Speculation and Risk Sharing with New Financial Assets
Alp Simsek
Harvard University
May 2012
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
1 / 22
Does …nancial innovation reduce risks?
Traditional view: Financial innovation helps diversify and share risks.
But new assets generate new uncertainties.
Belief disagreements and speculation come as by-product. Tends
to increase risks.
Example from recent crisis: Subprime CDOs and their CDSs.
This research: E¤ect of …nancial innovation on portfolio risks when
traders have both risk sharing and speculation motives.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Consider a risk sharing setting with belief disagreements
Standard risk sharing model with mean-variance preferences:
Background risks and …nancial assets.
New assumption: Belief disagreements about asset payo¤s.
Financial innovation = Expansion of assets.
Measure of portfolio risks:
Average variance = Uninsurable variance + Speculative variance.
Main result: Financial innovation always decreases uninsurable variance
and always increases speculative variance.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Important mechanism: Hedge-more/bet-more
Speculative variance increases through two channels:
1
New assets generate new disagreements.
2
New assets amplify speculation on existing disagreements
(hedge-more/bet-more).
New asset on which there is agreement increases speculative variance!
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Speculation and Risk Sharing
May 2012
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Is risk sharing a major factor in endogenous innovation?
Endogenous …nancial innovation: Both risk sharing and speculation
motives for trade generate innovation incentives.
1
With common beliefs, endogenous assets minimize the average
variance among all choices.
2
With large belief disagreements, endogenous assets maximize the
average variance among all choices.
Belief disagreements change the nature of endogenous …nancial innovation!
Calibration for national income markets of Ath-Shiller (AER, 2001):
Small belief disagreements su¢ cient for speculation to swamp risk sharing.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Outline of the talk
A simple example to illustrate the two channels.
The main result.
Brief discussion of welfare implications.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Consider a standard risk sharing setting
One consumption good (a dollar), two dates, f0; 1g.
Trader, i 2 I , has:
Endowment, e, at date 0.
Background risks: Random endowment, wi , at date 1.
Consumes only at date 1. Investment options:
Cash: Yields one dollar for dollar.
Risky assets, j 2 J, in …xed supply (zero).
Asset j pays aj dollars at date 1, and trades at price p j date 0.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Consider mean-variance preferences with het. priors
Trader i solves:
max Ei [ni ]
xi
s.t. ni =
i
2
vari [ni ] ,
e x0i p
| {z }
+ wi + x0i a.
investment in cash
Key assumption: Traders have heterogeneous prior beliefs.
Equilibrium: Prices, p, and allocations, fxi gi , such that traders optimize
P
and markets clear ( i xij = 0 for each j).
Next: Simple example.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Example: Traditional common-beliefs benchmark
Risks, v1 ; v2
N (0; 1), i.i.d. De…ne v = v1 + v2 .
Two traders with
1
=
and risks w1 = v and w2 =
2
v.
Benchmark: Common (and correct) beliefs.
Autarky: Net worths, n1 = e + v and n2 = e
Innovation: Asset with payo¤
a1
v.
= v introduced.
Trader 1’s position and net worth:
x11 =
1 and n1 = n2 = e.
With common beliefs, …nancial innovation reduces portfolio risks.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Channel 1: New assets generate new disagreements
Next consider the case with belief disagreements:
Traders’beliefs for v2 is as before. Belief for v1 :
Trader 1: N ("; 1) .
Trader 2: N ( "; 1) :
Parameter, ", captures the level of disagreement.
Trader 1’s position and net worth:
x11 =
1
|{z}
1
2
1
+
| {z }
"
+
risk sharing portfolio
n1
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speculative portfolio
" v1 + v2
= e+
.
1+ 2
Large belief disagreements, " >
increases risks.
,
1+
2
: Financial innovation
Speculation and Risk Sharing
May 2012
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Channel 2: New assets amplify existing disagreements
Next consider the introduction of a second asset:
Earlier single asset case:
x11 =
1+
"
1
.
