All questions, if not otherwise specified, are based on the following information.

A fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term bond fund, and the third is a money market fund that provides a safe return of $8\%.$ The characteristics of the risky funds are as follows

$\backslash$table$[[,$Expect$],[$Stock Fund,$20\%$

All questions, if not otherwise specified, are based on the following information.

A fund manager is considering three mutual funds. The first is a stock fund, the second is a long$-$term bond fund, and the third is a money market fund that provides a safe return of $8\%.$ The characteristics of the risky funds are as follows

Stock Fund

Expected Return

Bond Fund

$20\%$

$12\%$

The correlation between the fund returns is $0\mathrm{.}1$

rho

$0\mathrm{.}1$

rf

$8\%$

To answer the questions, please round the answers to two decimal places. For example, if you answer is $1\mathrm{.}95\%,$ please fill $1\mathrm{.}95$ in the slot. If you answer is $11\mathrm{.}95\%,$ please fill $11\mathrm{.}95$ in the slot. When the answer is a Sharpe ratio, don't use the percentage format. For example, you should fill in $0\mathrm{.}58$ in the slot if you get a Sharpe ratio of $0\mathrm{.}58.$

Before you start this problem set, please help yourself understand the procedures in $04\_$Efficient$\_$Frontier.xlsx$.$

$7$

$1$ point

Find the tangency portfolio using Excel Solver. What is the weight in the stock fund for your tangency portfolio?

$8$

$1$ point

Suppose you are an investor with the utility function $U=ER=0\mathrm{.}5A{o}^2,$ and your risk aversion is $4.$ What is your optimal allocation in the stock funds?

$9$

$1$ point

Suppose you are an investor with the utility function $U=ER=0\mathrm{.}5A{g}^2,$ and your risk aversion is $2.$ What is your optimal allocation in the stock funds?

$1$ point

Suppose you are an investor with the utility function $U=ER-0\mathrm{.}5A{o}^2,$ and your risk aversion is $2.$ But your borrowing cost is $10\%,$ rather than the risk$-$free lending rate $8\%.$ What is your optimal allocation in the stock funds?

$56\mathrm{.}04$

$1$ point

What is the covariance between the stock fund and the bond fund? $($Please round the answer to four decimal places. e$.$g$.,0\mathrm{.}0014.)$

$21$ point

Suppose you invest in a portfolio with $60\%$ in the stock fund and $40\%$ in the bo fund. What is the expected return for your investment?

$3$

$1$ point

Suppose you invest in a portfolio with $60\%$ in the stock fund and $40\%$ in the b fund. What is the standard deviation for your investment?

$4$

$1$ point

Suppose you invest in a portfolio with $60\%$ in the stock fund and $40\%$ in the fund. What is the Sharpe Ratio for your investment?

$51$ point

Find the global minimum variance portfolio $($GMVP$)$ using Excel Solver. Wh: weight in the stock fund for your GMVP$?$

$6$

$1$ point

What is the standard deviation for your GMVP$?$

Answer questions $5,6,7,8$ and $9.$