Assume the standard deviation of the U.S.market portfolio is 18.2%,the standard deviation of the non-U.S.portion of the world portfolio is 17.1%,and the correlation between the U.S.and non-U.S.market portfolios is .47.Suppose you invest 25% of your money in the U.S.stock market and the other 75% in the non-U.S.portfolio.What is the standard deviation of your portfolio?

Question

Quizplus · Accepted Answer

Using the formula for portfolio variance:
σ^2 = w1^2σ1^2 + w2^2σ2^2 + 2w1w2σ1σ2ρ
where
w1 = 0.25 (weight of US market)
w2 = 0.75 (weight of non-US market)
σ1 = 0.182 (SD of US market)
σ2 = 0.171 (SD of non-US market)
ρ = 0.47 (correlation between US and non-US markets)

Plugging in the values:
σ^2 = (0.25^2)(0.182^2) + (0.75^2)(0.171^2) + 2(0.25)(0.75)(0.182)(0.171)(0.47)
σ^2 = 0.0273
Taking the square root, we get the standard deviation:
σ = 0.165 = 16.5%
Therefore, the answer is B) 15.5%.

Assume the Standard Deviation of the U