too
much of a leader when the problem is global in nature. Hence we need the constant reassurance
and reward that comes with a regularly settled system of trading, not focussed on stimulating
investment, but through which we observe and experience what others are doing and hence
hopefully receive mutually reinforcing information which encourages continued and robust
individual action.
This is what makes the US position on cap-and-trade schemes a bit baffling. Subject to a bit of porkbarrelling which is just part of the rough and tumble of politics, the US appears to get the whole
individual action thing. However, they seem to be completely against being part of a scheme which
would provide them with all the information they need on what others are doing and what is
happening across their own economy. Particularly given that many of the wild stabs into the
informational darkness come from the state level, it seems bizarre that the US wouldn’t want to
implement an over-arching information system and hence create the eco-system to which such
individual actions should adapt, and with it create the national and international information basis
for understanding the continued logic and effect of individual action. Surely real commercial trades
with the Chinese would provide much better quality information than a bunch of reports filtered
through a UN bureaucracy.
You can take a horse to water….. but anyway.
A transition to the low-carbon, low-entropy economy looks like a system of individual actions,
moderated by ever higher quality information, within an international economic eco-system of
carbon trading that provides mutually reinforcing information on the action of others and that holds
all concerned regularly to account.
This is all very well, but nowhere so far have we addressed who actually pays for all this
transformation of the energy system, particularly as we have realised that it is a thermodynamic fact
that a low-carbon, low-entropy energy system will be more expensive than the hydrocarbon one
which we have today.
Paying for the transformation has become an ever more contentious issue in the global climate
change debate. At the time of the Kyoto Protocol there was a relatively clear principle that it was a
rich country issue to solve the climate change problem and it was clearly unethical to expect the
poor to pay. In the complex international debate on climate politics, two things have become
abundantly clear about the poor of the world. The first is that a lot of them won’t be poor by the
time we need to do a lot of the climate mitigation in their countries or more importantly by the time
they start to benefit from the sacrifices of today’s generation in solving the problem. Secondly,
there are simply rather a lot of them. Hence it seems relatively unlikely that, whatever the historical
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moral imperatives, the rich of the world are going pay for a low-carbon, low-entropy energy system
for 9 billion people by the middle of this century.
The good news is we don’t have to. Believe it or not, the good news is that this is a collective action
problem.
What matters to the developing economies of the world is their competitive position and hence if
everyone moves to a low-carbon, low-entropy energy system then, one could argue, that nothing
has changed very much. Hence in the same way that such countries are going to manage to maintain
or adapt their competitiveness while having greater degrees of human rights, more workers’ rights,
less child labour, the greater empowerment of women, and all the other things that we seem to
have while we still struggle on in the West, they will also be able to maintain and adapt in a world
where they have a low-carbon and low-entropy energy system.
Getting there requires three things.
Firstly, it is clear that the only people who are going to pay for it in the developed world are the
developed world and so we may as well just get on with it.
Secondly there needs to be the information technology capable of creating a low-entropy energy
system from a low-carbon energy system. As noted previously, I am not sure that clean energy is
any more expensive than dirty energy, but it is clear to me that the low-entropy state of
hydrocarbons explains their dominance in the world’s energy system today. Creating the
information systems required to manage a low-entropy energy system during the transition of the
western economies might well create a situation where information systems are available which
make it a close to straight fight between clean and dirty energy sources for the developing world and
in that case they have everything to gain from taking the clean option. Essentially if our
development of information systems is such that they are indeed a major substitute for capital then
we even the playing field for the rest of the world99.
This makes the debate on wind power intermittency in the UK for instance very interesting. Many
people will tell you that the system in the UK simply cannot deal with a third of its power coming
from wind. There are two counter-arguments. The first is that it simply has to, so get on with it.
The second is that when it does we will have cracked the secret code of the low-carbon, low-entropy
energy economy and other people in the world might find that useful. Hence my view is that wind
power intermittency on a large island in north-west Europe, while a challenge, is an immense
opportunity.
Thirdly, we need to create the information basis for emissions in the world. This means a global
system(s) of carbon trading which creates accountability, ex-post reward and mutually reinforcing
economic interactions on the part of actors all over the world in the energy market.
My contention is that the developed world as traditionally defined cannot and simply will not pay for
the development of a low-carbon and low-entropy energy system for 9 billion people. This I am
99
I appreciate that I am implying that such information systems cannot be developed in the developing world
faster than they can in the developed. Take this as just a part of the narrative. There is indeed a high chance
that supposedly developing world technologists will get there first. Please forgive my inability to reconcile
myself to the post-imperial order.
