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, a risk free asset, or a combination of the two. In the risk-free asset, the lending rate is 4% while borrowing rate is 9% per year.

Suppose you have a target risk level of 25% 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 on the portfolio you constructed? Who would hold this portfolio as the optimal portfolio?

What is the range of risk aversion for which a client will neither borrow nor lend, that is, for which the optimal allocation to this risky investment is 100%?

Draw the Capital Allocation Line. Indicate the points corresponding to (i) 50% in the risk-less asset and 50% in the risky asset; and (ii) -50% in the riskless asset and 150% in the risky asset.

Compute the expected rate of return and standard deviation for (i) and (ii) in (c).