Assume that the risk-free rate of return is 3% and the market portfolio on the Capital Market Line (CML)has an expected return of 11% and a standard deviation of 14%.How should you invest $100,000 if you are only willing to accept a total portfolio risk of 8%?
A) Invest $140,000 in the market portfolio and by borrowing $40,000 at the risk-free rate.
B) Invest $80,000 in the market portfolio and the remainder in the risk-free security.
C) Invest $63,636.36 in the market portfolio and the remainder in the risk-free security.
D) Invest $36,363.64 in the market portfolio and the remainder in the risk-free security.
E) Invest $100,000 on another portfolio on the CML that does not contain any of the market portfolio or the risk-free security, but has a standard deviation of 8%.

Question

Quizplus · Accepted Answer

Let X represent the amount of investment in the market portfolio.Then you can compute the desired standard deviation of 7% as a weighted average of the two portfolios as follows (Note the standard deviation for the risk-free security is 0):
0.08 = (X/(100,000 - X))(0.14)+ 0
0.08 = 0.14X/(100,000 - X)
0.08(100,000 - X)= 0.14X
8,000 - 0.08X = 0.14X
8,000 = 0.22X
36,363.64 = X

Assume That the Risk-Free Rate of Return Is 3% and the Market