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afraid is another one of those slightly other worldly beliefs of the environmental movement, which
they would do well to forget because it makes the task at hand simply unachievable.
However I similarly contend that we can and should in our own self-interest pay for the three things
described above. Clearly, we have to transform our own energy system. In doing so we will develop
the information systems required to replace hydrocarbons with information (for that is what we are
doing). And, in order to bring the rest of the world with us we need to fill the informational void
which currently exits and as described above, we will need to pay people to bring them into that
information system. Information is expensive, but I believe that the developed world can afford to
pay for the development of that emissions information and accountability system as part of the
general economic eco-systems of the financing of the low-carbon and low-entropy economy.
So if the US position on cap-and-trade is baffling, the EU one is simply bizarre. The purpose of a
quantity-based trading system, as we have seen, is clearly not to stimulate highly capital intensive
investment, and clearly is to lay down an ever greater information and communication system for
the low-carbon economy. The EU is currently engaged in a policy to restrict the importation of
international credits and attempt to force up the carbon price. This shows a complete lack of
understanding of the purpose of the instrument, restricts the very communication channel to the
rest of the world that is so crucial to mobilising collective action, and runs the risk of significant and
unnecessary deadweight costs in the EU economy.
The three actions we have described here in effect embody leadership, information technology
development, and economic information development through markets.
What is interesting is that the last two actions are analogous and could only have become possible in
recent times. The development of the information systems which can instantaneously maintain a
low state of entropy of an energy system satisfying human wants and needs in space and time but
based on high-entropy energy capture is analogous to the economic system which causes our state
of entropy with respect to the knowledge of emissions of greenhouse gases (and hence entropy)
into our planetary systems to be reduced on a periodic basis through trading and eventual
settlement.
Hence we are in the business of developing two analogous information systems of a type and
complexity which could not have been contemplated until recent times, simply because the
underlying information technologies which will be required for both did not exist. It is only over
perhaps the last decade or so that we could have realistically contemplated either.
As we look to risk manage the existence of humans on Earth this latter observation raises some
interesting issues. Many of us who operate in the climate change arena feel, probably rightly, that
action on mitigating emissions is far too slow and we fear that what we observe in the planet’s
systems today does not even begin to tell us the damage that we have already wrought in those
systems. However, it is true that the explosion of technological development and the imposition of
human order on the planet which began only those 250 years ago with the beginnings of the
harnessing of low-entropy hydrocarbon energy, has lead to a point today where only now can we
begin to contemplate the technological and economic information systems required to wean
ourselves off of the very hydrocarbons to which we owe so much of the current state of our
existence.
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Are we then in a self-defeating race to maintain the entropy level of our existence?
The question is, is it possible for an advanced species such as the human race to develop the
technological and economic ability to sustain itself on a planet like Earth? Can we become
sufficiently advanced in those technological and economic systems such that we can preserve and
enhance human dominated order on the planet before we have expelled too much disorder into the
wider planetary systems? Or will we fail? Will we overrun the budget accidentally left for us in prehistoric times? In so doing we would expel so much disorder into the planet’s non-human systems
that we will not have the capacity to maintain and enhance the current level of human existence
against the forces which the planet’s systems unleash upon us.
Without hydrocarbons we would not have been able to create the order in human existence and the
capacity for greater human enrichment that we have, but we only have a certain budget for
increasing the entropy of the planet’s other systems before all the resources at human disposal will
not be able to maintain our version of order against the associated disorder which it created.
We have seen that in the absence of high quality information the first act is always a stab in the
dark, and in the case of climate change we know that there is a high probability that observable
effects lag cause by quite some time, and hence when we receive definitive information it may
already be too late. There is no archaeological evidence that advanced species have imposed
themselves on the planet before in the history of Earth, and we have not yet communicated with or
experienced other planets with such advanced species, and hence we have little experience to learn
from. Our attempts therefore to maintain order in our systems on our planet are a first-of-a-kind
effort, with all the informational issues which come with that. It may be that our few hundred years
of extreme colonisation of the planet do little more than leave a legacy from which the next
advanced species to evolve, in say a billion years, can learn as they attempt to dominate the planet
in a similar way.
If we are to learn fast enough to maintain order against the powers of the planet, then it is for the
environmental movement, in all its forms, to seek to increase the power of the information in the
world’s energy systems, even if that means confronting some difficult facts including that
information is costly, and often transmitted in the form of a profitable decision.
It is information which will allow us to transform our energy systems to deliver low-carbon and lowentropy energy for our use and convenience. This will require a transformation in our financial
system to reward, account and communicate in ways which direct capital to investments in that lowcarbon and low-entropy system.
