Chapter 10: Risk
Management
Objective
Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley
•Risk and Financial Decision Making
•Conceptual Framework for Risk
Management
•Efficient Allocation of
1
Risk-Bearing
Chapter 10 Contents
• 10.1 What is Risk?
• 10.2 Risk and Economic Decisions
• 10.3 The Risk Management Process
• 10.4 The Three Dimensions of Risk Transfer
• 10.5 Risk Transfer and Economic Efficiency
• 10.6 Institutions for Risk Management
• 10.7 Portfolio Theory: Quantitative Analysis
for Optimal Risk Management
• 10.8 Probability Distributions of Returns
• 10.9 Standard Deviation as a Measure of Risk
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10.1 What is Risk?
• Uncertainty
– An unrealized event is uncertain for an
observer at a given time if he/she does not
know its outcome at that time
– I enter a sealed bid on a public contract
• The value of my bid is certain to me
• Before unsealing, my bid is uncertain to you
• After unsealing, my bid is known to you
3
Uncertainty that matters
• Risk is uncertainty that “matters” to the
observer
– You manage “The Intergalactic Herrings” and
have a choice between two contracts for the
concert hall
• 1 Pay the hall owner $2 for each ticket sold
• 2 Pay a specified lump-sum for the hall that
has a lower expected cost than (1)
4
Contractual Outcomes
• “Ticket sales” is the “risk that matters”
– While each fan may be certain about
attending or not attending, management is
not fully informed, and is at risk because
• if sales are in fact higher than N*, it pays
more if it selected choice 1
• if sales are in fact lower than N*, it pays
more if it selected choice 2
5
Strategies for Controlling Risk
• Herring’s management has several
strategies for reducing cost-uncertainty
– Do research to determine the number of fans
and the percentage of fans who will attend
– For a fee, obtain the right to select between
contract 1 and 2 at a later date
– Hedge with contracts to third parties, (radio
station, concessionaires, contractors, …)
6
Naming the Strategies:
Research
• The first strategy is purchasing
information by research
– There is a cost associated with collecting
information, but information enables one to
make better-informed decisions
– Information is often collected incrementally,
and a decision is made at each step whether
to continue collecting further information
7
Naming the Strategies:
Insurance or Option
• The second strategy entails purchasing
the right to make a choice before a
specified time
– Having the right take an action when
information becomes clearer can be valuable
– In this case, the option is the right to delay
selection of the exact contractual terms
• The obligation to rent the hall might be a
good quid pro quo for the
option
8
Naming the Strategies:
Hedging
• The third strategy creates secondary
contracts that reduce overall exposure to
the risk created by the primary contract
– A primary fixed-fee rental contract creates a
forward position in (unknown) future sales
– Herring may offset this risk by requiring its
concessionaires to enter into fixed rental fee
contracts rather than % of sales contracts
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What is Risk? Risk Aversion
• Herring’s ultimate contracting strategy
will depend upon its level of risk aversion
• Risk aversion
– A measure of an individual’s willingness to
pay for a reduction in exposure to risk
10
What is Risk? Upside-Down
• Herring has a choice of contracts, and
each has an upside and a downside,
depending on the variable that controls
the “risk that matters”
• Upside: favorable outcome
• Downside : unfavorable outcome
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What is Risk? Both Upside
and Downside
• Some risks are more complex. A
computer mother-board manufacturer
that
– underestimates demand will lose current
sales and market share
– overestimates demand will own an inventory
with a market price that is being eroded by
rapid technological obsolescence
• Any deviation is unfavorable
12
What is Risk? 20/20
Hindsight
• The appropriateness of a riskmanagement decision should be
determined using only the information
available when the decision was made
• We should avoid coloring our judgement
of a earlier decision with facts know after
the decision
• But ...
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What is Risk? Preserving your
Options
• But …
– a decision that preserves the ability to make
in-flight corrections (at a small cost) over
one that disposes of that ability characterizes
a well-made decision
– “Preserve your options”
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What is Risk? Knowing when
to Purchase Information
• But …
– a decision that was based on timely and
carefully purchased information characterizes
a well-made decision
• “Know when to buy a vowel”
15
What is Risk?
