Investment Scenarios and Variance of Rate of Return

Explanation

The expected return equals 0.6 * 30% + 0.3 * 7% + 0.1*(-25%) = 17.6%. To calculate the variance, an easy way is to first calculate the second moment, which is the expected value of the square of the return. Thus, the second moment equals 0.6*[(30%)^2] + 0.3*[(7%)^2)] + 0.1*[(-25%)^2] = 617.2%%.

The variance of a random variable equals the second moment minus the square of the mean. In this case, the variance equals 617.2%% - 17.6%^2 = 307.4%%