Mean Reversion

Explained:

Mean reversion is a tendency for a stochastic process to remain near, or tend to return over time to a long-run average value. For example, interest rates and implied volatilities tend to exhibit mean reversion. Exchange rates and stock prices tend not to. Stock market returns, however, do tend to exhibit mean reversion. Exhibit 1 provides an intuitive illustration of the difference between mean reverting and non-mean reverting behavior.

Mean Reversion
Exhibit 1

Mean reversion is a tendency for a stochastic process to remain near, or return over time to a long-run average.

Mean reversion is a model. We choose either to, or not to, model any given quantity with a mean reverting stochastic process. In some cases, the decision is obvious, as in the examples cited above. Other cases are more subtle. Looking at a time series over a few weeks—or even a few years—may be misleading. Mean reversion may only reveal itself over very long horizons. Usually, a decision to model a quantity with a mean reverting stochastic process is based both on empirical observation of that quantity over time, as well as some theoretical argument as to why it should be mean reverting.

Can you think of a theoretical argument why interest rates or implied volatilities should be mean reverting but exchange rates or stock prices should not be?