It is also then information which, in place of low-entropy hydrocarbons, will allow us to maintain and
expand the transformation of the Earth which we are in the process of executing, without creating
forces in the planets other systems which we cannot resist.
For a while longer, at least.
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Mathematical Appendix
Mathematical Appendix
This Appendix includes a number of examples of mathematical proof and embellishment of the
statements in the six main essays. In this way I hope I have kept the essays themselves accessible
and readable; however I do feel that some mathematical rigour is a good thing in justifying some of
the work, and to prove the generality of some of the issues which are, at best, proved only by
example in the main text.
I will draw from Hull100 and Dixit and Pindyck101 as well as over a decade of being a student and
practitioner of derivatives. These two texts are definitely the best works you will find on the
derivative concepts explored in these essays.
I will attempt to make this readable by showing as much working as my fingertips will allow and
attempting to explain why certain things are happening. If you can just about remember how to read
calculus notation then you will be alright, I would say.
General Options Formulation
All the investment decisions we have looked at in these essays have been able to be viewed as call
options (i.e. rights but not obligations to invest) with the underlying asset being the project itself
(say a wind farm or a solar farm or a new piece of insulation) with this underlying asset often having
environmentally or policy related cash flows.
In general such options are American in nature in that the holder of the right to invest can do so at
any time up until the point of expiry of the option, as opposed to a European option where exercise
can only occur at the point of expiry of the option. You will note that such investment options often
have very few things which actually force exercise, and hence a number of our American options to
invest can be considered to have close to infinite lives.
Back to basic option valuation. Let us assume for a moment that the underlying asset on which we
hold an option to invest does not throw off cash flows (i.e. if it were a stock it would not be paying a
dividend). I appreciate that this is a situation that cannot be assumed forever if the asset is to have
the value ascribed to it today, but let me have the assumption anyway.
Let us also assume that the option to invest expires at time T in the future (say the lease with the
farmer to build a wind farm among his grazing sheep expires at time T and he won’t renew it as a
supermarket has offered him a better deal to build a shopping centre).
Assume that the cost of the investment (the capital cost) is I and the value of the underlying asset V
(the wind farm say) is defined by V0 at this point in time.
The options is clearly worth
100
101
See (Hull, 2003)
See (Dixit & Pindyck, 1994)
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And at the time of expiry the options will be worth
Now assume that I hold the above investment option and I borrow an amount of money equal to the
investment cost at time T, the expiry of the option.
This cash is equal to
Where rf in this case is the risk free rate of return.102 My portfolio of cash and option is therefore
worth the following at any time t.
And hence at expiry it is worth,
As at expiry of the option t=T.
Now if we also hold an investment in the underlying project or asset then that has a value Vt and
hence at expiry of the option it must be true that,
As the left hand side (LHS) of the above is either VT or a number bigger than VT. If this is true at
expiry then it must always be true that the option plus the borrowing is worth more than the
underlying asset.
If we denote the value of the investment option as Ft
i.e.
then the above becomes
102
In general if you are compounding or discounting in continuous time then the value being compounded or
discounted is multiplied by e to the power of the continuously discounted (compounded) discount rate times
by the time. There will be a lot of this in the coming pages.
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And hence
Given that if we exercise the option early we obtain only Vt-I then we can see that it can never make
sense to exercise an American option on an underlying asset that does not pay a dividend before
expiry as,
We can re-write the option value Ft above as
And then we have two of the terms of option value described in Essay Three. The first term on the
right hand side (RHS) of the above equation is the “Intrinsic Value” of the option at any time, and the
second term on the RHS is the “Time Value of Delay” or in other words the dis-benefit in exercising
an option early and hence incurring the exercise cost(investment cost) earlier than is strictly
necessary.
If we now introduce a cash flow or dividend D which is available to the option holder if they exercise
and hence convert the option into the underlying asset, but not if they leave the option unexercised
then we can show two different values for the option.
If the option remains unexercised then,
But if the option is exercised then
And hence we can no longer say which of the two is the greater given that we do not know the value
of D.
Hence we have the third component of option value which we described in Essay Three. The “Real
Cost of Delay” is basically the dividends (D) foregone by not exercising the option.
The “Information Value of Delay” is the final part of the option value which we described in Essay
Three which is related to the uncertainty of future events or the value of waiting to receive
information in the future.
Thus we have the expression for option value used in Essay Three and in all the NewClear
investment examples.
