Question

You are managing a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. You think that this risky portfolio is best one that you can construct to deliver the best tradeoff between risk premium and return. The T-bill rate is 7%.

(1)Your client Eric chooses to invest 70% of a portfolio in your fund and 30% in a T-bill money market fund.

(a) What is the expected return and standard deviation of your Eric’s portfolio? (2pts)

(b) Suppose your risky portfolio includes the following investments in the given proportions:

Stock A … 27%

Stock B … 33%

Stock C … 40%

What are the investment proportions of your client’s overall portfolio, including the position in T-bills? (4pts)

(c) What is the Sharpe ratio of your risky portfolio and Eric’s overall portfolio? Should they be the same? (2pts)

(d)Draw the CAL of your portfolio on an expected return/standard deviation diagram. What is the slope of the CAL? Show the position of your client on your fund’s CAL. (4pts)

Answer 1

Question 1:a) Mean = (0.30 x 7%) + (0.7 x 17%) = 14% per year.

Standard deviation = 0.70 x 27% = 18.9% per year.

b) Mean return on portfolio = Rf + (Rp - Rf)y = 7% + (17% - 7%)y = 7% + 10%y

If the mean of the portfolio is equal to 15%, then solving for y we will get:

Please post the next two questions seperately

15% = 7% +10%y => y = (15% - 7%)/10% => y = 0.8

Thus, in order to obtain a mean return of 15%, the client must invest 80% of total funds in the risky portfolio and 20% in Treasure bills.

(b) Investment proportions of the client’s funds:

• 20% in T-bills •

0.8 x 27% = 21.6% in Stock A •

0.8 x 33% = 26.4% in Stock B •

0.8 x 40% = 32.0% in Stock C