mean final

Can You Rely on Mean Reversion to Outsmart the Market?

mean final

Mean reversion is the idea that following a period of above-average returns, there is more likely to be a period of below-average returns and vice versa. It can be applied not just to the overall stock market but to different segments of it such as small cap vs. large cap or value vs. growth. The concept is somewhat problematic because it implies that future returns are at least partially dependent on past returns. It also contradicts the Efficient Market Hypothesis which states that future returns are purely a function of risk, implying that every future point in time has the same expected return as the present. Nevertheless, there is an overwhelming psychological urge to act on the belief that a winning or losing streak must eventually reverse and perhaps compensate in the opposite direction to balance everything out. Of course, one huge problem is getting the timing of the reversal correct. We recall that Alan Greenspan coined the term "irrational exuberance" in 1996, but the frothy bull market he was describing continued for an additional three years, and the bears who were counting on mean reversion went extinct.

Professor James L. Davis of Dimensional Fund Advisors asks1 if there is any evidence that a trading strategy built on mean reversion (with respect to the premiums of market, size, value, and profitability) can be expected to earn profits in excess of a simple buy-and-hold strategy. He analyzed returns data from 15 different equity markets (including the U.S.) over differing time periods beginning 1/1/1927 and ending 12/31/2013. Overall, he ran 780 simulations that were broken down into two types of trading rules, moving average-based and runs-based. A moving average rule switches sides (e.g. small cap to large cap) when the trailing moving average premium is above its historical level by a given amount. A runs-based rule switches sides after 3, 4, or 5 years of consecutive returns in one direction. Of Davis’s 780 simulations, 5.8% produced reliably positive excess returns (t-stat greater than 2) at a 95% confidence level. The pie chart below summarizes the results.

Here is the rub. Purely from chance, we expect to see 5.0% of the simulations having reliably positive excess returns. To correct for this, Davis utilized an advanced statistical technique2 that was introduced only thirteen years ago. After applying this correction, only 0.2% of the trading simulations yielded reliably positive excess returns, as shown in the pie chart below. 0.2% is a number that we would consider to be statistically indistinguishable from zero.

Davis reported the average excess return of all 780 simulations as -1.48% which would not include the impact of trading costs and taxes associated with executing these strategies.

According to Davis, the procedure of trying many different trading rules in the hope of finding some that work is considered data mining. As the Nobel Laureate economist Ronald Coase said, "If you torture the data long enough, it will confess to anything." Davis deemed the most interesting result of his study to be that in spite of vigorous historical data mining, no trading rule was found that consistently generated reliable excess returns across markets and premiums. We at Index Fund Advisors echo Davis in cautioning investors not to rely on strategies that were uncovered by data mining because their past success could be attributable to chance.

1Davis, James L., "Mean Reversion in the Dimensions of Expected Stock Returns", Dimensional Research, November 2014.

2Benjamini, Yoav, and Daniel Yekutieli. 2001. "The Control of the False Discovery Rate in Multiple Testing Under Dependency." Annals of Statistics 29:1165-1188.