$1.$Suppose the following is the result from a regression where the dependent variable is excess returns to T$-$Mobile US Inc. $($Ri$),$ and the independent variable is excess returns to $S$&$P500(Rm).$

$\backslash$table$[[$Slope$,$Intercept$],[0\mathrm{.}95,0\mathrm{.}26]]$

a$.$ Write down the equation for the securities market line $($SML$),$ and use $1$ sentence to interpret what the estimated Alpha term tells us about Ri$.$

b$.$ Use $1$ sentence to explain what the estimated Beta term tells us about the relationship between $Ri$ and $Rm.$

$2.$ Suppose the returns and the standard deviation to two different mutual funds, US stock funds $($U$)$ and Japan stock funds $($J$),$ are the following:

$\backslash$table$[[$Mutual funds,Expected return $($in $\%),$Standard deviation $($in $\%)],[$US stock funds $($U$),12,25],[$Japan stock funds $($J$),6,15]]$

Suppose the correlation between both funds is $0\mathrm{.}4.$

a$.$ If both $U$ and $J$ are open$-$ended funds, briefly explain one characteristic that are common to both funds.

b$.$ How would a mix of both funds help reduce the risk investors face, and which type of risk will be reduced through asset diversification?

c$.$ Complete the investment opportunity set of both $U$ and $J$ by filling in the missing values in the below table. Show ALL calculation steps to receive full credit.

$\backslash$table$[[$Weights on US stock $(w_U),0,0\mathrm{.}5,1],[\backslash$table$[[$Expected return of risky$],[$portfolio $($P$)]],6,,12],[\backslash$table$[[$Standard deviation of risky$],[$portfolio $($P$)]],15,,25]]$

$(20$ points total$)$ Refer to graphs A and $B$ on page $4$ for this question.

a$.$ Consider an efficient frontier, graph A$.$ What is wrong with this graph? Why is it impossible for an efficient frontier to look like this?

b$.$ Now, consider a corrected efficient frontier, graph B$.$ On the same graph, identify the optimal portfolio on the frontier for a given risk$-$free rate Rf$,$ and briefly explain the characteristics of an optimal portfolio

Above: Graph A for Question $3$a$.$

Above: Graph B for Question $3$b$.$

$4.$ Suppose the payout for asset $x$ is $100$ under high inflation rates, and $-10$ under low inflation rates. Also suppose the probability of inflation is $20\%.$

$($a$)$ Calculate the expected payout and standard deviation of the payout for this asset. Show ALL calculation steps to receive full credit.

$($b$)$ Calculate the Sharpe ratio for this asset, and write down the equation for the capital allocation line between this asset and Treasury Bills if the pavout for Treasurv Bills is $1.$