Question

Consider the following capital market: a risk-free asset yielding 2.25% per year and a mutual fund consisting of 80% stocks and 20% bonds. The expected return on stocks is 13.25% per year and the expected return on bonds is 3.95% per year. The standard deviation of stock returns is 40.00% and the standard deviation of bond returns 14.00%. The stock, bond and risk-free returns are all uncorrelated. The expected return on the mutual fund. =(13.25*.8)+(3.95*.2)

Using the data from problem 1, what is the standard deviation of returns for the mutual fund?

Answer 1

standard deviation of returns for the mutual fund = (w₁²₁² + w₂²₂² + 2w₁w₂₁₂p_1,2)^1/2

w₁ = weight of stock; w₂ = weight of bonds; ₁ = standard deviation of stock; ₂ = standard deviation of bonds; p_1,2 = correlation between stock and bond returns

Since stock and bond returns are all uncorrelated, so the correlation between stock and bond returns is 0.

standard deviation of returns for the mutual fund = (0.8²*0.40² + 0.20²*0.14² + 2*0.80*0.20*0.40*0.14*0)^1/2 = (0.64*0.16 + 0.04*0.0196 + 0)^0.5 = (0.1024 + 0.000784)^0.5 = 0.103184^0.5 = 0.3212 or 32.12%

the standard deviation of returns for the mutual fund is 32.12%.