Speculation and Risk Sharing with New Financial Assets
Alp Simsek
MIT and NBER
March 2013
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
1 / 20
Does …nancial innovation reduce risks?
Recent …nancial innovations vastly increased trading opportunities.
Roughly 1200 types of derivatives as of 1994 (Du¢ e and Rahi, 1995).
Traditional view: Facilitates risk sharing.
Doesn’t account for belief disagreements.
Naturally creates speculation which 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 (MIT and NBER)
Speculation and Risk Sharing
March 2013
2 / 20
A risk sharing model with belief disagreements
Standard risk sharing model with mean-variance preferences:
Background risks and …nancial assets.
Key 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 (MIT and NBER)
Speculation and Risk Sharing
March 2013
3 / 20
Important mechanism: Hedge-more/bet-more
Speculative variance increases through two channels:
1
New assets generate new bets.
2
New assets amplify existing bets (hedge-more/bet-more).
New asset on which there is agreement increases speculative variance!
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
4 / 20
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.
Belief disagreements change the driving force behind …nancial
innovation.
Calibration for national income markets (Ath-Shiller): Small belief
disagreements su¢ cient for speculation to swamp risk sharing.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
5 / 20
Related literature
Financial innovation and security design: Has not explored belief
disagreements.
Exceptions: Brock, Hommes, Wagener (2009), Dieckmann (2009),
Weyl (2007)...
Belief disagreements and asset pricing: Has not focused on portfolio
risks.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
6 / 20
Outline of the talk
Simple example to illustrate the two channels.
The main result.
Welfare implications.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
7 / 20
Consider a standard risk sharing setting
One consumption good (a dollar), two dates, f0; 1g.
Trader, i 2 I , has:
Endowment, ei , 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 (MIT and NBER)
Speculation and Risk Sharing
March 2013
8 / 20
Consider mean-variance preferences with het. priors
Trader i solves:
max Ei [ni ]
xi
s.t. ni = ei
i
vari [ni ] ,
2
x0i p+ wi + x0i a.
Key assumption: Heterogeneous beliefs (agree to disagree).
Equilibrium: Traders optimize and markets clear (
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
P
i
xij = 0 for each j).
March 2013
9 / 20
Simple example to illustrate channels
Two traders, i 2 f1; 2g, with
for each i.
i
Risks perfectly negatively correlated:
w1 = v and w2 =
v:
where
v = v1 + v2 and v1 ; v2
N (0; 1) are uncorrelated.
No trade benchmark:
n1 = e1 + v and n2 = e2
v:
Portfolios are risky because background risks cannot be hedged.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
10 / 20
Financial innovation with pure risk sharing
Suppose traders have common beliefs v1 ; v2
N (0; 1).
Suppose asset with payo¤ a1 = v introduced.
Trader 1’s position and net worth:
x11 =
1 and n1 = e1 .
Traditional view: Financial innovation facilitates risk sharing and
reduces risks.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
11 / 20
Channel 1: New assets generate new bets
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
n1
Alp Simsek (MIT and NBER)
1+
,
speculative portfolio
" v1 + v2
= e1 +
.
1+ 2
Large disagreements, " >
1
2
1
+
| {z }
"
+
2
: Innovation increases risks.
Speculation and Risk Sharing
March 2013
12 / 20
Channel 2: New assets amplify existing bets
Next consider a second asset, a2 = v2 . Agreement on payo¤.
Earlier single asset case:
x11 =
1+
"
1
.
2
1
+
| {z }
dampening
Two assets, hedge-more/bet-more:
x11 =
1 +
"
|{z}
and x12 =
asset 1, betting
"
n1 = e1 + v1 .
"
| {z }
asset 2, hedging
Innovation further increases risks by amplifying speculation.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
13 / 20
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.
Closed form solution for both prices and portfolios.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
14 / 20
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 (MIT and NBER)
S
+
|{z}
.
speculative variance
Speculation and Risk Sharing
March 2013
15 / 20
Main result: Financial innovation increases spec. variance
Compare economies with JO and JO [ JN assets (old and new).
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
Alp Simsek (MIT and NBER)
(JO [ JN )
S
(JO ) .
Speculation and Risk Sharing
March 2013
16 / 20
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
i ei
|{z}
relative
i
SharpeiS
| {z }
.
Speculator’s Sharpe ratio
With more assets, SharpeiS increases through the two channels.
Thus, the speculative variance also increases.
Financial innovation generates a Pareto improvement.
But welfare conclusion can be overturned in two alternative settings...
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
17 / 20
Ine¢ ciencies driven by belief distortions
Disagreements might stem from psychological distortions:
Pareto arguably not appropriate.
Belief-neutral criterion by Brunnermeier, Simsek, Xiong (2012).
Consider welfare with respect to any convex combination belief, h:
Nh =
X
i 2I
=
i
Eh [ni ]
Eh
|
"
2
X
i 2I
varh (ni ) ;
ei + wi
{z
#
}
constant independent of portfolios
:
2
|{z}
belief-neutral welfare measure
Financial innovation is belief-neutral ine¢ cient i¤ it increases
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
.
18 / 20
Ine¢ ciencies driven by externalities
Portfolio choices might be associated with externalities:
Financial intermediaries under government protection.
Negative externalities depend on portfolio risks.
Innovation might be ine¢ cient even in the Pareto sense.
Common element across the two sources of ine¢ ciencies:
Portfolio risks are central to (partial) welfare analysis.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
19 / 20
Conclusion
Belief disagreements can change the e¤ect of recent innovations on
portfolio risks, as well as the driving force behind those innovations.
Future work: Empirical analysis and policy implications.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
20 / 20
A true story of famous economists
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
21 / 20
They decide to bet, at some cost
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
22 / 20
They realize that this is Pareto optimal
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
23 / 20
The end of the story is unknown
The increase in portfolio risks ~Destroyed pillow.
Alp Simsek (MIT and NBER)
Speculation and Risk Sharing
March 2013
24 / 20