Question #$3$: Asset Allocation $[21$ Points$]$

Suppose that a portfolio consisting of risky stocks has an expected return of $E(r_p)=0\mathrm{.}128$ with a standard deviation $({}_p)=0\mathrm{.}094.$ Suppose that the risk$-$free asset $($treasury bills$)$ has an expected return of $r_f=0\mathrm{.}042.$

Suppose that y is the proportion of the overall portfolio that is invested in the risky asset.

$($a$)$ Calculate the expected return of the overall $($complete$)$ portfolio that has a mix of the risky asset and the risk$-$free asset, $E(r_c).[$Hint: Your answer will be a function of y $][4$ Points$]$

$($b$)$ Calculate the standard deviation $({}_c)$ of the overall $($complete$)$ portfolio that has a mix of the risky asset and the risk$-$free asset. $[$Hint: Your answer will be a function of y$][3$ Points$]$

$($c$)$ Graph the capital allocation line $($CAL$)$ for the overall portfolio. Be sure to properly label the x and y axis. Clearly identify the $y-$intercept on the graph. $[4$ Points$]$

$($d$)$ Calculate the Sharpe ratio of the risky portfolio. Round your answer to $3$ decimal places. $[3$ Points$]$

$($e$)$ Calculate the expected return and standard deviation of the overall $($complete$)$ portfolio if the investor has chosen a weight of $y=0\mathrm{.}85.$ Round your answer to $4$ decimal places. $[3$ Points$]$

$($f$)$ Suppose that an investor has a risk$-$aversion parameter of $A=9\mathrm{.}9.$ Calculate the fraction of this investor's portfolio that will be held in risky portfolio $($y$).$ Round your answer to $4$ decimal places. $[4$ Points$]$