The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition

MEAN REVERSION

The geometric random walk provides the foundation for modeling the dynamics for asset prices of many different securities, including stock prices. However, in some cases it is not justified to assume that asset prices evolve with a particular drift, or can deviate arbitrarily far from some kind of a representative value. Interest rates, exchange rates, and the prices of some commodities are examples for which the geometric random walk does not provide a good representation over the long term. For example, if the price of copper becomes high, copper mines would increase production in order to maximize profits. This would increase the supply of copper in the market, therefore decreasing the price of copper back to some equilibrium level. Consumer demand plays a role as well—if the price of copper becomes too high, consumers may look for substitutes, which would reduce the price of copper back to its equilibrium level.

Exhibit 6.8 illustrates the behavior of the 1-year Treasury bill yield from the beginning of January 1962 through the end of July 2009. It can be observed that, even though the variability of Treasury bill rates has changed over time, there is some kind of a long-term average level of interest rates to which they return after deviating up or down. This behavior is known as mean reversion.

The simplest mean reversion (MR) model is similar to an arithmetic random walk, but the means of the increments change depending on the current price level. The ...