Question

Given the following information:

Expected return on Stock A	.15 (15%)
Standard deviation of return	0.3
Expected return on Stock B	.18 (18%)
Standard deviation of return	0.4
Correlation coefficient of the returns on Stock A and Stock B	0.75

a. What are the expected returns and standard deviations of the following portfolios?

1. 100 percent of funds invested in Stock A

2. 100 percent of funds invested in Stock B

3. 50 percent of funds invested in each stock?

b. What would be the impact if the correlation coefficient were -0.42 instead of 0.75?

Answer 1

Ans:- 1 Expected return of the portfolio if 100 invested in stock A will be 15% and the standard deviation will be 30%.

2 Expected return of the portfolio if 100 invested in stock B will be 18% and the standard deviation will be 40%

3 The expected return of the portfolio if 50% invested in each stock will be given by Respective weights * Respective return

= 0.50*15% + 0.50*18% = 16.50%

The standard deviation of the portfolio is calculated by [ W1^2*SD^2+W2^2*SD2^2+2*W1*W2*SD1*SD2*r ]^(1/2), where W is the weight, SD is the standard deviation and r is the correlation coefficient.

SD = [ 0.50^2*30%^2+0.50^2*40%^2+ 2*0.50*0.50*30%*40%*0.75 ]^(1/2) = 32.79%

(b) If the correlation coefficient were -0.42 instead of 0.75, then only SD of the portfolio will change in Ans (3) else will remain the same.

if r is equal to -0.42 then SD will be   [ 0.50^2*30%^2+0.50^2*40%^2+ 2*0.50*0.50*30%*40%*-0.42 ]^(1/2) = 19.31%.