Friday, 17 August 2012

Mean Reversion and Equity Prices: background research and implications for investments

Following on from the previous article discussing Cyclical Variations in Equity Prices, below is another excerpt from an academic paper I wrote back in 2001 which is still as relevant as ever for equity investments. The concept of mean reverting equity prices and returns is a very powerful notion especially as related to stock market peaks and troughs when it always, by definition, shows its true colour. Having knowledge on this matter is I believe extremely important for the long term investor.

The Concept of Mean Reversion – background research and implications for investments

Since Fama’s thesis (1965a, 1965b) and Fama’s (1970) survey of studies supporting a random walk in stock prices, several departures from this hypothesis have been documented. Stock prices that exhibit mean reverting behaviour when measured over long horizons is one category of these departures. Mean reversion is said to exist when share prices or index levels contain a temporary component, in which case they tend to revert to their trends in the long run. If the share price exhibits such a tendency, then the cumulative returns will also partially revert to the mean in the long run (Jegadeesh (1991)). Statistically speaking, a time series exhibiting mean reversion comprises two components of return: a stationary (permanent) component and a non stationary (temporary) component. If a time series is stationary, its mean variance, and auto covariance at various lags remain the same no matter at what time we measure them. A random walk is an example of a non stationary time series.

Another way of thinking about mean reversion is in terms of return reversals where periods of out performance are followed by periods of underperformance. Ball (1995) refers to mean reversion as “cyclical patterns”. The potential existence of mean reversion, implying that a fraction of stock returns is predictable from past returns, poses a serious challenge to stock market efficiency and the long-held view that share prices follow a random walk. Bodie, Kane and Marcus (1999) interpret stock market predictability as follows: “Indeed, if stock price movements were predictable, that would be damning evidence of stock market inefficiency, because the ability to predict prices would indicate that all available information was not already reflected in stock prices”.

The idea of forecastable returns from past price information suggests that investment strategies yielding excess returns may be possible to construct. The concept of mean reversion is thought to be slow and can only be picked up over long horizons (Balvers, Wu and Gilliland (2000)) and goes back many years. For example, Stigler ((1963), states “There is no more important proposition in economic theory than that, under competition, the rate of return on investment tends toward equality in all industries. “Entrepreneurs will seek to leave relatively unprofitable industries and enter relatively profitable industries” (Fama and French (2000)). There exists a fairly large body of literature that examines whether asset returns are mean reverting, and most financial economists appear to have accepted that aggregate returns do contain an important predictable component (Campbell (2000)). Broadly speaking, this research can be divided into three categories: mean reversion in the U.S. stock market, mean reversion in international stock markets and seasonal mean reversion. Furthermore, much of the academic research (except to some extent Fama and French (1988)) have focused on the cross-section of securities returns, i.e. over the broader market, as opposed to specific industries and companies.

Mean reversion has been examined most extensively for the U.S. stock market. In what is often referred to as a pioneering work, DeBondt and Thaler (1985, 1987) obtain empirical results documenting that returns tend to be mean reverting for stocks on the NYSE for the period 1926 to 1982. Poterba and Summers (1988) conclude that a substantial part of the variance in monthly returns is due to a transitory, or predictable, component. Cochrane (1994) find that the stationary components in GNP and stock prices account for a large fraction of the variances. This transitory component results in prices that are mean reverting and returns that exhibit negative serial correlation. Fama et al (1988) also find significant mean reverting behavior in long-horizon real returns on NYSE during 1926 to 1985, “adding to the mounting evidence that stock returns are predictable”. They sort companies in deciles based on size and also split the companies into industries consisting of firms engaging in similar activities. Their estimates suggest that stationary price components account for a large fraction of the variation of returns and that these components are relatively more important for small-stock portfolios. Such a finding could be contributed to overshooting if one assumes smaller companies have shorter histories and operate in newer, less efficient markets where the information is less than perfect. Fama et al (1988) conclude that stock prices for the period tested have both random walk and stationary components. Fama et al (2000) confirms Stigler’s (1963) proposition that profitability is mean reverting. Specifically, they find that mean reversion is faster when profitability is below its mean and when it is further from its mean in either direction, and they show that this produces predictable variation in earnings. Their results from the U.S. stock market confirm their hypothesis that much of what is predictable about earnings is due to the mean reversion of profitability and assert that real-world forecasts of earnings should incorporate this mean reversion in profitability. They argue further that mean reversion in profitability implies that changes in profitability and earnings are to some extent predictable. Extending this argument, this implicitly means that stock prices are also partially predictable given extensive research showing a positive relation between accounting earnings and stock prices (See for example Fairfield (1994), Rees (1995), Sloan (1996), Abarbanell and Bushee (1997), Lamont (1998) and Penman and Sougiannis (1998)).

As for the international evidence, Cochran and DeFina (1994) in their study of 18 country indexes, find that the majority of the indexes are not stationary and that mean reversion in stock prices occurs in eight of the country indexes. For these indexes that do mean revert, stationary components account for an economically significant part of the total return variance. Balvers et al (2000) report strong evidence of mean reversion in relative stock indexes, also consisting of 18 countries, during the period 1969 to 1996 and demonstrate that the results obtained are robust. For seasonal mean reversion, using data from the New York Stock Exchange (NYSE) from 1926-1988, Jegadeesh (1991) finds significant evidence of mean reversion, but concludes that the phenomenon is entirely concentrated in January. He finds a similar seasonal mean reversion in shares traded on the London Stock Exchange (LSE) in the period 1955-1988, and suggests it may be an international phenomenon. In a subsequent paper, Gangopadhyay (1996) finds that bond default premiums and excess market returns are mean reverting in January. Willems (2001) detected mean reversion across industry portfolios with relatively large differences between industries in mainly Norway and the UK stock markets. The mining industry produced the largest negative autocorrelation of returns (highest mean reversion). The Finance industry displayed the lowest mean reversion. The findings are consistent with the hypothesis of this research, discussed in the section Cyclical Variations in Equity Prices, that industries with more exposure to the general business cycle are more likely to exhibit higher levels of mean reversion.

Altogether, there is a growing body of evidence supporting the notion of mean reversion in asset returns. A discussion of how these findings might be interpreted and the implications of the various interpretations for the efficient market hypothesis follows next.