Tests of CAPM

1
Tests of CAPM

• Security Market Line (ex ante)
• E(Ri) Rf Bi(E(RM) - Rf)
• SML in terms of historical returns (ex post)
• Ri Rf bi(RM - Rf)
• Assumes
• b values are true estimates for B
• Index we use is the market portfolio
• CAPM is correct
• Regression tests
• Ri a0 a1bi ei
• a0 should not be different from Rf
• a1 should be Rm - Rf
• Ri and beta should be linearly related
• No variable other then bi should explain R

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Tests of CAPM
Early Studies Black, Jensen and Scholes
(1972) Fama and MacBeth (1973) Findings - a0
is higher than Rf, a1 is smaller than RM -
Rf - beta is the only measure of risk that
explains average returns - The model is linear
in beta Recent Studies Fama and French
(1992) Anomalies
3
Rolls Critique of CAPM tests
- Tests of CAPM are tests of the market
portfolios mean-variance efficiency - Market
portfolio can never be observed - As long as the
proxy used for M is ex-post efficient, the
betas calculated using this proxy will be
linearly related to the returns. - CAPM cannot
be used for performance evaluation
4
Arbitrage Pricing Theory
Return generating process Ri ai bi1F1
bi2F2 . binFn ei Taking expectations E(Ri)
ai bi1E(F1) bi2E(F2) . binE(Fn) ei Ri
- E(Ri) bi1(F1 - E(F1)) bi2(F2 - E(F2))
... bin(Fn - E(Fn)) ei or Ri E(Ri)
bi1f1 bi2f2 . binfn ei where fj Fj -
E(Fj) unanticipated change in Fj In
Equilibrium E(Ri) ?0 bi1?1 bi2?2 .
bin?n where ?0 Rf, ?1, ?2 ?n are the risk
premiums associated with each factor.
5
Roll Ross and their four factors
E(Ri) Rf Unexp Change in Inflation Unexp
Change in Industrial Prod. Unexp Change in bond
risk premium Unexp Change in yield curve