Based on current dividend yields and expected capital gains, the expected rates of

return on portfolios A and $B$ are $13\mathrm{.}0\%$ and $15\mathrm{.}0\%,$ respectively. The beta of $A$ is $\mathrm{.}8,$ while

that of $B$ is $1\mathrm{.}3.$ The T$-$bill rate is currently $7\%,$ while the expected rate of return of the S&P

$500$ index is $14\%.$ The standard deviation of portfolio $A$ is $20\%$ annually, while that of $B$ is

$41\%,$ and that of the index is $30\%.$

Think about what are the appropriate performance measures to use in question a and $b.$

and why.

a$.$ If you currently hold a market index portfolio, you would use Jensen's alpha to

compare the performance of portfolios A and B$.$ What will be the alpha for Portfolios

A and $B?($Negative value should be indicated by a minus sign. Do not round

intermediate calculations. Enter your answer as a percentage rounded to $1$

decimal place.$)$

b$-1.$ If instead you could invest only in $T$ bills and one of these portfolios, you would use

Sharpe ratio to compare the performance of portfolios A and $B.$ Calculate the

Sharpe measure for Portfolios A and $B.($Enter your answer as a decimal rounded

to $2$ decimal places.$)$

Sharpe Measure

Portfolio $A$

Portfolio $B$