It is November, 2017. The following variance-covariance matrix, for the market (S&P 500) and stocks T and U, is based on monthly data from November 2012 to October 2017. Assume T and U are included in the S&P 500. The betas for T and U are T = 0.727 and U = 0.75.

Average monthly risk premiums from 2012 to 2017 were:

S&P500: 1.0%

T: 0.6%

U: 1.1%

Assume the CAPM is correct, and that the expected future market risk premium is 0.6% per month. The risk-free interest rate is 0.3% per month.

a. (13 points) What were the alphas for stocks T and U over the last 60 months?

b. (13 points) What are the expected future rates of return for T and U?

c. (14 points) What are the optimal portfolio weights for the S&P 500, T and U? Explain qualitatively.

\begin{tabular}{|c|c|c|c|} \hline & S\&P500 & T & U \\ \hline S\&P500 & 0.0256 & 0.0186 & 0.0192 \\ \hlineT & 0.0186 & 0.1225 & 0.0262 \\ \hlineU & 0.0192 & 0.0262 & 0.0900 \\ \hline \end{tabular} \begin{tabular}{|c|c|c|c|} \hline & S\&P500 & T & U \\ \hline S\&P500 & 0.0256 & 0.0186 & 0.0192 \\ \hlineT & 0.0186 & 0.1225 & 0.0262 \\ \hlineU & 0.0192 & 0.0262 & 0.0900 \\ \hline \end{tabular}