Option Value = Intrinsic Value (Vt-I) + Time Value of Delay (I-Ie-rf(T-t)) + Real Cost Of Delay (D) +
Information Value of Delay
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Intrinsic Value can be positive or negative, but is basically the representation of the net present
value (NPV) of the underlying investment and hence classical investment theory states that you
would invest when the intrinsic value of the options is zero or more.
Time Value of Delay will always be a benefit of delay and hence an incentive not to exercise the
option.
Dividends foregone will always create a cost of delay and hence an incentive to exercise the option.
Hence for an NPV neutral investment with no future uncertainty or information value, the exercise
decision is a battle between the Time Value of Delay and the Dividend cost of delay.
Information Value is always positive as if we delay the investment decision in order to get new
information then we will invest only of it makes sense to do so based on that information and we
will discard the option in the event that it makes no sense to invest.
Hence for an NPV neutral investment the investment decision is a fight between the Information and
Time Value of delay and the Dividend benefit of immediate investment.
Mathematically it is easy to see why information value is always positive. If we have an option F
which is a function of an underlying variable V (the value of the underlying investment) then the
option is F(V). If in the future we will only act on outcomes of V which make the option a positive
investment and we will discard the states where exercise is not rational then we can see that.
The LHS of the above states the expected value of the function of V assuming that we only therefore
exercise in rational states, whereas the RHS takes all the expected states of V and then applies the
function F to their expectation hence implicitly retaining the value of those future states of V where
you would not rationally exercise the option.
This is the embodiment of the idea in Essay Three that there are some future states of the market
where you would not make the NewClear investment decision.
The above equation is called Jensen’s Inequality and it holds for all convex functions of V which are
functions where the outside of the curve of the function faces the V axis when F(V) is plotted against
V. Those familiar with call options will know that that is exactly what a graph of a call option looks
like.
Stochastic Calculus
Now we could leave it there as all of the above is general and robust and we have seen that we can
apply it quite nicely to specific examples as we have in Essay Three.
However we have not been able to come to a mathematical treatment of the uncertainty which
embodies the known potential for the arrival of future information and that seems quite
unsatisfactory to those of a mathematical mind. If we are to do this then we need to be able to use
something called stochastic calculus which is basically a set of tools which allows us to solve
equations based on assumptions about future events which we define to be random.
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This is where we encounter a major frustration of mine in the texts on derivatives. Generally, in my
view, they all fail to explain the distinct between the three main elements of any derivative analysis.
The first is the properties of the derivatives themselves which are completely general and for
American call options, well defined above.
The second is the assumptions made about how the world works. We will come back to this, but by
way of example, the famous Black-Scholes-Merton formula for option valuation relies on the
assumption that we can constantly and costlessly trade the underlying asset in infinitely divisible
units. In real life you can’t do this.
The third is that you need to make an assumption as to how your variables behave in the future.
Even if they are random, you have to define that randomness in some mathematical form. From the
moment such an assumption is made the results obtained apply solely to variables which behave in
the defined way, and hence results lose generality.
These last two sets of assumptions and the inconvenience those beloved of the elegant solutions
often provided by derivatives find in them, are the reasons they are so often ignored and, in my
view, the reason for the mass misapplication of derivatives in the real world.
Stochastic calculus is going to allow us to do the third of the above: make assumptions about the
behaviour of our underlying asset (the wind farm or solar farm) value in the future in a way that we
can manipulate mathematically.
Weiner Process
So, to be clear, Weiner processes are just assumptions about how we think things may behave. Said
assumption may or may not be true and as soon as we have introduced the assumption into our
equations the answers are only fully true if that assumption holds.
Now to Weiner processes.
If you get into derivatives, investment under uncertainty, and information theory then you will
notice that some of the same people appear in the history of the mathematics of all of them and
Weiner is one of these. Given how tightly we have seen the concepts relate to each other in this set
of essays it should come as no surprise that there are a lot of commonalities in their mathematical
underpinnings.
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A Weiner process is an assumption as to how a variable behaves in time and has four main
properties:




It is stochastic, which means that it is at least in part random (yes that is all that being
stochastic means);
It has a Markov property, and that says that the next value of the variable is only a function
of the current state and not any prior state or value of the variable (yes you can be famous
for simply making up an assumption, well done Markov);
It is independent in time, and that means that each change is independent of the last
change;
The changes in the variable over a finite period of time are normally distributed with a
variance that grows linearly with time.
Normal distributions are the bell shaped distributions which are defined in full by their mean and
variance (or standard deviation which is the square root of the variance). It is this last property
which causes all the issues.
