7 Testing the CAPM
Jianguo Xu
Beijing University
2014.03.15
The CAPM
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n Derived from market equilibrium
n With simplifying assumptions
n Frictionless competitive market
n Investors are mean-variance optimizers
n Homogeneous expectations
n Claims:
n Market portfolio is the optimal risky portfolio
n Linear expected return-beta relationship
CAPM in two pictures: the CML and the SML
Testing CAPM
n Market portfolio is the efficient portfolio.
n Not observable.
n “Efficient” is not measurable.
n Linear beta-expected return relationship
n Derived from the first claim
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E[Ri ] = rf + βi
Mkt (E[RMkt ] − rf )
Two-Pass Test Procedure
n Step 1: Data
n N+2 by T matrix (N stocks, 1 risk free rate, 1 market proxy)
n Estimating Beta (SCL) (Frist Pass)
n Recording: average stock returns, beta estimates, market average
return, residual variance
n Time series
n Estimate the SML (Second Pass)
n Add residual variance
n Cross sectional
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Scatterplot of Monthly Excess Returns and
Security Characteristics Line (SCL)
Test Result
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Return %
Beta
Predicted
Actual
Residual variance significant.
Explain the Failure
n Is the beta dead? Or the test is flawed?
1. Expected vs. realized returns
2. Beta are estimated with error
3. The market portfolio employed is not the “market
portfolio”.
n Market inefficient?
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Human Capital and Cyclical Variations in Asset
Betas: Jaganathan and Wang (1996)
n Beta-labor: beta on changes in aggregate labor income as a
proxy for changes in human capital
n Beta-premium: beta on changes between low-and-high-grade
corporate bonds as a proxy for business cycle state
n Also include size in the second pass regression
n Sort stocks into 100 portfolios based on size and beta
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E[Ri ] = c0 + csize log(ME) + cVWβi
VW + cpremβi
prem + claborβi
labor
Jaganathan and Wang (1996)
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Suggested Reading
n Berk and Demarzo
n Chapter 12. The Capital Asset Pricing Model
n Bodie, Kane, and Marcus
n Chapter 9. The Capital Asset Pricing Model
n Chapter 13. Empirical Evidence on Security Returns
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