Tailor the Contract
• But …
– Risk reduction clauses may often be included
in a contract at very little cost when the
contract is written, but are expensive to add
as a contract amendment
– Develop a standard set of risk-related
clauses that may be incorporated into draft
contracts
• When negotiating, think in terms of both
expected costs and their associated risks
16
What is Risk? Looking Back
• But …
– Revisit risky decisions in the light of their
outcomes to improve future decision making
• This is not to praise lucky management nor
scold unlucky management
• Ask: “How could the infrastructure supporting
decision making be improved by preparing for
them in advance?” (e.g. Maintain current
data base of key variables)
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What is Risk? Risk Exposure
• If you face a particular kind of risk
because of the nature of your job,
business, or pattern of consumption you
have a particular risk exposure
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What is Risk? Risk-Controlling
Tools
• Many tool that may be used to reduce
risk may also be used to increase risk
– If you insure your house against fire, you are
reducing your risk (Hedger)
– If I insure your house against fire, I am
increasing my risk (Speculator)
• (Probably not an insurable risk:
– moral hazard
– lack of a legitimate economic purpose)
19
10.2 Risk and Economic
Decisions
• Risk exposure of households:
– Sickness, disability, & death risks
– Unemployment risk
– Consumer-durable asset risk
– Liability risk
– Financial asset risk
20
Risk exposure of firms
• Input/output channels
strike, boycott, embargo, war, safety, supply/ demand
• Loss of production facilities
fire, legislation, civil action, strike, nationalization, war
• Liability risk
customer, employee, community , environment
• Price risks
input, output, foreign exchange, interest
• Competitor risk
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technology, intellectual property,
economic
Government:
– Major calamities
• weather, forest fires, riots
– Guarantees
• exports, small business loans, mortgages, and
student loans, crop prices
– Interventions
• bank failures, strategic firm failures, crop
failures, medical coverage
22
10.3 The Risk Management
Process
• Risk identification
• Risk assessment
• Selection of risk-management techniques
• Implementation
• Review
23
Risk identification
• Some risks are commonly underidentified, and so are not hedged
– disability coverage is often too low
• Some risks that do not exist are ‘hedged’
– life insurance is often over-prescribed
• Some risks offset each other
– liability of a car within a fleet;
price/quantity
24
Risk assessment
• The quantification of the identified risks
– quantification of exposure to risk requires
specialized skills
• Actuaries
• Investment counselors
25
Selection of risk-management
techniques
• Risk avoidance
• Loss prevention and control
• Risk retention
• Risk transfer
26
Implementation
• Risk transfer requires finding a suitable
transfer vehicle at an acceptable price
– Obtain competitive quotations and look at
alternative ways to hedge
– Consider the mix of upside to downside risk
• Options shed downside risk, while
maintaining upside potential (at a price)
• Futures shed both down- and up-side risks
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Implementation
• Some risks may be shed only imperfectly
– A specialty rice grower may be able to lower
but not eliminate risk using cereal futures
– A seed grower may not be able to
significantly reduce price risk
28
Review
• Management of risk should be an
ongoing systematic activity because risk
exposure changes as people mature
• Maintaining flexibility will enable you to
react more appropriately to change
– Term life insurance with an annual renewable
term is more flexible than policies without
this clause
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10.4 The Three Dimensions of
Risk Transfer
• Hedging
• Insuring
• Diversifying
30
Hedging
• A risk is hedged when the action taken to
reduce adverse risk exposure also causes
the loss of unexpected gain
– A farmer who sells her crop before it is
harvested reduces the risk of lower prices
and lower yields, but surrenders the right to
increased prices and yields
– (Note: We sometimes use “hedge” to include “insure”)
31
Insuring
• Insuring is the payment of a premium to
avoid losses
• Insurance is not hedging because you
maintain ownership in the upside
potential
– A farmer has the right, but not the obligation
to sell soy to the government at a set price
32
Diversifying
• Diversification means holding similar
amounts of a risky asset instead of a
larger amount of a single risky asset
– I have identified 10 corporations that each
have an expected return m = 0.15, a
standard deviation s = 0.20, and are
correlated with each other with rho = 0.9
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Standard Deviations of Portfolios
0.20
Standare Deviation
0.19
s = 0.2000
0.18
s = 0.1421
0.17
0.16
0.15
0.14
0.13
0
1
2
3
4
5
6
Portfolio Size
s* = 0.1342
Theoretical Minimum
34
7
8
9
10
Observation
• Most of the diversification is obtained by
including just a few stock in the portfolio
• Risk can only be reduced to a fixed level
that depends on the correlation
• Progressively adding one more new stock
has a diminishing affect on risk
35
Equation for Homogeneous
Diversification with n Stocks
s
port
 s stock
1 nn  1


