Question

Suppose you own a portfolio with two securities. Security A has an expected return of 13.4% and a standard deviation of 55% per year. Security B has an expected return of 9.3% and a standard deviation of 32% per year. Considering that your portfolio is composed of 35% of Security A and 65% of Security B, and that the correlation between their returns is .25, what is the standard deviation of your portfolio?

Select one:

a. 31.68%

b. 40.05%

c. 8.53%

d. 8.61%

e. 10.03%

Answer 1

Given that

Standard Deviation of A = σ_A = 55% = 0.55

Standard Deviation of B = σ_B = 32% = 0.32

Weight of Security A in Portfolio, W_A = 35% = 0.35

Weight of Security B in Portfolio, W_B = 65% = 0.65

Coefficient of Correlation, R_AB = 0.25

Let the Covariance between A and B be Cov_AB = R_AB x σ_A x σ_B

Standard Deviation of Portfolio = [(W²_A x σ²_A )+(W²_B x σ²_B) + (2 x W_A x W_B x Cov_AB ) ]^1/2

= [(W²_A x σ²_A )+(W²_B x σ²_B) + (2 x W_A x W_B x R_AB x σ_A x σ_B ) ]^1/2

= [((0.35)² x (0.55)² ) + ((0.65)² x (0.32)² ) + (2 x 0.35 x 0.65 x 0.55 x 0.32 x 0.25) ] ^1/2

= 0.316765 = 31.68%

Answer is a. 31.68%