$2.$ Suppose that you are considering investing in three mutual funds. The first is a U$.$S$.$ stock fund, the second is an emerging market stock index fund, and the third is a T$-$bill money market fund that yields a risk$-$free rate of $4\%.$ You can also borrow at the risk$-$free $4\%$ rate. The expected returns and standard deviations of the two risky funds are:

Expected Return

Standard Deviation

U$.$S$.$ stock fund

$9\%$

$14\%$

Emerging market stock fund

$13\%$

$26\%$

The correlation coefficient between the returns of the two stock funds, is $0\mathrm{.}5$

a$)$ If you can only choose either the U$.$S$.$ stock fund or the emerging market stock fund to combine with the risk$-$free T$-$bill fund and you want an expected return of $7\%,$ which stock fund will you choose? What is the standard deviation of your portfolio?

b$)$ You can invest only in the two stock funds. If you invest $50\%$ of your money in the U$.$S$.$ stock fund and $50\%$ in the emerging market stock fund, what is the expected return and standard deviation of your portfolio?

c$)$ You can invest in all three funds. Use the formula for the weights of the optimal risky portfolio or Excel Solver to compute the optimal portfolio weights. What is the Sharpe ratio of the best CAL? For the same level of risk as in b$),$ is the expected return higher or lower than b$)?$