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** =
[(W^{2}_{A} x σ^{2}_{A}
)+(W^{2}_{B} x σ^{2}_{B}) + (2 x
W_{A} x W_{B} x Cov_{AB} )
]^{1/2}

= [(W^{2}_{A} x σ^{2}_{A}
)+(W^{2}_{B} x σ^{2}_{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%**

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