A portfolio consists of two securities: Nervy and Goofy.The expected return of Nervy is 12.0% with a standard deviation of 15.0%.The expected return of Goofy is 9.0% with a standard deviation of 10.0%.What is the portfolio standard deviation if 35% of the portfolio is in Nervy and the two securities have a correlation of 0.6?
A)9.02%
B)10.52%
C)11.75%
D)12.18%

Question

Quizplus · Accepted Answer

First, calculate the expected return of the portfolio:

Portfolio expected return = (0.35 x 12.0%) + (0.65 x 9.0%) = 9.15%

Next, use the formula for portfolio standard deviation:

Portfolio standard deviation = sqrt[(w1^2 x σ1^2) + (w2^2 x σ2^2) + 2(w1)(w2)(ρ1,2)(σ1)(σ2)]

Where:

w1 = weight of Nervy = 0.35
σ1 = standard deviation of Nervy = 15.0%
w2 = weight of Goofy = 0.65
σ2 = standard deviation of Goofy = 10.0%
ρ1,2 = correlation between Nervy and Goofy = 0.6

Substituting the values:

Portfolio standard deviation = sqrt[(0.35^2 x 15.0%^2) + (0.65^2 x 10.0%^2) + 2(0.35)(0.65)(0.6)(15.0%)(10.0%)]

Portfolio standard deviation = 10.52%

Therefore, the best choice is B.

A Portfolio Consists of Two Securities: Nervy and Goofy