You are facing the problem of investing in a portfolio of T$-$bills, with a risk$-$free rate of return

of $7\%,$ and a portfolio of stocks, with an expected return of $17\%$ and a standard deviation of $27\%.$

a$)$ Draw the CAL of your portfolio decision problem.

b$)$ You choose to invest $70\%$ of your resources in the risky asset and the remaining $30\%$ in Tbills.

Determine the expected rate of return and standard deviation of your overall portfolio.

c$)$ Suppose that you decide to invest in the risky asset a proportion, call it y$,$ of the total

investment budget so that the overall portfolio will have an expected return of $15\%.$

Determine the proportion invested in the risky asset, y$.$ Also determine the standard deviation

of the rate of return of your overall portfolio.

d$)$ Suppose instead that you prefer to invest a proportion in the risky asset, y$,$ that maximizes the

expected return on the overall portfolio subject to the constraint that the overall portfolio$$s

standard deviation does not exceed $20\%.$ Determine the proportion invested in the risky asset,

y$.$ Also determine the expected rate of return on your overall portfolio.

e$)$ Suppose that you have the following standard utility function over the expected rate of return

and the variance of the rate of return of your portfolio: U $$ Ebrg$0\mathrm{.}005$A$2.$ Furthermore,

suppose that your coefficient of risk aversion is A $=3\mathrm{.}5.$ Determine what proportion, y$,$ of

your total investment budget that you should invest in the risky asset in order to maximize

your utility. Also, determine the expected rate of return and the standard deviation of the rate

of return on this optimal portfolio.