The estimates of βP and αPobtained from the regression are the realized or historical β and α.
Looking forward (ex ante, or before the event), alpha is a forecast of residual return. This is the focus of the reading.
where θn is residual return on stock n.
Alpha has the portfolio property. For example, the alpha of the portfolio which has two stocks can be estimated as follows:
where hP(1) and hP(2) are holdings for stock 1 and 2, respectively.
By definition, the benchmark portfolio, risk-free portfolio and cash portfolio all have a residual return of zero. That is, alphas are benchmark-neutral.
I. benchmark portfolio.
II. risk-free portfolio.
III. cash portfolio.
A. average of excess returns.
B. forecast of residual return.
C. historical expected return.
A. hP(1) α1 + hP(2) α2.
This is because alpha has the portfolio property.