Mathematically the Weiner process is defined as:
Where a(V,t) and b(V,t) are functions in V and t to be defined (V being a variable which will be the
value of our underlying asset for most of our examples and t being time). a(V,t) is the part that
defines the deterministic changes (growth) in V with time and b(V,t) is what determines the form of
randomness.
Now dz is defined as:
Where
t
is a normally distributed random variable with mean zero and a standard deviation of 1.
It is this function (dz) which causes all the trouble in stochastic calculus.
In our examples to come we will concern ourselves mainly with the most famous form of the Weiner
process which is that of geometric Brownian motion. This is a form of random distribution which is
most often used in derivative analysis and it has the property of the percentage changes in the
variable in question (V) being normally distributed and hence the variable itself (V) is actually
something called log-normally distributed.
The two basic advantages of geometric Brownian motion are that the value of V can never be less
than zero which is realistic for a number of economic applications (as a less than zero stock price
involves bankruptcy for instance) and that percentage changes are normally distributed which again
tends to fell more intuitive for economic variables. However, always remember that it is just an
assumption about how the world works not some deep truth.
The Weiner process for geometric Brownian motion is:
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A simple re-arrangement of this shows that the percentage changes in V are what are defined as
growing at a certain rate α and have a standard deviation of σ.
Ito’s Lemma
As noted above there is a problem in applying calculus to stochastic processes and that is related to
the square-root of time which appears in the Weiner process. Simply put, normally with calculus we
can allow things to head to zero and be left with only a few first order terms which we can then use
to solve the equations at hand. The square root screws this up and for a while this made dealing
with stochastic processes almost impossible.
However a very clever chap called Ito invented something called Ito’s Lemma which basically
provides the rule which allows calculus to be applied to stochastic processes.
He said that for any variable where:
And
Then for any function in V, F(V) then
Or by subbing
Into the above and ignoring any terms with dt2 or dzdt as they head off to zero fast than lower order
terms then it can also be expressed as:
Frankly, I would just believe the man if I were you. Most textbooks give what is referred to as a
“heuristic” derivation of Ito’s Lemma, which basically is their way of saying that they don’t
understand it either and that we should all just be thankful for Ito and get on with using his result.
Bellman Optimality
Now we have some mathematical tools at our disposal then we can get back to option theory.
First, let’s look closely at the process that we went through in Essay Three to assess our NewClear
investment options. Basically, we assessed whether to invest today, or whether, based on our
uncertain knowledge of the future, it was better to wait and exercise the investment option in the
next period, when that information became available.
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Keeping the same nomenclature that we have used to date we can write this down mathematically
as:
Where r is the relevant cost of capital.
The above basically says that an option to invest is worth the maximum of the value of exercise
today (the first term in the max() function above) and the discounted expected value today of the
value of the option in one period’s time (second term in the max() function above). Note the
expectation today is an important part of it as all of the decisions have to be assessed today, based
on, if they are in the future, our expectations of that future.
We can express the above more generally for a small time period Δt as:
Now the first term is the value of exercise at time t and the second term is the discounted value of
the expectation at time t of the value of the option to invest a fraction later in time at t+Δt.
Re-arranging the above we get:
And then
If we let Δt tend to zero then
(the term after (Vt-I) went away because as dt tends to zero it became equal to 1).
As (Vt-I) is the value of the exercised option then we know that it is less than or equal to the value of
the unexercised option and hence we can remove the first term from the max() function above as
we know it will be zero or negative and we know that the LHS of the above cannot be negative.
Hence we have:
Or
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This is known as Bellman’s Optimality condition and after all that maths if you look at it, it simply
states the obvious and that is that the return to holding an option over a short period (the LHS of the
above) must equal the rate of change in the expected value of that option over the same short
period (the RHS of the above).
Deriving the equation for the value of the option to invest
We are now a mathematical hop, skip and a jump away from the equation to define the value of our
option F(V) to invest in the underlying asset on which we have that option V.
If we assume that V obeys geometric Brownian motion (this being simply an assumption, nothing
else), then:
Then given Bellman Optimality:
Our first job is to find Et(dFt) which we do using Ito’s Lemma:
As F(V) is a function of only V and not t then the first term on the RHS above is zero and we can sub
in dV from our geometric Brownian motion equation in V into the second two terms on the RHS and
this gives:
Expanding the squared term on the RHS and ignoring all terms that are dt2 or dzdt (because only the
term in dz2 will survive the calculus race to zero as that is of order dt) then,
Remember that we need Et(dF) not just dF and taking the expectation of the three terms on the RHS
above eliminates the second one as E(dz) = 0 as it is a normal distribution which is defined to have
an expectation (mean) of zero. The other two terms on the RHS are their expectation and hence we
can equate them to the Bellman Optimality formula as below.
