Consider two stocks: WMT and IBM with the following properties:

E$($rWMT$)=8\%$ ; sigmaWMT $=13\%$

E$($rIBM$)=12\%$ ; sigmaIBM $=20\%$

The correlation of the two stock returns is ${}_{WMT,\text{I}\text{B}\text{M}}=9\%,$

and the risk$-$free rate is $r_f=1\%.$

You are advising a client who has $$1$ million invested. Currently $50\%$ of this money is in WMT and $50\%$ is in IBM.

a$)$ What are the expected return and standard deviation of the return on your client's portfolio?

B$)$ You are told that the MVE $($mean$-$variance efficient$)$ portfolio formed with WMT and IBM has weights $w_{WMT}=60\%$ and $w_{\text{I}\text{B}\text{M}}=40\%.$

$($B$\mathrm{.}1)$ What are the expected return and standard deviation of the MVE portfolio?

$($B$\mathrm{.}2)$ What is its Sharpe ratio? How does it compare with the Sharpe ratio of your client's current portfolio? Explain your finding.

C$)$ You wish to match the expected return of your client's current portfolio using only WMT$,$ IBM, and the risk$-$free security. What is the minimum standard deviation you can achieve?

D$)$ Suppose the correlation between the two stocks increased to ${}_{WMT,\text{I}\text{B}\text{M}}=20\%.$ What would happen qualitatively $($i$.$e$.,$ don't do any calculations, just tell me the general direction$)$ to the Sharpe Ratio of the optimal portfolio? Justify your answer.