Question

Stock A has an expected return of 7% and Stock B has an expected return of 11%. Stock A has a standard deviation of 5% while stock B has a standard deviation of 15%. The correlation coefficient between the returns on A and B is 0.28. What are the expected return and standard deviation of a portfolio that has 40% of funds in stock A and 60% in stock B?

Answer 1

Expected return of stock A = 7%

expected return of stock B = 11%

Standard deviation of stock A = 5%

Standard deviation of stock B = 15%

Correlation coeff = 0.28

Weight of Stock A in portfolio = 40%

Weight of Stock A in portfolio = 60%

Expected return of portfolio = sum of product of return and weight of individual stocks

= .07*.4 + .11*.6 = .028 + .066 = 0.094 or 9.4%

Formula for portfolio std dev

putting in values

we get

portfolio std dev = sqrt (.4^2*.05^2 + .6^2*.15^2 + 2*.4*.6*.05*.15*.28)

= sqrt(.0004 + .0081 + .001008)

= sqrt ( .009508)

= 9.75%