$7.$ Assume that the expected rate of return on the market portfolio is $23\%$ and the rate of return

on T$-$bills $($the risk$-$free rate$)$ is $7\%.$ The standard deviation of the market is $32\%.$

$($a$)$ What is the equation of the capital market line? Answer.

$($b$)$ i$.$ If an expected return of $39\%$ is desired, what is the standard deviation of the corresponding optimal portfolio? Answer.

ii$.$ If you have $$100$ to invest, how should you allocate it to achieve the above portfolio?

Answer.

$($c$)$ If you invest $$300$ in the risk$-$free asset and $$700$ in the market portfolio, how much

money should you expect to have at the end of the year? Answer.