The following table summarizes the return and risk of an actively managed portfolio P and the market portfolio M:

Summary of Portfolio Performance

Active Portfolio P Market Portfolio M

Average return $11\%12\%$

Beta $0\mathrm{.}81\mathrm{.}0$

Standard deviation $17\%21\%$

The T$-$bill $($risk$-$free$)$ rate is $1\%.$

a$.$Compute the Sharpe ratios for P and M$.$

b$.$If you must choose only one portfolio among P and M$,$ which portfolio should you choose? Briefly explain why.

c$.$Compute the Treynor ratios for P and M$.$

d$.$Calculate Jensen's alpha for P$.$

e$.$The estimated residual variance of P is $0\mathrm{.}0036.$ What is the information ratio for P$?$