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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. Tendsto increase risks.
Example from recent crisis: Subprime CDOs and their CDSs.
This research: E¤ect of �nancial innovation on portfolio risks whentraders have both risk sharing and speculation motives.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 2 / 22
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 varianceand always increases speculative variance.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 3 / 22
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!
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 4 / 22
Is risk sharing a major factor in endogenous innovation?
Endogenous �nancial innovation: Both risk sharing and speculationmotives for trade generate innovation incentives.
1 With common beliefs, endogenous assets minimize the averagevariance among all choices.
2 With large belief disagreements, endogenous assets maximize theaverage 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 5 / 22
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 6 / 22
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 pj date 0.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 7 / 22
Consider mean-variance preferences with het. priors
Trader i solves:
maxxi
Ei [ni ]��i2vari [ni ] ,
s.t. ni = e � x0ip| {z }investment in cash
+ wi + x0ia.
Key assumption: Traders have heterogeneous prior beliefs.
Equilibrium: Prices, p, and allocations, fxigi , such that traders optimizeand markets clear (
Pi xji = 0 for each j).
Next: Simple example.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 8 / 22
Example: Traditional common-beliefs benchmark
Risks, v1; v2 � N (0; 1), i.i.d. De�ne v = v1 + �v2.Two traders with �1 = �2 � � and risks w1 = v and w2 = �v .
Benchmark: Common (and correct) beliefs.
Autarky: Net worths, n1 = e + v and n2 = e � v .Innovation: Asset with payo¤ a1 = 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 9 / 22
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}risk sharing portfolio
+"
�
11+ �2| {z }
speculative portfolio
,
n1 = e +"
�
v1 + �v21+ �2
.
Large belief disagreements, " > ��1+ �2
�: Financial innovation
increases risks.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 10 / 22
Channel 2: New assets amplify existing disagreements
Next consider the introduction of a second asset:
Earlier single asset case:
x11 = �1+"
�
11+ �2| {z }dampening
.
Additional asset with payo¤, a2 = v2 (agreement on payo¤).Trader 1�s position and net worth:
x11 = �1 +"
�|{z}asset 1, betting
and x21 = ��"�| {z }
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 11 / 22
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 ;�): trader�s belief for asset payo¤s.
�i : common belief for covariance of wi and a.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 12 / 22
Characterization of equilibrium
Equilibrium portfolios: xi = xRi + xSi where:
xRi = ���1~�i| {z }Risk sharing portfolio
and xSi = ��1~�i�i| {z }
Speculative portfolio
,
Relative covariance: ~�i = �i ���
�i
1jI jX{2I�{,
Relative optimism : ~�i = �i �1jI jX{2I
��
�{�{.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 13 / 22
Average variance and its decomposition
De�ne average variance of net worths:
=1jI jXi2I
�i��vari (ni ) .
Lemma: With common beliefs, the equilibrium portfolios minimize subject to resource constraints,
Pi xi = 0.
De�ne uninsurable variance, R , as the minimum possible .
De�ne speculative variance as the residual:
= R|{z}uninsurable variance
+ S|{z}speculative variance
.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 14 / 22
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 (JO [ JN ) � S (JO ) .
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 15 / 22
Intuition for the main result
Consider the economy with only speculation reason for trade.
Then, a textbook result applies:
�Si|{z}std. of speculative portfolio return
=1�ie|{z}�relativei
SharpeSi| {z }Speculator�s Sharpe ratio
.
With more assets, SharpeSi 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 16 / 22
Based on a true story of famous economists
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 17 / 22
They decide to take a side bet, at some cost
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 18 / 22
They realize that this is Pareto optimal
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 19 / 22
The end of the story is unknown
The increase in portfolio risks ~Destroyed pillow.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 20 / 22
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 anyconvex combination of agents�beliefs.
Financial innovation is belief-neutral ine¢ cient when it increases .
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 21 / 22
Conclusion
E¤ect of �nancial innovation on portfolio risks when traders have risksharing 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.
Alp Simsek (Harvard University) Speculation and Risk Sharing May 2012 22 / 22