What is the standard deviation of a portfolio's returns if the mean return is 15 percent, the variance of returns is 184 percent, and there are three stocks in the portfolio?
A)7.83 percent
B)13.56 percent
C)41.00 percent
D)225.00 percent

Question

Quizplus · Accepted Answer

The standard deviation can be calculated using the formula: σ = √(Σ(wi^2 x σi^2) + 2 x Σ(wi x wj x σi x σj)), where wi is the weight of the ith stock in the portfolio, σi is the standard deviation of the ith stock's returns, and σij is the covariance between the ith and jth stock's returns.

Since there are three stocks in the portfolio, we need to calculate the covariance between each pair of stocks. However, this information is not given in the question. We can assume that the stocks are uncorrelated, which means their covariance is 0.

Using this assumption, we can simplify the formula to: 
σ = √(Σ(wi^2 x σi^2))

We know that the mean return is 15%, so each stock's expected return must also be 15%. The variance of returns is 184%, so the standard deviation of returns for each stock is √184% = 13.56%.

Assuming an equal weighting for each stock (i.e. wi = 1/3 for each stock), we can plug in these values to get: 
σ = √((1/3)^2 x (13.56%)^2 + (1/3)^2 x (13.56%)^2 + (1/3)^2 x (13.56%)^2) 
σ = 7.83%

Therefore, the standard deviation of the portfolio's returns is 7.83%.

What Is the Standard Deviation of a Portfolio's Returns If