Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 21% and a standard deviation of return of 39%. Stock B has an expected return of 14% and a standard deviation of return of 20%. The correlation coefficient between the returns of A and B is 0.4. The risk-free rate of return is 5%. The standard deviation of the returns on the optimal risky portfolio is :_______

a. 25.5%
b. 22.3%
c. 21.4%
d. 20.7%

Answer 1

Option c (21.4%) is the right approach.

Step-by-step explanation:

As we know.

• wA and wB = weights of the securities
• SDA and SDB = standard deviations
• Cor(A,B) = correlation coefficient.

On applying the formula:

⇒
`SD \ Portfolio = [wA^2* SDA^2+wB^2* SDB^2+2* wA* wB* SDA* SDB* Cor(A,B)]^(0.5)`

On substituting the values, we get

⇒
`(0.29^2* 39^2+0.71^2* 20^2+2* 0.29* 0.71* 39* 20* 0.4)^(0.5)`

⇒
`21.40 \ Percent` (%)