Question

How to use mean-variance analysis with a normal distribution?

Answer 1

data that is forcasted which goes beyond point estimations to multi-valued results may be converted to quasi-risk with the use of the technique of mean- variance analysis. Based on classical probability theory, management assumes cash flows are random variables, that conform to a normal distribution with a symmetrical bell-shaped curve as in attached image.

The mean is derived by first multiplying annual cash flows C by probabilities Pi respectively. Then the products C Pi for any number of cash flows (n) are summated to derive an expected monetary value(EMV) at time period t.

Assume that returns are statistically normal, the standard deviation is determined as:

Calculate the mean of distribution (EMV) by multiplying each variable's value by its probability of occurrence and adding the products. Subtract the EMV from each possible value and square the result. Multiply each squared deviation around the mean by its probability to determine certainty equivalents and add them together. This sum is the variance. Calculate the square root of the result which will give standard deviation.