You have developed the following regression analysis to describe the returns to a portfolio, rp, in terms of the returns to an index, rIndex, a mean-zero disturbance term, ε, and two constants, α and β:

Here, the systematic part of the portfolio return is α + βrIndex, and the idiosyncratic part is ε. Prove that the attribution of risk to systematic and idiosyncratic parts is additive for variance. Is the same true for standard deviation?

Transcribed Image Text:

rp = a + Brindex +