Consider the following data for a particular sample period when returns were high:

Portfolio X Portfolio Y Market

Average return 17.5% 11.6% 12.2%

Beta 1.25 0.9

Standard deviation 21.7% 8.2% 14.8%

Residual Std. Dev. 17.8% 4.6%

The T-bill rate during the period was 3.2%.

. a. Calculate the Jensen measure (alpha) of portfolio performance for each portfolio (X and Y).

b. Calculate the Sharpe ratio for both portfolios and the market.

c. Calculate the Treynor ratio for both portfolios and the market.

d. Construct a portfolio, X*, using a combination of X and the risk free asset, that matches the standard deviation of the market. What is the proportion of investment (the weight) of X* that should be in X? Calculate the M2 measure for portfolio X (both directly and through the use of the Sharpe ratio to show you get the same answer).

e. Repeat part d for portfolio Y (construct Y*, etc.).

f. Which portfolio do you prefer and why?

Please show your work!