Exercise $5.$ Assume that the mean$-$variance opportunity set is constructed from only two risky

assets, A and $B.$ Their variance$-$covariance matrix is

$=\left[\begin{array}{cc}0\mathrm{.}0081& 0\\ 0& 0\mathrm{.}0025\end{array}\right].$

Asset A has an expected return of $30\%,$ and Asset B has an expected return of $20\%.$ This

numerical example demonstrates that although investors I and J estimate different betas, they

will have the same expected return for asset A$.$ Answer the following questions:

a$.$ Suppose investor I chooses his $$market portfolio$$ to consist of $75\%$ in asset A and $25\%$

in asset B$,$ whereas investor J chooses a different $$market portfolio$$ with $50\%$ in asset

A and $50\%$ in asset B$.$ Given these facts, what beta will each investor calculate for asset

A$.$

b$.$ Given your answer to part a$,$ which of the following statement is true and why?

i$.$ Investor I will require a higher rate of return on asset A than will investor J$.$

ii$.$ They both require the same return on asset A$.$

iii. Investor J will require a higher rate of return on asset A than will investor I.

c$.$ Compute the zero$-$beta portfolios and the equations for the security market line for each

investor where the zero$-$beta portfolio is the minimum variance portfolio which has

zero covariance with the index portfolio.