Assume that the expected rate of return on the market portfolio is $23\%$ and the risk$-$free return is $7\%.$ The standard deviation of the market is $32\%.$ Assuming that the market portfolio is efficient.

$($a$)$ Derive the equation of the capital market line. Interpret the slope of the line.

$($b$)$ What will be the standard deviation of this position if an expected return of $39\%$ is desired?

$($c$)$ If you invest $600$ in the risk$-$free asset and $1,400$ in the market portfolio, how much money should you expect to have at the end of the year?

$($d$)$ Consider an asset with expected pay$-$off $1,000$ and covariance of $0\mathrm{.}154$ with the market. Determine the current value of the asset.

$(2+2)+1+2+3$