Suppose that the risk$-$free T$-$Bills pay a rate of interest of $6\%,$ while the only

alternative risky asset you can invest, the S&P$500$ index, has an expected return

of $9\%$ and a volatility of $15\%.$ Moreover, suppose that you have mean variance

preferences with coefficient of risk$-$aversion $.$

$1.$ If $=2,$ and you had to invest in either one asset or the other all your

wealth, which of the two assets would you choose?

$2.$ What is the level of $\backslash$alpha that would make you indifferent?

$3.$ If $\backslash$alpha $=4,$ what is your optimal portfolio? Draw your solution n the standard deviation$/$expected return space and comment on your findings.

$4.$ Derive analytically the mean and the standard deviation of your optimal

portfolio, and comment on your findings.