Assume there are initially only two assets in which to invest, A and B$.$ Further assume

no short$-$sale restrictions and that short$-$sale proceeds can be used to invest. The structure

of the market portfolio, and the expected return and standard deviation of return of the

market portfolio are given below.

Market Portfolio

Expected return rate $=11\mathrm{.}5\%$

$=0\mathrm{.}015$

Weight of A in the portfolio $=0\mathrm{.}30$

Weight of B in the portfolio $=0\mathrm{.}70$

The expected return and standard deviation of return of asset A is as follows:

Asset A

Expected return rate $=15\%,=0\mathrm{.}02$

Assume that assets A and B are perfectly negatively correlated, i$.$e$.,$AB $=-1.$

$($a$)(8$ points$)$ What is the expected return rate of asset B$?$

$($b$)(8$ points$)$ What is standard deviation of return of asset B$?($c$)(8$ points$)$ Assuming that the risk$-$free rate as well as the borrowing rate is $3\mathrm{.}5\%,$ a

client, with total wealth $$20,000,$ wants a portfolio with an expected return of $15\mathrm{.}5\%.$

How could you achieve the client$$s objective using the market portfolio?

$($d$)(8$ points$)$ What is the standard deviation of the portfolio created in part $($c$)?$

$($e$)(8$ points$)$ What is the Sharpe ratio of the portfolio created in part $($c$)?$