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%

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