Looking backward (**ex post**, or after the fact), alpha is the average of the realized residual returns.

r_{p}(t): portfolio excess return.

r_{B}(t): benchmark excess return._{P} and α_{P}obtained from the regression are the realized or historical β and α.**ex ante**, or before the event), alpha is a forecast of residual return. This is the focus of the reading._{n} is residual return on stock n._{P}(1) and h_{P}(2) are holdings for stock 1 and 2, respectively.

where,

r

r

The estimates of β

Looking forward (

where θ

Alpha has the portfolio property. For example, the alpha of the portfolio which has two stocks can be estimated as follows:

where h

By definition, the benchmark portfolio, risk-free portfolio and cash portfolio all have a residual return of zero. That is, alphas are benchmark-neutral.

Which portfolio has a zero residual return?

Correct Answer: I, II and III

I. benchmark portfolio.

II. risk-free portfolio.

III. cash portfolio.

Correct Answer: I, II and III

Alpha, on ex ante basis, reflects:

Correct Answer: B

A. average of excess returns.

B. forecast of residual return.

C. historical expected return.

Correct Answer: B

If we have a two-stock holding with holdings h_{P}(1) in stock 1 (with α_{1}) and h_{P}(2) in stock 2 (with α_{2}), the alpha of the portfolio will be:_{P}(1) α_{1} + h_{P}(2) α_{2}.

B. α_{1} x α_{2}.

C. cannot be calculated based on the data given.

Correct Answer: A

A. h

B. α

C. cannot be calculated based on the data given.

Correct Answer: A

This is because alpha has the portfolio property.