Standard deviation’s role in the stock market

Standard deviation can be an extremely useful tool that should be used by every investor, seasoned or not, to gauge risk and make important considerations about the markets’ behavior. Let’s see how to calculate it first.

On average, a third of past years in the stock market have been “normal”, another third characterized by rapid growth, and the remaining third by “stagflation”. It’s reasonable to take these frequencies and treat them as our best guesses of future business conditions.

Roughly speaking, one-third of the time the market grows by 30 percent, another one-third by 10 percent, and the rest of the time it suffers a 10 percent loss.

This means that, on average, the yearly return will turn out to be 10 percent.

Expected return = 1/3 (0.30) + 1/3 (0.10) + 1/3 (-0.10) = 0.10

The actual yearly returns will be quite variable, however, ranging from a 30 percent gain to a 10 percent loss.

This is where the standard deviation as a measure of risk comes into play. To calculate it, we must first compute the “variance”, a measurement of the dispersion of returns.

The variance is defined as the average squared deviation of each possible return from the average (or expected) value, which we just saw was 10 percent.

Variance = 1/3 (0.30–0.10)^2 + 1/3 (0.10–0.10)^2 + 1/3(-0.10–0.10)^2