A result from statistics is the following. Dene a random variable Z = 1Y1 + 2Y2 + ... + NYN . So Z is a weighted average of other random variables (this should look to you like a portfolio re- turn). Then:

UESTION 4 A result from statistics is the following. Define a random variable Z-w1Y1 +W2Y2 + +wNYN. So Z is a weighted average of other random variables (this should look to you like a portfolio re- turn). Then Using this new found knowledge, calculate the following (a) what is the beta (CAPM beta) of a portfolio with 35% in a risk free asset with 2% annual return, and 65% in an asset X that has expected return of 10% and variance of 10%. Assume the market portfolio has expected return 8% and variance 15% (b) What is the expected return of the portfolio in (a)? Its variance? Its covariance with the mar- ket? (c) What is the beta on a portfolio that has 40% in X and 60% in asset Y, where mean return of Y is 12%, and a variance of 24%. d) What is the expected return of the portfolio in (c)? Its variance? Its covariance with the mar- ket? (e) would an investor ever hold an asset Z that has market beta of .35 and expected return of 7% if another asset, call it W, had a market beta of .7 and expected return of 15%? Explain your an- swer. Suppose M and the risk-free asset are the same as in part (a) (although this is unnecessary for a correct