You are amean$-$variance investor. You invest your savings into wto available funds, S&P $50$ Index fund and Risk$-$free T$-$bil fund. Until very recently, you have chosen ot hold the folowing optimal portfolio, having relied on your estimation about annual expected returns and standard deviations given below sa wel.

Asset Allocation weights

S&P $500$ Index Fund $60\%$ Risk$-$free Treasury Fund $40\%$

Expected return Standard Deviation

$8\%20\%\%2$

You are now making a different expected return estimation for the upcoming year, although you are not changing your estimation about standard deviation:

Asset Expected return S&P $500$ Index Fund $12\%$

Risk$-$free Treasury Fund

$2\%$

You now get a new set of optimal allocation weights given this new estimation for the upcoming year. You currently have atotal $$1\mathrm{.}5$ milion invested ni the wt o funds.

A$)(10$ points$)$ what allocation weights would you divide between the two funds? $($write down the weights ni percent$)$

S&P $500$ Index Fund Risk$-$free Treasury Fund

Total $10\%$

B$)(5$ points$)$ What is the expected dollar profit on your overall portfolio over the next year? $($The unit should be ni dollars; profit si the net payoff from an investment$)$

C$)(5$ points$)$ What is the standard deviation of the dollar profit on your portfolio over the next year? $($The unit should be ni dollars; profit si the net payoff from an investment$)$

You believe that Client As$\text{'}$ monthly return has a standard deviation of $\%4$ and si expected ot exceed the T$-$bil rate by $04.\%$ per month. You also believe that this portfolio ofers the highest possible expected return for its level of standard deviation. Also, short selling and borrowing at T$-$ bill rate are allowed.

A$)(10$ points$)$ Client B would like you ot recommend a combination of the same three assets having the highest expected return for a monthly return standard deviation of $2\%.$ What allocation would you recommend? $($Write down the weights on Smal stocks, Large stocks and T$-$bils that you would recommend; write down the weights ni percent$)$