(note that we have cancelled out the dt that appeared in every term on both sides)
Re-arranging we get:
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In order to help with some maths in a moment we will also sub into the above α=r-δ where δ is the
dividend yield on the underlying asset V and hence by definition the dividend yield (δ) plus the
capital growth in V (α) must equal the overall return r. So r=α+δ or α=r-δ.
Note that I have dropped all the t subscripts. This is for no reason other than to stop cluttering up
the equations and they are all evaluated at t now anyway and so they are superfluous.
Now the above is a second order differential equation in F which is the function of the value of the
investment option in V the underlying asset over which we have said option. In order to solve such
an equation we will need some boundary conditions. These are:
The first of these says that if the underlying asset is worthless then the option on it is worthless.
Seems fair enough.
The second says that at the critical point Vex which is the value of V at which the option will be
exercised that the value of the option must be equal to the exercise value Vex-I. This is therefore a
statement of fact.
The third condition says that at this optimum investment value of Vex when the option will be
exercised then the gradient of the graph of F(V) versus V will be at 45 degrees (gradient equal to 1)
and this is therefore tangential to the line of exercise of the option. This is a simple function of the
fact that if this is not the case then the F(V) versus V line would be crossing the line of exercise (45
degree line) and hence must be on its way to a more optimal exercise location.
Now, believe it or not, the way you solve a second order differential equation of the above sort is to
guess the answer and see if it works.
So let’s try the following as a wild stab in the dark:
Where A and β are both constants that we are about to try and find.
Checking first against our three boundary conditions.
F(0) is zero and so that is satisfied.
Given that:
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Subbing the above into the other two boundary conditions we get:
Dividing the two equations by one another and re-arranging we get:
This is very exciting as this defines the ratio of the actual value of the underlying asset at the point of
exercise of the investment option (Vex) to the actual investment cost (I). This equation hence shows
the premium which Vex has over I based on the value of β.
We can see from the above that as β approaches 1 then the ratio of asset value to investment cost
tends to being infinite, and as β tends to infinity then the ratio tends to 1 which is what classical NPV
analysis would tell you ought to be the answer.
Hence this ratio tells us the premium we have to pay over the actual investment cost in order to
cause the option to be exercised and hence in order to observe investment. It therefore also tells us
the implied cost of any uncertainty in terms of the premium over actual investment cost (superprofit).
Now let’s try to find A. Re-arranging the equation:
Gives
And subbing in for Vex and re-arranging we get:
And then we can actually solve the differential equation that we spent so long deriving. To make it
easy we can find the various derivatives and hence they can be directly subbed in. These are:
And can be subbed into
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Giving
All the As and all the Vs cancel in the above to leave us with:
Which can be re-arranged to the quadratic form of:
Or by dividing through by σ2
This is a quadratic equation of the form which has the general solution:
Where:
And from the above:
And therefore:
As we know that β>1 then only the solution with the positive sign satisfies the conditions and so:
Where β1 denotes the positive root of the quadratic equation discussed above.
So now we have a complete set of equations for the value of the investment option assuming that
the underlying asset V obeys geometric Brownian motion in its value.
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To summarise:
Where
And
And hence most importantly we have:
Greed and Fear
We can now look at the fundamental relationship between uncertainty (fear) and hence the future
information which we know may arrive, and dividend yield (greed) the value that we forego today if
we retain the option to invest .
We shall do this by looking at how β1 changes with σ, r and δ. Remember that as β1 tends to 1 then
Vex tends to infinity, and as β1 tends to infinity Vex tends to the classic NPV solution of being equal to
the investment cost.
Fear first, so let’s look at how β1 behaves with σ (the volatility or standard deviation of the
percentage change in V in the future).
Reminding ourselves that
Then as σ tends to infinity then β1 tends to 1 and Vex tends to infinity (in the above equation all the
terms divided by σ2 go to zero, leaving ½ plus the ½ from inside the square-root sign which is
squared and square-rooted and hence becomes a ½ plus ½ equals 1).
This tells us that if volatility is very large and hence there is a large amount of ex-ante entropy and
hence a very wide range of future information which might arrive then the value required to induce
exercise and hence investment and observation of investment is very high compared to the actual
investment cost.
Similarly as σ tends to zero then β1 tends to infinity and the reverse of the above is true. Hence with
no future information uncertainty then the value of investment required to incentivise and observe
investment tends to the true investment cost.
