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

2. 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. Roll’s Critique of CAPM tests
- Tests of CAPM are tests of the market
portfolio’s 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 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