Vocabulary questions about CAPM

[wrongsaidfred]

Hi David,

I found the video on CAPM really helpful. One thing I am struggling with a bit is some of the vocabulary and how it will be used on the exam. Most of it has to do with the term "excess return". According to CAPM, "expected excess return" is just Beta*(expected market return-risk free rate) and, ex-ante, alpha is assumed to be zero. Is this correct so far?

When looking back on an actual return over a certain time period, is "excess return" still defined as Beta*(market return-risk free rate)" or does alpha come into play at all? In other words, if expected excess return was 5% and alpha is 2%, is the excess return 5% or 7%? I know that it is all semantics, but I would hate to get a question wrong on the test because I am not 100% sure how they are using a certain term.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

Great observations! Glad the video was helpful.

"Excess return" is (technically, unless further clarified) the return in excess of (above) the risk-free rate, such that the ex-ante CAPM says:
E[return] = riskfree rate + beta * ERP; note E[] is an ex ante concept!
E[return] - riskfree rate = beta * ERP,
ex ante = E[excess return] = beta * ERP, or just as you say (and Grinold actually spells this out):
ex ante = E[excess return] = beta * ERP + E[alpha], where the point of the CAPM is that E[alpha] = 0
Under CAPM and related multi-factor models, since the premise is that excess returns are a linear combination of exposure(s) to beta factors, it is generally a rule that the expected [alpha] is zero, even as we know the realized alpha will be non-zero.

Then after the return is realized,
ex post (realized) excess return = beta * ERP + alpha; i.e., Jensen's alpha is by definition an ex post (realized) concept

So, if beta = 1.5, Rf rate = 4%, ERP = 6% and portfolio returned 14%, then
portfolio's excess return = 14% - 4% = 10% = beta * ERP + alpha = 9% + 1% alpha;
... the excess return remains the return above the riskfree rate
... the expected (alpha) was 0, per CAPM, but the realized alpha is 1% (and that 1% is some unknown blend of luck and skill, only a time series of persistent alpha could lead us to assert it contains skill).

Hope that helps, David