$2$ Use the information in the table to answer questions $($a$)($e$).$

Expected Return Standard Deviation

Stocks, S $8\%15\%$

Bonds, B $2\mathrm{.}50\%6\%$

The correlation between stocks and bonds is $\backslash$rho $($S$,$B$)=0\mathrm{.}05$

a Calculate the covariance of the returns for stock and bonds.

b Calculate the variance of returns for a portfolio that is $60\%$ invested in stocks and $40\%$ invested in bonds.

c You are trying to decide among three possible allocations: $100\%$ in Stock, $100\%$ in Bonds, or $60\%$ Stock$/40\%$ Bonds $($these are the only $3$ choices$)$

Your utility function depends on expected return and variance and your risk aversion coefficient is A$=3.$ Which of the three allocations is best for you?

Briefly explain your answer.

d The risk$-$free rate is $1\mathrm{.}0$ percent. The CAL that is tangent to the portfolio frontier of stock and bonds has an expected return equal to $4\mathrm{.}95$ percent $($this is an approximation, but you should use this information$)$

Note $1$: The tangency portfolio does not have any money invested in the risk$-$free asset$).$

Note $2$: The $60/40$ portfollio from part $($a$)$ is not the tangency portfolio

You wish to construct an efficient portfolio with an expected return equal to $4$ percent. What are the asset weights in the portfolio?

That is$,$ what are the weight of stocks, bonds and bills in the portfolio?

e Tabulate and graph the investment opportunity set of the two risky funds.

Use investment proportions for the stock fund from $0\%$ to $100\%$ in increments of $10\%.$ Please show your work in the sheet labelled Graph.