Question

What is the variance of a portfolio formed by 50% stocks and 50% bonds if the standard deviation of the stocks is 10% and the standard deviation of bonds is:

a. 5%
b. 7.5%
c. 10%
d. 12.5%

Answer 1

To calculate the variance of a portfolio formed by 50% stocks and 50% bonds, use the weighted average of the variances of the individual securities. In this case, considering the given standard deviation values, the variance of the portfolio is 0.00390625.

Step-by-step explanation:

To calculate the variance of a portfolio formed by 50% stocks and 50% bonds, we need to consider the standard deviations of both stocks and bonds. The formula for calculating the variance of a portfolio is:

Variance of Portfolio = (Weights of Stocks)^2*(Standard Deviation of Stocks)^2 + (Weights of Bonds)^2*(Standard Deviation of Bonds)^2

In this case, since the portfolio consists of 50% stocks and 50% bonds, the weights of stocks and bonds would be 0.5 each. Assuming the standard deviation of stocks is 10% and the standard deviation of bonds is 7.5%, we can plug in these values into the formula:

• (0.5)^2*(10%)^2 + (0.5)^2*(7.5%)^2 = 0.25*(0.1)^2 + 0.25*(0.075)^2 = 0.0025 + 0.00140625 = 0.00390625

Therefore, the variance of the portfolio is 0.00390625.