1. You are given a one-factor model of the form:

ra rf = a + a(rm rf) + a.

Your occasionally nice professor also tells you the formula for R2 is: R2 = 2a2m/ 2a2m + 2(a)

According to your calculations, a = 2, 2m = 10%, and 2(a) = 50%. Calculate the systematic component of the variance of a.

Now assume you are given a multi-factor model with second factor Z and excess return on the factor given by rZ rf. Write down the equation of the model and the equation for the multi-factor R2.