Rare Disasters and Asset Markets in the Twentieth Century

BarroQJE, 2006

Presentation by Serdar AldatmazSpring, 2010

Background

• Mehra-Prescott, 1985– Equity premium puzzle

• Rietz, 1988– Low-probability economic disasters might

be the solution

Preview of Results

• Inclusion of rare disasters into Mehra and Prescott’s model can explain asset-market puzzles– Equity-premium puzzle– Low real rate of return on government bills– Low expected real interest rates during

major wars

Outline

• The Model

• Review of economic disasters

• Calibration Results

• Extensions

• Concluding Remarks

The Model

• Lucas Tree Model– Exogenous, stochastic production– Neither investment, nor depreciation

• Allows for capital formation in the extension

– Consumption equals output– Two assets

• Equity claim on t+1 output

• Risk-free asset, which partially defaults in disasters

Solution without Rare Disasters

• Solving for the agent’s maximization problem;

Modelling Rare Disasters

• ut+1 is i.i.d w/ N(0, σ2)

• σ and γ are known

• p is the probability of disaster (constant)

• b is the size of contraction in case of a disaster

Modelling Default

• Default occurs with probability q when a v-type disaster occurs

• Default wipes out the fraction d of the return on the government bill

• Default does not affect equities and real GDP

Solution of the Model - Price

• Price of one-period equity claim:

Solution of the Model - Returns

• Expected rate of return on one-period equity: Et(Re

t+1)=Et(At+1)/Pt1

• Return on government bills:

(Assumption: d=b)

Solution of the Model - Equity

Premium

• The difference between the two returns:

– Increasing in p & θ & b=d– Decreasing in q

Outline

• The Model

• Review of economic disasters

• Calibration

• Extensions

• Concluding Remarks

Economic Disasters

Stock and Bill Returns

Outline

• The Model

• Review of economic disasters

• Calibration

• Extensions

• Concluding Remarks

Calibration of Disaster Parameters

• Probability of disasters– 60 occurrences for 35 countries over 100

years• p = 1.7%

• Distribution of b from realized contractions

• Default probability– 25 partial defaults out of 60 events

• q = 40%

Calibration of Other Parameters

• σ = 0.02 • γ = 0.025• ρ = 0.03• θ = 3 or 4

Calibration Results

What other puzzles can be explained?

• Why do expected real interest rates fall during wars?– Perceived probability, p, of future

economic disaster increases

Outline

• The Model

• Review of economic disasters in the twentieth century

• Calibration

• Extensions

• Concluding Remarks

Duration and Capital Formation

• Main results do not change when we allow for finite and various length disasters

• When we incorporate capital formation, invested and depreciation, the model still predicts similar equity premium results based on the calibration

Outline

• The Model

• Review of economic disasters in the twentieth century

• Calibration

• Extensions

• Concluding Remarks

Concluding Remarks

• Low-probability disasters explain the equity premium puzzle along with other asset market puzzles

• Future research– Incorporate stochastic variations in p

• Option prices, insurance premiums, prices of gold etc.

– Relax i.i.d assumptions