Question

You are an invesment manager and your client, Marge, has decided to trust you to manager her complete portfolio. You offer Marge a risky investment in your expertly crafted mutual fund as well as a risk free investment in Treasury bills. Your mutual fund's expected return is 14% and its standard deviation is 38%. The T-bill rate is 5%. Marge thinks it over and decides to invest 85% of her money in your mutual fund and 15% in T-bills.

a. What is the expected return and standard deviation of Marge's complete portfolio? (Round your answers to 2 decimal places.)

b. Suppose your risky mutual fund includes the following investments in the given proportions:

Stock A	22	%
Stock B	31
Stock C	47

What are the investment proportions of your client's complete portfolio, including the position in T-bills? (Round your answers to 1 decimal places.)

c. What is the reward to variability ratio (i.e., Sharpe Ratio) of your risky mutual fund and your client's overall portfolio? (Round your answers to 4 decimal places.)

Answer 1

1.
Expected Returns=85%*14%+15%*5%=12.6500%

2.
Standard deviation=85%*38%=32.3000%

3.
Stock A=85%*22%=18.7000%

Stock B=85%*31%=26.3500%

Stock C=85%*47%=39.9500%

T Bills=15%

4.
Risky Mutual Fund=(14%-5%)/38%=0.23684

Client's overall portfolio=(14%-5%)/38%=0.23684