In March 2012, the Office of the Superintendent of Financial Institutions (OSFI) released a paper titled “Evidence for Mean Reversion in Equity Prices.”

The paper attempts to justify their decision not to allow segregated fund guarantee reserve and capital requirements for insurance companies to be based on equity return models using the assumption of mean reversion.

I have long advocated that OSFI release their internal research and analysis to the public. This paper only exacerbates my fears regarding OSFI’s ability to execute its mandate to “monitor and evaluate system-wide or sector issues that may impact institutions negatively.” Regrettably, I don’t think the arguments made in the paper hold up to serious scrutiny.

Mean reversion in equity prices

Mean reversion is often confused with sampling error in what is referred to as the “regression fallacy” or “regression to the mean.” For example, for coin tossing we can predict the long-term proportion of heads and tails is 50:50. If the first three tosses are all heads, the chances of a head on the fourth toss remains 50%. The expected average will be 50%, but only because the probability on every toss is 50%.

This can be contrasted with an experiment of drawing from a box that contains an equal number of red and white balls, without replacing the balls once drawn. Just as with coin tossing, the expected proportion for any sample is 50:50. But in this case, if the first three draws are all white, then the probability a red ball is drawn increases because the proportion of red balls in the box has increased.

This example of drawing balls from a box illustrates mean reversion: we must adjust future probabilities based on prior results. Anyone who believes the odds in a coin toss change because of the first three results has fallen victim to the regression fallacy.

Do equity prices exhibit long-term mean reversion? OSFI stated that the evidence was not strong enough to support “the large reduction in segregated fund guarantee reserve and capital requirements from assuming mean reversion in equity returns.” While the conclusion may be correct, their supporting arguments show a faulty understanding of the issue.

The questionable nature of their decision is exemplified by the fact that they disregard the Canadian Institute of Actuaries (CIA) 2002 report that’s heretofore served as the basis for segregated fund guarantee capital requirements in Canada.

This report specifically allows state-dependent models (a class that includes mean-reverting models) provided they are based on historical data and meet calibration criteria (i.e., a minimum probability of various levels of poor results over a variety of time frames).

Problem #1: The efficient market hypothesis

OSFI claims mean reversion contradicts the efficient market hypothesis (EMH), stating “traders would be able to earn excess returns […] by buying stocks that have had lower-than-average returns in prior periods and shortselling stocks that have had higher-than-average returns.”

This begs the question of whether mean reversion exists at the universe level. After a stock index has declined substantially, mean reversion implies that expected future returns for the index increase. This has no bearing on the relative returns of any two individual stocks; past winners and losers may be assumed to have precisely equal distributions of future returns.

In addition, as Burton Malkiel, one of the great defenders of the EMH, states in The Efficient-Market Hypothesis and the Financial Crisis: “It is highly unlikely that either real interest rates or required risk premiums are stable over time. Stock prices should adjust with changes in required rates of return, and such price volatility may be entirely consistent with EMH.

“Over short holding periods, there is some evidence of momentum in the stock market, while for longer holding periods, mean reversion appears to be present.”

Problem #2: Mean reversion of economic indicators

OSFI claims, “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.”