Some more CAPM, and fair values of risky assets
What does the CAPM say?
: The "market portfolio" is the same as the tangency portfolio : What portfolio should you hold? "Portfolio choice" Everyone should hold Mkt and Rf in "some" proportions So each person will evaluate any single stock based on its beta . So everyone hates high beta stocks SML: E(Ri)=Rf+beta*[E(Rm)-Rf]
We can ask analysts what they expect a stock to make We can "ask the CAPM" what this stock's expected return is These two need not be the same : Difference is called "alpha" Example: a stock has a beta of 2. The MRP is 10% over the next year, and Rf=1%. Analysts say that the stock is expected to make 20%. What is the alpha of the stock over the next year?
Measuring beta
Ways: Formula: Cov(Ri, Rm)/Var(Rm) Regress Ri on Rm, get slope Problems: We want sensitivity of Ri to Rm (slope) Rf varies through time Affects both Ri and Rm Causes measurement problems Simple solution: use excess returns. Regress (Ri-Rf) on (Rm-Rf), get slope Or find Cov(Ri-Rf, Rm-Rf)/Var(Rm-Rf)
Suppose I run this for IBM, and find that beta=2, Average (Rm-Rf) was 5. Average (Ri-Rf) was 13. What does the CAPM say that E(Ri-Rf) *should have been*? :What is the CAPM equation? ."Averages look like expectations" What was "E(Ri-Rf)" actually? IBM "beat its CAPM benchmarks" : It had a historical alpha It did better than it should have, given its beta Do we expect IBM to beat its CAPM benchmarks next period?
Do we expect historical alpha to persist?
Asset
To determine this, ask: :What is E(Rm-Rf) over the next period? :What is the beta of the stock over the next period? What is Rf over the next period? Calculate what the CAPM says E(Ri) should be Then independently get an estimate of E(Ri) over the next period, from analysts (say) Co