Question

Assume that you manage a risky portfolio with an expected rate of return of 15% and a standard deviation of 30%. The T-bill rate is 5%. Your client chooses to invest 120% of a portfolio in your fund and -20% in a T-bill money market fund.

a. Suppose your risky portfolio includes the following investments in the given proportions:

Stock A 30%

Stock B 50%

Stock C 20%

What are the investment proportions of your client’s overall portfolio, including the

position in T-bills?

b. Your client’s Sharpe ratio must be equal to your portfolio’s Sharpe ratio. Do you agree? Why?

c. If the standard deviation of your client’s portfolio is 35%, what is the expected return?

              d. If the interest rate increases from 5% to 7% and your portfolio’s return drops to 12%, how should you         help your clients to achieve the same expected return in a).

Answer 1

a)stock A=120%*30%=36%
stock B=120%*50%=60%
stock c=120%*20%=24%
t bill=-20%

b)for clients portfolio the
expected return=(120%*15%)+(-20%*5%)=17%
standard deviation is the std deviaiton of our portfolio with weight invested
=120%*30%=36%
sharpea ratio my portfolio=(epxected return-risk freE)/std
=(15%-5%)/30%=0.33
clients =(17%-5%)/36%=0.33
and here it is same

c)std of client=35%=x*30%
x=116.67% invested as per my fund and -16.67% in tbill so expected return
=(116.67%*15%)+(-16.67%*5%)=16.67%