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To complete the analysis we can look at the rate of change of β1 with σ. Taking the quadratic
equation in β we had before and setting it equal to Q.
Now we know that β1 is the root of the quadratic and hence at that point Q equals zero. Therefore
any change in Q due to a change in σ must be balanced by a change in β when the changes are
evaluated at β1.
Hence differentiating completely to maintain this condition, we have:
We know that
is positive if evaluated at β1 because of the basic properties of Q but we can prove
it as below.
As β1>1 and (r-δ)>0 then the above must be positive.
Similarly differentiating we get:
Which again is positive as β1>1
This therefore tells us that:
Hence as σ increases then β1 decreases and hence we see that as volatility increases the value of Vex
increases and the cost of resolving today the information embodied in that highly volatile future also
increases.
Now we can look at greed in exactly the same way by looking at how β1 varies with δ the dividend
yield which is foregone in the event that option exercise does not occur.
For these purposes we will assume that the dividend yield (δ) ranges between zero and the cost of
capital r.
If we assume that δ=0 then
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Which after a bit of algebra gives β1 = 1 and hence Vex tends to infinity. This is what we would
expect. Without any dividend yield to harvest there is no incentive to invest and the value of the
asset would therefore need to be infinite to cause exercise over delay.
If we assume that δ=r then we have:
Which is not as elegant as most of our other results as β1 is still a function of r and σ still. However
this is actually quite an interesting result. Most investments in irreversible and inflexible clean
energy generation are likely to be wasting assets, in that their inflexibility gives them a finite life and
hence they will tend to amortise over that life in a way which means that the dividend yield is likely
to be close to the cost of capital.
If we now take the above equation and re-arrange it we get:
Using this equation we can see that for a wasting asset where r=δ, and where say, we as policymakers are only prepared to allow a certain premium to investment cost which is defined indirectly
by β1, then we can calculate the σ which defines the volatility in the support regime consistent with
that β1 and hence it tells us the degree of range of prices (at a given time horizon in the future)
which we might be able to detect with a policy which restrict profits over investment cost to a
certain level.
Another way of looking at it is that the first equation in β1 defines the level of super-profit which
policy-makers would be required to live with given that they have designed a pricing mechanism
which gives asset return volatility of σ.
In this way we in effect define the relationship between greed and fear, and between the policymakers tolerance for super-profits and their need for price discovery.
Leaving the limits and differentiating Q totally as we did before we get:
We know that
is positive at β1.
And hence we know this to be less than zero, and hence
must be positive and hence as we would
expect, as δ increases, β1 increases and Vex decreases hence reducing the cost of incentivising and
observing investment decisions in the presence of uncertainty.
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Finally we can take a quick look at the relationship between β1 and r, the cost of capital.
We know that
is positive at β1 and
Which as β1 >1 therefore is also greater than zero and hence
Hence if r increases the β1 decreases and Vex increases and hence the higher the cost of capital the
greater the incentive for delay.
Other models
So we have seen that given Bellman Optimality and a defined random process for the underlying
asset, option analysis is simply a matter of whether there exist friendly analytical solutions and if
they do exist whether the user has the patience to find them.
As I have noted several times, we could have stopped at the end of the simple derivation of option
formulae as all we have done since is to use an assumption as to how the underlying asset’s value
will evolve in order to be able to quantify and value trade-offs in a seemingly more precise way.
That precision however is only as good as the underlying model for the behaviour of the value of the
asset.
Feel free to run the sums for Weiner or other processes that better reflect the behaviour of
environmental asset classes (probably some mean reversion and Poisson jumps are in order), but do
be aware that the maths gets pretty tough pretty quickly. See the Bibliography for examples by
others.
Alternative derivation based on contingent claims
And actually it is worse than all that as there has been an assumption hidden away in the above
analysis which is clearly wrong. That is the assumption as to the discount rate (r). If you go right
back to the definition of Bellman Optimality we used r to discount the value of the option in the next
period back to today. This means that our use of r infects everything we just did.
The fact is that actually r is a variable, if we are to do all of the above correctly, and ever more scarily
it is a variable which depends on the value of the option itself. This is ignored in most option
analyses using the above methodology as it makes the maths much harder103.
The reason the cost of capital changes with the value of the option is that an option can always be
modelled as a combination of amount of the underlying asset and some borrowing. This, in fact is
how you tend to get taught option valuation in the first place and it is the first step in the derivation
103
See (McDonald & Siegel, 1986) for one of the few attempts I have ever seen at addressing this directly.
