Volatility

The volatility of the price of a security is a statistical measure of the risk of holding it.

The volatility is the standard deviation of expected return on a security. The volatility therefore changes with the period of times over which it is measured.

Beta is a slightly more sophisticated measure of risk, based on both relative volatility and the correlation between movements in the price of a security and the market are a whole. Although beta is useful for valuation, volatility is a better measure of the risk an investor takes. It is the basis of measures such as value at risk.

The problem with volatility is that it can only be measured with certainty for the past, but what matters to investors is the volatility now - over time periods starting from the current time and ending at some future time. There are two simple approaches:

1. Assume that the volatility is unchanged in the long run and therefore use the average volatility over a past period.
2. Use the implied volatility.

More complex models can be used. Approaches such as using a weighted average of past volatilities (with more recent data getting a higher weighting) have proved successful.

Methods for estimating volatilities do usually have the advantage of being well suited to back-testing.