What is the standard deviation of a stock and bond portfolio?

16. A portfolio contains $30,000 in bonds and $70,000 in stocks. The expected return on bonds is 6% with standard deviation of 1%. The expected return on the stocks is 14% with standard deviation of 9%. Assuming that the bonds and stocks are uncorrelated, determine the standard deviation of the above bond and stock portfolio.|||This is actually very easy question!





Correlation of bond and stock = 0 as it was given, so this means;


Covariance of bond and stock = 0


Therefore,


Sp^2 = Wb^2(Sb^2) + Ws^2(Ss^2) + 2WbWsCOVbs


Sp^2 = 0.3^2(0.01^2) + 0.7^2(0.09)^2 + 0


Sp^2 = 0.003978


Sp = 0.0631 = 6.31%





So the standard deviation of the portfolio is approximately 6.31%.