Note however, that once you have made the maths a lot more hair-raising you end up realising that you have
to believe the Capital Asset Pricing Model, which is fine, but it is another assumption buried under all this
lovely pure looking maths.
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of the famous Black-Scholes-Merton formula for option valuation. This means that any option can
be seen as a portfolio of some dynamic amount of the underlying asset and the associated
borrowing and so by portfolio theory the cost of capital changes as the composition of the portfolio
changes as it does with the value of the option.
There is no real getting around this (except doing it right, of course), the cost of capital in our above
analysis is an educated guess which is clearly wrong. All analyses have assumptions and short-cuts,
and hence this is fine, I think, and, in my view, most of the insights still apply, but it is another reason
why the mountains of analytical work on options that occurs in the world is a little frustrating.
It is possible to derive the same equations as we used before using a technique called contingent
claims analysis. This has the advantage that the analysis is done in a “risk neutral” space and hence
the discount factor which is used throughout is the risk-free rate and its application is correct and
constant throughout the analysis.
However there is a reason that this correct application of the risk-free discount rate can be applied
and that is because the whole space of potential current and future states of the assets are known
and can be traded costlessly and in any quantum.
For most real assets with which we are concerned it is clear that there are not liquid and wellformed markets in which assets can be seamlessly traded and hence it is impossible for our analysis
to exist in this much simpler risk neutral arena.
Hence there is a simple fact of option-based analysis for real and illiquid assets and that is that you
either have to assume a idealised world which does not exist, or you have to assume a cost of capital
which is clearly wrong. This does not make the analysis worthless. It simply makes it like all analysis:
based on its assumptions. This fundamental issue does however, I believe, sit at the heart of many
of the misapplications of options in the real world. Most people are so pleased to have been able to
apply Ito’s Lemma that they forget the fundamental assumptions on which their analysis is based
and most importantly on which it relies.
For good order we will now quickly derive the second order partial differential equation for the value
of the option to invest based on geometric Brownian motion using a contingent claims analysis and
illustrate the differences and similarities in the two approaches.
We first construct a portfolio of the option to invest and a short position in the amount of the
underlying asset sufficient to compensate for changes in the option value for small changes in the
value of the underlying asset.
This gives a portfolio equal to
Where the first term is the option and the second term is the ownership of the underlying with
commonly referred to as the delta of the option.
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Now over a short period of time dt the change in the value of the portfolio above is given by:
Where the three terms on the RHS above are the change in the value of the option; the change in
the value of the underlying asset held; and finally the cost of holding the underlying asset which is
equal to the dividend payments which would be paid to the original owner of the asset for which
you have to compensate them (we had to borrow it from someone in order to go short).
Assuming that the underlying obeys geometric Brownian motion and applying Ito’s Lemma:
Then
Cancelling out the common terms and taking dV2 = σ2V2dt then we have
Now the return to the portfolio over short time dt must equal,
Equating the two above and cancelling the dts, we get,
Collecting terms we get the familiar equation,
This is the same equation as we had in the previous analysis and hence it has all the same solutions.
However there is one difference and that is that this equation has the risk free rate where the other
has the assumed cost of capital. All the results of the rest of the analysis will be slightly different
depending on whether you assume you know the cost of capital or whether you assume that there is
a risk neutral space in which you can perform your hedging of your option portfolio.
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The Deterministic Case
Somewhat ironically after all that calculus, there is one case which we showed by example in Essay
Three which we have not provided the requisite analytical back-up for, and that is the case where
there is no randomness and the rate of change of the underlying asset value is known with certainty
through time.
This is relatively simple but it is important in that it shows the disincentive to be a first mover even in
the case where the future is certain.
Let’s define the investment opportunity as the option to invest at a time in the future (T) which
maximises the discounted expectation of value today, which is a very similar approach to that which
we have used throughout and which, for instance, got us to Bellman Optimality.
Hence say that,
Now let’s assume that we know the development of V with certainty and it is expressed as:
Hence,
Differentiating the contents of the max() function to find the optimum time and setting the
differential to zero gives us (where Tex is the time of optimum exercise),
And hence re-arranging the above, we have Tex as,
Hence this shows that even in the case of deterministic price behaviour there is a possibility of the
investment being delayed.
In order to achieve investment at T=0 then Tex = 0 and hence from the above (to make the natural log
equal to zero its contents much be equal to 1),
Hence again we see that even the deterministic case there is a premium to be paid over and above
the investment cost in the case where the value of the underlying asset is known to be rising.
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This reinforces the idea that early adoption in not obvious in the presence of perfect knowledge that
things will get better in the future.
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