Mean Reversion: Gravitational Super Force Or Dangerous Delusion? by Aswath Damodaran

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In my last post on the danger of using  single market metric to time markets, I made the case that though the Shiller CAPE was high, relative to history, it was not a sufficient condition to conclude that US equities were over valued. In the comments that followed, many disagreed. While some took issue with measurement questions, noting that I should have looked at 10-year correlations, not five and one-year numbers, others argued that this metric was never meant for market timing and that the real message was that the expected returns on stocks over the next decade are likely to be low. I was surprised at how few brought what I think is the central question, which is the assumption that the CAPE or any other market metric will move back to historic norm. This unstated belief that things revert back to the way they used to be is both deeply set and at the heart of much of value investing, especially of the contrarian stripe. Thus, when you buy low PE stocks and or sell a stock because it has a high PE, you are implicitly assuming that the PE ratios for both will converge on an industry or market average. I am just as prone to this practice as anyone else, when I do intrinsic valuation, when I assume that operating margins and costs of capital for companies tend to converge on industry norms. That said, I continue to worry about how many of my valuation mistakes occur because I don’t question my assumption about mean reversion enough. So, you should view this post as an attempt to be honest with myself, though I will use CAPE data as an illustrative example of both the allure and the dangers of assuming mean reversion.

Mean Reversion: Basis and Push Back

The notion of mean reversion is widely help and deeply adhered to not just in many disciplines but in every day life. In sports, whether it be baseball, basketball, football or soccer, we use mean reversion to explain why hot (and cold) streaks end. In investments, it is an even stronger force explaining why funds and investors that fly high come back to earth and why strategies that deliver above-average returns are  unable to sustain that momentum.

In statistics, mean reversion is the term used to describe the phenomenon that if you get an extreme value (relative to the average) in a draw of a variable, the second draw from the same distribution is likely to be closer to the average. It was a British statistician, Francis Galton, who first made official note of this process when studying the height of children, he noted that extreme characteristics on the part of parent (a really tall or short parent) were not passed on. Instead, he found that the heights reverted back to what he called a mediocre point, a value-laden word that he used to describe the average. In the process, he laid the foundations for linear regressions in statistics.

[drizzle]In markets and in investing, mean reversion has not only taken on a much bigger role but has arguably had a greater impact than in any other discipline. Thus, Jeremy Siegel's argument for why "stocks win in the long term" is based upon his observation that over a very long time period (more than 200 years), stocks have earned higher returns than other asset classes and that there is no 20-year time period in his history where stocks have not outperformed the competition. Before we embark on on examination of the big questions in mean reversion, let's start by laying out two different versions of mean reversion that co-exist in markets.

  • In time series mean reversion, you assume that the value of a variable reverts back to a historical average. This, in a sense, is what you are using when looking at the CAPE today at 27.27 (in August 2016) and argue that stocks are over priced because the average CAPE between 1871 and 2016 is closer to 16.
  • In cross sectional mean reversion, you assume that the value of a variable reverts back to a cross sectional average. This is the basis for concluding that an oil stock with a  PE ratio of 30 is over priced, because the average PE across oil stocks is closer to 15.

At the risk of over generalization, much of market timing is built on time series mean reversion, whereas the bulk of stock selection is on the basis of cross sectional mean reversion. While both may draw their inspiration from the same intuition, they do make different underlying assumptions and may pose different dangers for investors.

The nature of markets, though, is that every point of view has a counter, and it should come as no surprise that just as there are a plethora of strategies built around mean reversion, there are almost as many built on the presumption that it will not happen, at least during a specified time horizon. Many momentum-based strategies, such as buying stocks with high relative strength (that have gone up the most over a recent time period) or have had the highest earnings growth in the last few years, are effectively strategies that are betting against mean reversion in the near term. While it is easy to be an absolutist on this issue, the irony is that not only can both sides be right, even though their beliefs seem fundamentally opposed, but worse, both sides can be and often are wrong.

Mean Reversion: The Questions

You can critique mean reversion at two levels. At the level at which it is usually done, it is more about measurement than about process, with arguments centered around both how to compute the mean and the timing and form of the reversion process. There is a fundamental and perhaps more significant critique of the very basis of mean reversion, which is based on structural changes in the process being analyzed.

The Measurement Critique

Let’s say that both you and I both believe in mean reversion. Will we respond to data in the same way and behave the same way? I don't think so and that is because there are layers of judgments that lie under the words “mean” and “reversion”, where we can disagree.

  • On the mean, the numbers that we arrive at can be different, depending upon the time period you look at (if it time series mean reversion) or the cross sectional sample (if it is a cross sectional mean reversion), and you can get very different values with the arithmetic average as opposed to the median. With cross sectional data, for instance, the oil company analysis may be altered depending on whether your sample is of all oil companies, just larger integrated oil companies or smaller, emerging market oil companies. For time series variations, consider the historical time series of CAPE and how different the "mean" looks depending on the time period used and how it was computed.

Mean Reversion