nvest equally in 2 mutual funds. ABC stock index and XYZ long-term goverment bond index
fund. Table provides monthly historical returns for the past 20 years.
What is the standard deviation of this portfolio?
A. 16.74%
B. 11.83%
C. 14.59%
D. 19.47%
E.12.38%ABC StockXYZ BondReturn15.25%7.5%Std. Dev21.5%5.85%Correlation0.25
Solution
Portfolio Standard Deviation=Underroot(A2A2+B2B2+2AABB)
Where,
A = weight of asset A in the portfolio;
B = weight of asset B in the portfolio;
A = standard deviation of asset A;
B = standard deviation of asset B; and
= correlation coefficient between returns on asset A and asset B.
Portfolio Standard
Deviation=(((0.5^2)*(0.215^2))+((0.5^2)*(0.0585^2))+(2*0.5*0.5*0.215*0.0585*0.25))^(1/2)
= 11.83%