rare disasters and asset markets in the twentieth century barro qje, 2006 presentation by serdar...
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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