2
|1 +
{z }
dampening
Additional asset with payo¤, a2 = v2 (agreement on payo¤).
Trader 1’s position and net worth:
"
"
x11 = 1 +
and x12 =
|{z}
| {z }
asset 1, betting
asset 2, hedging
"
n1 = e + v1 .
New asset with agreement increases portfolio risks.
Intuition: Hedge-more/bet-more (and risk more).
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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General environment
Risks: v = (v1 ; ::; vm )0 .
Net worths, wi , and asset payo¤s, aj , are linear combinations of v.
Assumption (A1). Traders’beliefs are given by fN ( vi ; v )gi .
=) They agree on variance of v. Might disagree on means.
Su¢ cient statistics:
N(
i:
i;
): trader’s belief for asset payo¤s.
common belief for covariance of wi and a.
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Characterization of equilibrium
Equilibrium portfolios: xi = xRi + xSi where:
xRi =
|
{z
1~
i
}
Risk sharing portfolio
Relative covariance:
and
xSi =
|
{z
1 ~i
}
Speculative portfolio
~i =
i
i
Relative optimism : ~i =
i
1 X
jI j
Speculation and Risk Sharing
^{ ,
^{2I
1 X
jI j
^{2I
Alp Simsek (Harvard University)
,
i
^{
^{ .
May 2012
13 / 22
Average variance and its decomposition
De…ne average variance of net worths:
=
1 X
jI j
i
vari (ni ) .
i 2I
Lemma: With common beliefs, P
the equilibrium portfolios minimize
subject to resource constraints, i xi = 0.
De…ne uninsurable variance,
R,
as the minimum possible
.
De…ne speculative variance as the residual:
=
R
|{z}
uninsurable variance
Alp Simsek (Harvard University)
S
+
|{z}
.
speculative variance
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May 2012
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Main result: Financial innovation increases spec. variance
Notation: Economy E J^ with assets J^
J.
Compare E (JO ) and E (JO [ JN ) (old and new assets).
Theorem (Financial Innovation and Portfolio Risks)
(i) Financial innovation always reduces the uninsurable variance:
R
(JO [ JN )
R
(JO ) .
(ii) Financial innovation always increases the speculative variance:
S
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(JO [ JN )
S
(JO ) .
Speculation and Risk Sharing
May 2012
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Intuition for the main result
Consider the economy with only speculation reason for trade.
Then, a textbook result applies:
S
i
|{z}
=
std. of speculative portfolio return
1
ie
|{z}
relative
i
SharpeiS
| {z }
.
Speculator’s Sharpe ratio
With more assets, SharpeiS increases through the two channels.
Thus, the speculative variance also increases.
Caveat: Equilibrium is Pareto e¢ cient. Should we be worried?
Alp Simsek (Harvard University)
Speculation and Risk Sharing
May 2012
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Based on a true story of famous economists
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They decide to take a side bet, at some cost
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They realize that this is Pareto optimal
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The end of the story is unknown
The increase in portfolio risks ~Destroyed pillow.
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Alternative welfare criterion: Belief-neutral ine¢ ciency
Suppose belief di¤erences come from behavioral distortions.
Practical problem: Which belief to use for welfare?
Solution by Brunnermeier, Simsek, Xiong (2012): Use all beliefs!
An allocation is belief-neutral ine¢ cient if it is ine¢ cient under any
convex combination of agents’beliefs.
Financial innovation is belief-neutral ine¢ cient when it increases
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Speculation and Risk Sharing
May 2012
.
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Conclusion
E¤ect of …nancial innovation on portfolio risks when traders have risk
sharing and speculation motive for trade.
Main result: Financial innovation increases speculative variance.
Important channel: Hedge-more/bet-more.
Endogenous innovation: Driven in part by belief disagreements.
Future work: Welfare e¤ects and policy implications.
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May 2012
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