2
n
n
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10.5 Risk Transfer and
Economic Efficiency
• Institutional arrangements for transfer of
risk contribute to economic efficiency by
– allocating existing risks to those most willing
to bear them
– reallocation of resources to production and
consumption in accordance with the new
distribution of risk-bearing
37
10.6 Institutions for Risk
Management
• A complete market for allocating risk
would permit the separation of
productive activity and risk-bearing
– While technology is driving the risk marketplace towards completeness, this will not be
achieved because:
• transaction costs
• incentive costs
38
10.7 Portfolio Theory:
Quantitative Analysis for
Optimal Risk Management
• Portfolio theory
– quantitative analysis for optimal risk
management
• Portfolio theory selects from a set of (usually
divisible) risks by optimizing risk-return
• Consumption and risk preferences are
exogenous
• It is sometimes possible to devise a strategy
that reduces the risk of all contracting parties
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10.8 Probability Distributions
of Returns
• Assume that there are two stock
available, GENCO and RISCO, and each
responds to the state of the economy
according to the following table
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Returns on GENCO & RISCO
State of Return on Return on ProbEconomy RISCO
GENCO
ability
Strong
50%
30%
0.20
Normal
10%
10%
0.60
Weak
-30%
-10%
0.20
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•Probability Distributions of Returns of GENCO and RISCO
•0.6
•0.5
•0.4
•Probability •0.3
•0.2
•0.1
•0
•50%
•GENCO
•30%
•RISCO
•10%
•-10%
•Return
42
•-30%
Observation
• Both companies have the same expected
return, but there is considerably more
risk associated with RISCO
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10.9 Equations: Mean
m r  E r   P1r1  P2 r2  P3r3  ...Pn rn
 P r
n
  Pi ri
i 1
mr
 0.2  0.3  0.6  0.10  0.2  (0.10)
mr
 0.10  10%
GENCO
GENCO
Also :
mr
RISCO
 10%
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Equations: Standard Deviation

s r  E r  E r 2

 P1 r1  m r   P2 r2  m r   ...  Pn rn  m r 
2

n
2
2
 Pi ri  m r 
2
i 1
sr
 0.2  0.30  0.10  0.6  0.10  0.10  0.2  (0.10  0.10) 2
sr
 0.016  0.1265
2
GENCO
GENCO
2
Also :
sr
RISCO
 0.2530
45
Observation
• The expected returns of GENCO and
RISCO happen to be equal, but the
volatility, or standard deviation, of RISCO
is twice that of GENCO’s
• However, we would expect share prices
to follow a continuous distribution, rather
than the discrete distribution illustrated
46
Continuous Distributions
• A very common assumption is that the
returns of a stock are distributed
normally. Assume:
– NORMCO’s has an expected return of 10%
and a standard deviation of 0.1265
– VOLCO also has an expected return of 10%,
but has a standard deviation of 0.2530
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Distribution of Returns on Two Stocks
3.5
Probability Density
3.0
2.5
NORMCO
2.0
VOLCO
1.5
1.0
0.5
0.0
-100%
-50%
0%
Return
50%
48
100%
Two New Distributions of
Return
• The next slide shows another two
distributions of return that have been
superimposed
• They appear to have the same mean,
namely 10%, but ODDCO appears to
have a higher standard deviation than
VOLCO
49
Two More Return Densities.
1.8
1.6
Probability Density.
VOLCO
1.4
ODDCO
1.2
1.0
0.8
0.6
0.4
0.2
-100.00%
-50.00%
0.0
0.00%
50.00%
Return.
50
100.00%
Caveat
• The ODDCO distribution actually has no
mean nor standard deviation
• If you drew samples from the distribution
and computed these two statistics, you
would quickly discover that for n = 100,
200, et cetera, neither statistic converges
to a constant number
51
Caveat
• The distribution of ODDCO’s returns
follow a Cauchy Distribution
• The Cauchy and Normal distributions are
special cases of the Stable distribution
• Some researchers believe that stock
returns are not normal, but are drawn
from a stable distribution without a SD
52
Caveat
• As we progress, we will assume that
stock returns do have a mean and a
standard deviation, but this is a key
assumption
53
Another Caveat
• You should reconcile financial models
with common understanding
– The distribution we have proposed for
returns, the normal, theoretically takes
values from -infinity to +infinity
– Returns on the other hand may only be from
-100% to +infinity
– Theoretically, the normal distribution is at
odds with the facts
54
Another Caveat: Resolution
• The return that is distributed normally is
the annual return compounded
continuously, and this takes values
from -infinity to +infinity
• The annual rate compounded annually
has a minimum of -1, that compounded
semi-annually a minimum of -2, et cetera
55
Another Caveat: Resolution
• One of the useful features of standard
deviation is that it has the same
dimensions as its random variable
– The standard deviation used with the normal
distribution is then also an annual rate
compounded continuously
• (that is, if you are being a stickler for detail)
56
Yet Another Caveat
• Recall that in Chapter 4 we investigated a
stock that
– paid no dividends
– was currently trading at its purchase price
– yet had a significant average return!
• The wrong average caused this problem
57
Yet Another Caveat:
Resolution
• If we restrict ourselves to the annual rate
compounded continuously, then the
problem disappears, and the correct
average is the arithmetic mean of returns
58