Question

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%. Suppose that you have a client that prefers to invest in your risky portfolio a proportion (y) of his total investment budget so that his overall portfolio will have an expected rate of return of 15%. (1) What is the investment proportion, y? (2.) What is the standard deviation of the rate of return on your client’s portfolio?

Answer 1

y -> proportion of risky portfolio

1 -y -> proportion of t bills

Expected return of risky portfolio = 17%

Standard Deviation of risky portfolio = 27%

T bill rate = 7%

Expected return of Portfolio = 15%

1)

Expected return of portfolio = y * Expected return of risky portfolio + (1-y) * T bill rate

15% = y*17% + (1-y) * 7%

y = 0.8 Answer

1-y =0.2

2)

T- bills are risk free.

Hence,

Standard Deviation of T-bills =0

Covariance of T - bills with risky portfolio = 0

(Standard deviation of portfolio )^2= (y*0.27)^2 +((1-y) * Standard Deviation of T-bill)^2 + 2*y*(1-y) * Standard Deviation of risky portfolio * Standard Deviation of T-bills * Covariance of T - bills with risky portfolio

(Standard deviation of portfolio )^2 = (0.8*0.27)^2 +(0)^2 + 0

Standard deviation of portfolio = 0.8*0.27 =0.216 = 21.6 % Answer

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