Q$1.$ Consider the two $($excess return$)$ index$-$model regression results for stocks A and B$.$ The risk$-$ free rate over the period was $10\%,$ and the market$$s average return was $20\%.$ Performance is measured using an index model regression on excess returns.

Stock A Stock B

Index Model Regression Estimates $0\mathrm{.}35+2($Rm $$ Rf$)0\mathrm{.}63+0\mathrm{.}8($Rm $$ Rf$)$

R$-$square $0\mathrm{.}5760\mathrm{.}436$

Residual standard deviation, $($e$)10\mathrm{.}3\%19\mathrm{.}1\%$

Standard deviation of excess returns $21\mathrm{.}6\%24\mathrm{.}9\%$

a$.$ Calculate the following statistics for each stock:

i$.$ Jensen$$s Alpha

ii$.$ Information ratio

iii. Sharpe ratio

iv$.$ Treynor measure

b$.$ Which stock is the best choice under the following circumstances?

i$.$ This is the only risky asset to be held by the investor.

ii$.$ This stock will be mixed with the rest of the investor$$s portfolio, currently composed solely of holdings in the market$-$index fund.