You can invest in a risky asset with an expected rate of return of $20\%$ per year and a standard deviation of $40\%$ per year or a risk free asset earning $5\%$ per year or a combination of the two. The borrowing rate is $6\%$ per year.

$($a$)$ Draw the Capital Allocation Line. Indicate the points corresponding to $(1)50\%$ in the risk$-$less asset and $50\%$ in the risky asset; and $(2)-50\%$ in the riskless asset and $150\%$ in the risky asset.

$($b$)$ Compute the expected rate of return and standard deviation for the two portfolios in part $($a$).$

$($c$)$ Suppose you have a target risk level of $50\%$ per year. How would you construct a portfolio of the risky and the riskless asset to attain this target level of risk? What is the expected rate of return of the portfolio you constructed?