Question

Your client has $96,000 invested in stock A. She would like to build a​ two-stock portfolio by investing another $96,000 in either stock B or C. She wants a portfolio with an expected return of at least 14.5% and as low a risk as​ possible, but the standard deviation must be no more than​ 40%. What do you advise her to​ do, and what will be the portfolio expected return and standard​ deviation?

	Expected Return	Standard Deviation	Correlation with A
A	15​%	49​%	1.00
B	14​%	39​%	0.12
C	14​%	39​%	0.26

The expected return of the portfolio with stock B is ?????​%.​(Round to one decimal​ place.)

The expected return of the portfolio with stock C is?????? ​%.​(Round to one decimal​ place.)

The standard deviation of the portfolio with stock B is ??????​%.​(Round to one decimal​ place.)

The standard deviation of the portfolio with stock C is ????​%.​(Round to one decimal​ place.)

You would advise your client to choose stock B? or stock C? because it will produce the portfolio with the lower standard deviation.  

Answer 1

Please find below the necessary replies:

If additional $ 96,000 is invested in Stock B

Weight of A (W_A) = 50%
Weight of B (W_B) = 50%

(Since $96,000 already invested in stock A and equal amount of $96,000 is being invested stock B)

Expected return of A (R_A) = 15%
Expected return of B (R_B) = 14%

Standard Deviation of A (σ_A) = 49%
Standard Deviation of B (σ_B) = 39%

Correlation = 0.12

Portfolio Returns = W_AR_A + W_BR_B

= (15%*50%) + (14%*50%) = 14.50%

Variance of portfolio with B = W_A² * σ_A² + W_B² * σ_B² + 2*(W_A)*(W_B)* σ_A* σ_B*Correlation_AB   

= (50%² X 49%²) + (50%² X 39%²) + (2 X 50% X 50% X 49% X 39% X 0.12)

= 0.109516

Standard Deviation of Portfolio with B = (Variance)^1/2 = (0.109516)^1/2 = 33.09%

If additional $ 96,000 is invested in Stock B

Weight of A (W_A) = 50%
Weight of C (W_C) = 50%

(Since $96,000 already invested in stock A and equal amount of $96,000 is being invested stock C)

Expected return of A (R_A) = 15%
Expected return of C (R_C) = 14%

Standard Deviation of A (σ_A) = 49%
Standard Deviation of C (σ_C) = 39%

Correlation = 0.26

Portfolio Returns = W_AR_A + W_CR_C = (15%*50%) + (14%*50%) = 14.50%

Variance of portfolio with C = W_A² * σ_A² + W_C² * σ_C² + 2*(W_A)*(W_C)* σ_A* σ_C*Correlation_AC

= (50%² X 49%²) + (50%² X 39%²) + (2 X 50% X 50% X 49% X 39% X 0.26)

= 0.122893

Standard Deviation of Portfolio with C = (Variance)^1/2 = (0.122893)^1/2 = 35.06%

The answers are as follows:

a) Expected return of portfolio with stock B = 14.50%

b) Expected return of portfolio with stock C = 14.50%

c) Standard Deviation of portfolio with stock B = 33.09%

d) Standard Deviation of portfolio with stock C = 35.06%

e) Which stock to select for investment - Since the expected return is same if invested in Stock B or C, but the standard deviation is lower if invested in Stock B, it is advised to invest the $ 96,000 in Stock B.

Trust the same will serve your purpose.

Should you need any clarifications, please feel free to comment.