Don’t Count on Mean Reversion

Sure, markets might bounce back but it could take a long time.

April 12, 2012

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bounce bungee jumpThere are all sorts of anomalies in stock market returns that test the credibility of the efficient markets hypotheses, namely that market prices are always correct. Still, contrarian asset managers are advised to heed the market wisdom. Value stocks, for example, may be selling at a discount, but it could be a very long time before markets recognize their intrinsic value, and bid up prices.

Among the more longstanding pieces of stock market lore is that prices eventually revert to the mean. In some sense, that was demonstrated with the release of Robert Shiller’s Irrational Exuberance in 2000, just months before the stock market crash. He pointed out that the 10-year rolling historical price/earnings ratio for stocks was just under 15. At the time, the S&P 500 was trading above 45 times earnings.

Well, there has been some mean reversion, with S&P stocks finally hitting 15 in 2009. But now the market is trading at 22 times earnings. For the average investor, this is simply a gauge of whether stocks are relatively cheap or expensive. Other metrics could be used and for individual stocks relative valuations may come to mind.

But what about for major institutions who have to keep capital reserves lest stock market values plunge. That applies not just to banks having a cushion against a collapse in housing prices. It also applies to insurance companies that offer a guarantee to retail investors on variable annuities and segregated funds – investment vehicles that promise, at very least, a 100% return of capital at maturity.

The insurance companies have recently argued that, given 10-year terms to maturity, current market conditions shouldn’t dictate how much capital they need to reserve, rather it should be a model that takes into account mean reversion.

The Office of the Superintendent of Financial Institutions (OSFI) isn’t buying it. In a recent research paper, “Evidence for Mean Reversion in Equity Prices,” Daniel Mayost writes: “From the perspective of an insurance company writing equity guarantees, mean reversion is highly desirable, as any decrease in stock prices during a period is more likely to be  offset by stock price increases in subsequent periods, which lowers the likelihood of having to make a guarantee payout. Thus, models that assume that stock prices revert to the mean over the long term will produce lower reserve and capital requirements than models that assume that stock prices are truly random (i.e. uncorrelated from period to period).”

There is some evidence of mean-reversion over three-to-five year periods. But the results are not statistically robust, nor is the sample size big enough. In any case, mean-reversion seems to have disappeared before the Second World War.

Which raises a troubling question, Mayost notes: “Kim et al. noted that previous tests depended on the assumption of normality of stock returns. Using computationally intensive methods that are free of distributional assumptions, they concluded that the behaviour of stock returns changed at the end of World War II, with the evidence for long-term positive correlation after the war being just as strong as the evidence for long-term negative correlation before the war. Richardson, using simulations, demonstrated that large autocorrelations between returns in the 3-5 year range are consistent with (i.e. do not disprove) the hypothesis that long-term stock returns are truly random, because autocorrelations within this range are subject to high sampling variation. Some researchers reject the existence of long-term mean reversion while accepting the existence of short-term mean reversion.”

That’s what the academic literature says: there may be mean-reversion, but the evidence is weak.

What kills the insurers case, however, is something very specific. First, there are factors that are exogenous to the model. Mayost cites two. The first concerns economic growth.

“Beyond detailed statistical analysis, there are more general economic reasons that suggest caution in assuming mean reversion. Past experience has shown that growth rates of national economies in real terms are not inherently mean reverting over the long run, even if they appear to exhibit cyclical fluctuations over short periods of time. Long run economic performance in real terms is generally a function of population and productivity growth, neither of which are inherently mean reverting.  Since the performance of many asset classes has a tendency to be broadly linked to economic growth prospects, this casts doubt as to whether mean reversion in equity prices will always occur.”

The second is the way that stocks react to the prospects of economic growth – in other words, investor confidence.

“Another factor affecting equity prices is the behaviour of risk preferences. Major shocks like the 1929 equity market crash and the collapse in Japanese equity prices in 1990 were accompanied by fundamental reassessments of risk and changes to the public’s risk appetite that lasted many years. Regardless of actual growth prospects, public distaste for holding equities following a crash may hamper price recovery.”

Indeed, it took 25 years for the Dow to recover its 1929 peak. The Nikkei has yet to retrace its 1989 peak.

Which presents the final difficulty for the mean-reversion model, or at least one that has been used in Canadian actuarial circles: which assumes “that after an index has crashed from a peak, the market will exert pressure for the index to return to the previous peak, so that average returns will be higher than when the index is on an upswing. This model is asymmetric: it contains an additional term that boosts returns when an index is below its previous peak, but there is no similar term that dampens returns when the index is rising above its previous peak. Consequently, the model assumes that all mean reversion is to a company’s benefit.”

Market logic can be mean. Peaks are always to be re-climbed on the way to the next mountain top. Few take seriously how long it may take to claw out of the gullies that line the way. Safer, it would seem, to revert to a margin of safety: well-padded capital reserves for harsh mountaineering weather ahead.

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