Q$3$ Consider a market that consists of only two assets, A and B$.$ Asset A has a weight of $0\mathrm{.}65(65\%)$ in the

market portfolio and a standard deviation of $0\mathrm{.}3(30\%).$ Asset B has a standard deviation of $0\mathrm{.}6(60\%).$ The

correlation between the two assets is $0\mathrm{.}5.$ The expected return on the market is $10\%$ and the risk free rate is

$4\%.$

$($a$)$ What is the variance of the market portfolio?

$($b$)$ What is the covariance of each assets with the market portfolio?

$($c$)$ What are the CAPM $\backslash$beta s of the two assets and the market portfolio?

$($d$)$ What are the reward$-$to$-$risk $($use variance as risk$)$ ratios of the two assets and the market portfolio?

$($e$)$ What are the contributions of each asset to the market excess return, E$[$rM$]$ rf $?$

$($f$)$ What are the contributions of each asset to the market variance, $\backslash$sigma

$2$

M$?$

$($g$)$ What are the contributions of each asset to the reward$-$to$-$risk ratio of the market?

$($h$)$ Suppose you had found that the contribution of asset A to reward$-$to$-$ risk ratio of the market was $1$ and

that the contribution of asset of B to the same ratio was $0\mathrm{.}8.$ How could you construct a portfolio that beats

the market? Could this be an equilibrium?