Question

# Suppose you own a portfolio with two securities. Security A has an expected return of 13.4%...

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%

Given that

Standard Deviation of A = σA = 55% = 0.55

Standard Deviation of B = σB = 32% = 0.32

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

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

Coefficient of Correlation, RAB = 0.25

Let the Covariance between A and B be CovAB = RAB x σA x σB

Standard Deviation of Portfolio = [(W2A x σ2A )+(W2B x σ2B) + (2 x WA x WB x CovAB ) ]1/2

= [(W2A x σ2A )+(W2B x σ2B) + (2 x WA x WB x RAB x σA x σB ) ]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%

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