Question

How to calculate the standard deviation of an investment, with the difference probability of states? (please explain it theoretically)

Answer 1

Let us consider three probability of states low,medium and high each with a probability of 0.2, 0.5 and 0.3 respectively. Now, if the returns in these probability states are 4%, 6% and 5% respectively, the expected returns X of the investment would be 0.2*4% + 0.5%6% + 0.3*5% = 5.3%

Thus, taking X as the expected returns and the individual returns as X1, X2 and X3, the standard deviation of the returns is nothing but the square root of variance of the returns with X as the expected returns.

Standard deviation, SD of the returns =