Mean-Variance Analysis

See: Variance Analysis.

Mean-variance analysis doesn’t require you to start cussing out some variance you run into for not being small (or large) enough. We can treat those variances quite nicely, thank you very much.

What we’re doing in mean-variance analysis is using a measure of center (the mean) and a measure of spread (the variance) to help us make decisions about which of two possible options might be better for us. The mean tells us, well, the average value, because it’s literally the average, so we can have one number to stick on a whole slew of data (like returns on a stock over many observations) and say, “The average return is about this number.” The variance tells us how close all the other return values are to that average return, so we can say, “The rest of the returns are pretty similar (or not so similar) to that average return.”

Mean-variance analysis is a way of trying to manage the risk of an investment with the possible reward for investing. An investor will examine the mean, or expected return, of an investment as a way to get a handle on the average reward for his or her investment. Ideally, the investor wants the expected return to be high (a high mean). Then the investor will examine the variance of the same investment’s returns as a way to get a feel for how volatile or risky the investment is. When all the returns are grouped closely around the mean return, this is a small variance indicative of a relatively stable stock, or one exhibiting low volatility.

Conversely, when the returns are not grouped closely around the mean, it produces a high variance indicative of a volatile stock. Ideally, the variance, or risk, will be low (a low variance). Additionally, an investor comparing two investments may look for the best balance between reward (high mean) and risk (low variance) depending on the investor’s risk/reward tolerance.