Question

Assume that you manage a risky portfolio with an expected rate of return of 17.8% and a standard deviation of 27.9%. The T-bill rate is 7.5%.

Required:
(a)	Your client chooses to invest 60% of a portfolio in your fund and 40% in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio? (Round your answers to 1 decimal place. Omit the "%" sign in your response.)

Expected return	%	per year
Standard deviation	%	per year

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

Stock A	25%
Stock B	45%
Stock C	30%

What are the investment proportions of your client’s overall portfolio, including the position in T-bills?(Round your answers to 1 decimal place. Omit the "%" sign in your response.)

Security	Investment   Proportions
T-Bills		%
Stock A		%
Stock B		%
Stock C		%

(c)	What is the reward-to-volatility ratio ( S ) of your risky portfolio and your client's overall portfolio?(Round your answers to 4 decimal places.)

Your Reward-to-variability ratio
Client's Reward-to-variability ratio

Answer 1

a)

Expected return of Client Portfolio = Weight of Risky portfolio*Expected return of Risky portfolio+Weight of T bill*Expected return of T bill

=17.8*0.6+7.5*0.4

=13.68

Std dev of Client Portfolio = Weight of Risky portfolio*Std dev of Risky portfolio+Weight of T bill*Std dev of T bill

=27.9*0.6+0*0.4

=16.74

b)

T bill = 40%

Stock A = risky portfolio weight*weight of stock A in risky portfolio = 0.6*25%=15%

Stock B = risky portfolio weight*weight of stock B in risky portfolio = 0.6*45%=27%

Stock C = risky portfolio weight*weight of stock C in risky portfolio = 0.6*30%=18%

c)

Risky portfolio reward to variability = (risky portfolio expected return-t bill return)/risk port folio std dev

=(17.8-7.5)/27.9=0.3692

client portfolio reward to variability = (client portfolio expected return-t bill return)/client port folio std dev

=(13.68-7.5)/16.74=0.3692

=(13.68-7.5)/16.74=0.3692