$$Based on current dividend yields and expected capital gains, the expected rates of return on portfolios$$A$$and$$B$$are $11\%$ and $14\%,$ respectively. The beta of$$A$$is $0\mathrm{.}8$ while that of$$B$$is $1\mathrm{.}5.$ The T$-$bill rate is currently $6\%,$ while the expected rate of return of the S&P $500$ Index is $12\%.$ The standard deviation of portfolio$$A$$is $10\%$ annually, while that of$$B$$is $31\%,$ and that of the index is $20\%.$

a$.$Between stocks A and B$,$ which one is a more desirable investment?

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b$.$If instead you could invest only in bills and one of these portfolios, which would you choose?