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 $5\%.$ You can also borrow at the risk$-$free $5\%$ rate. The expected returns and standard deviations of the

two risky funds are:

Expected Return

$10\%$

U$.$S$.$ stock fund

Emerging market stock

fund

Standard Deviation

$15\%$

$12\%$

The correlation coefficient between the returns of the two stock funds, is $0\mathrm{.}6$

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

$8\%,$ 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$)?$