1.Suppose 0.3 is the correlation of returns between any two stocks in an equal-weighted portfolio containing N stocks.Suppose the volatility of any stock is 25%.Calculate the volatility of a portfolio with

N = 24 stocks

N = 100 stocks

N = infinite stocks

2. The expected return on the Market Portfolio M is E(R_M)=15%, the standard deviation is s_M=25% and the risk-free rate is R_f=5%.

a.Suppose that stock X has standard deviation sX=30%, and correlation with the market portfolio rXM=0.5. Compute bX and E(RX) (the beta and the expected return of stock X) according to the Market Model (ie: alpha equals zero under the Market Model).

b.Suppose that stock Y has standard deviation sy=15%, and correlation with the market portfolio rYM=-0.1. Compute bY and E(RY) (the beta and the expected return of stock Y) according to the Market Model (ie: alpha equals zero under the Market Model).

c.Compute the beta of a portfolio composed 65% of stock X and 35% of stock Y.

3.Two portfolio managers, Mr. P and Mr. Q, claim that they are both good at picking under-priced stocks. Over the years, the average return on the portfolio managed by Mr. P has been 17%, with standard deviation 15%, while the average return of Mr. Q's portfolio has been 18%, with standard deviation 17%. Over the same period, the average return on the market portfolio has been 15%, with standard deviation 12%. You estimate that the covariance between Mr. P's portfolio and the market has been s_PM=0.0173, while the covariance between Mr. Q's portfolio and the market has been s_QM=0.0202. Finally, you estimate that the average return on money market funds (a proxy for the risk-free rate of return) has been 5%.

a.Compute the expected returns on Mr. P's and Mr. Q's portfolios that would be consistent with Market Model (ie: alpha equals zero under the Market Model).

b.Given the Market as the benchmark, are either of the two managers over-performing the market? Explain your answer carefully.