Question

You are managing a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. You think that this risky portfolio is best one that you can construct to deliver the best tradeoff between risk premium and return. The T-bill rate is 7%.

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

Stock A … 27%

Stock B … 33%

Stock C … 40%

1.) Eric just had a baby last year and he needs money. So he decides 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%.

(a) What is the proportion y? (2pts)

(b)What are your client’s investment proportions in your three stocks and the T-bill fund? (4pts)

(c) What is the standard deviation of the rate of return on your client’s portfolio? (2pts)

2.) Now Eric’s wife is a little bit worried about the risk of the new portfolio. She wanted Eric to make sure that the overall portfolio’s standard deviation should not exceed 20%.

(a) What is the investment proportion, y? (2pts)

(b) What is the expected rate of return on the overall portfolio? (2pts)

Answer 1

Given in the question :

About Risky portfolio :

Expected return of risky portfolio ( E[R_p]) = 17% = 0.17

Standard deviation of risky portfolio , = 27%= 0.27

Stocks in Risky portfolio :

.A , W_a = 27% = PROPORTION OF STOCK A in risky portfolio

B , W_b = 33% = PROPORTION OF STOCK B in risky portfolio

C, W_c = 40% = PROPORTION OF STOCK C in risky portfolio

Risk free rate ( T-bill rate ), R_f = 7%

Q1.)

Expected return of the overall portfolio of Eric , (E(R_C) ) = 15%

Proportion of his investment ( y) can be calculated from the following equation

E(R_C) = R_f + y * ( E[R_p] - R_f )

15 = 7 + y*(17-7) = 7 + y*10

y = (15-7)/10 = 0.8

y = proportion of investment of eric in the risky portfolio = 0.8

b.) Eric's investment proportion in the 3 stocks of the risky portfolio :

proportion in Stock A = y* W_a = 0.8*27= 21.6%

proportion in Stock B = y* W_b = 0.8*33 = 26.4%

proportion in Stock C = y* W_c = 0.8*40 = 32%

Proportion in T-bill fund = 100 - (proportion in Stock A + proportion in Stock B + proportion in Stock C)

= 100 -(21.6 + 26.4 +32) = 100 - 80 = 20%

c) Standard deviation of eric's portfolio = ,

= 0.8 *27 = 21.6%

Q2. )

Standard deviation of eric's portfolio = 20% ( REQUIRED CONDITION)

,

20 = y*27

y = 20/27 = 0.7407 =investment proportion

b) Expected return on overall portfolio = R_f + y * ( E[R_p] - R_f ) = 7 + 0.7407*(17-7) = 7 +7.407 = 14.407%