Mean Reversion Theory

The percentage spread (standard deviation) of the annualized return of stocks falls faster than 1/(the square root of N), where N is the number of years. (The variance falls faster than 1/N.) This is a precise definition of Reversion to the Mean (or Mean Reversion).

If each year’s stock return were totally independent of the past, the standard deviation would fall in accordance with the square root of N. Even if we were to allow for a short-term memory of two or three years (i.e., momentum), independence would still imply this square root of N behavior.

The Constraint

I have seen many arguments against the notion of Mean Reversion. Most of them fail because words are used too loosely, without definitions. Others fail because they use definitions that are overly restrictive.

Central to the notion of Mean Reversion is the existence of a constraint. Prices cannot rise and fall entirely independent of earnings.

History tells us that this is a loose constraint. A glance at Professor Robert Shiller’s P/E10 plot (Figure 1.3 when you download his S&P500 database) shows us that P/E10 varies slowly. It varies over a wide range of values. Until recently, it had stayed between 5 and 27. Today’s valuations are close to 27, the peak of the historical range. Today’s P/E10 is well below the peak of the bubble. It hit 44.

Professor Shiller’s Online Data

By using the average of ten years of (real) earnings, Professor Shiller avoids the effect of wildly varying one-year earnings, which creates huge fluctuations in single-year price-to-earnings ratios P/E.

Elements of the Total Return

The Gordon Equation or some other form of the Dividend Discount Model tells us what a rational investor would pay for stocks:

The Investment Return = the initial dividend yield + the growth rate of dividends.

The equation is exact only if the growth rate is constant, all money is reinvested in stocks with essentially identical characteristics and the price of a dividend income stream (discounted to the present) always stays the same.

There are variations. For example, using earnings instead dividends. This is because earnings can be converted to dividends at a later date (or because they can allow dividend increases from an acquiring company).

John Bogle defines the Speculative Return as the change in what people will pay for the same income stream at a different time.

The Total Return = the Investment Return + the Speculative Return.

In terms of the stock market as a whole, the earnings growth rate is slightly less than the growth rate of the Gross Domestic Product (GDP). (The Gross Domestic Product is defined to mimic corporate accounting. For example, it converts the price of homes into equivalent rents.) After adjusting for inflation and smoothing over several years, GDP growth has been remarkably stable.

Valuations enter into the Total Return because of the initial dividend yield and because of the Speculative Return. The (real) dividend growth rate has been in the range of 1.1% to 1.5% per year, when averaged over long periods of time.

Investment Return Constraints

The dividend yield is bounded by the earnings yield. Dividends come out of earnings. They cannot be sustained at a payout ratio above 100%.

When P/E10 is 20 or above, the earnings yield 100E10/P is 5% or less. Since some amount of reinvestment is needed to sustain growth, the dividend yield has to be below 5%. Typically, it would be around 3%. It could be as high as 4%. The (real) Investment Return, even after adding dividend growth back in, is of the order of 5% or less.

Perhaps, the enthusiasm for buying investments that return 5% (real) is high. What happens after P/E10 rises to 25 and the earnings yield falls to 4%? Unless there has been a sustainable, sharp increase in the (smoothed) GDP growth rate, the Investment Return would be expected to fall into the neighborhood of 4%. Perhaps, investors would still pay more. At some point, however, there will be limits as to how much investors are willing to pay. Sanity returns, eventually.

How low can valuations get? P/E10 has fallen close to 5 in the past. This corresponds to an earnings yield of 20%. This produces a sustainable dividend yield above 12% that grows faster than inflation. This level has attracted buyers in the past. I suspect that it will continue to attract buyers in the future.

The Investment Return helps us understand the constraints. Dividends come out of earnings and payouts cannot continue above 100%. P/E10 cannot rise without bound. Dividend yields would fall too low to attract buyers. P/E10 is unlikely to fall too low. Dividend yields would be compelling. These constraints restrict the Speculative Return.


We observe mean reversion when we look at the stock market as a whole. Mean reversion occurs because growth is constrained, when measured over a number of years.

Dividends come out of earnings. Dividend yields are constrained by earnings yields, when measured over a number of years. Valuations are constrained on the high side because there is a lower limit as to the returns that a buyer will accept. Valuations are constrained on the low side. Eventually, the bargains are compelling.

Valuations are declining slowly, partially because of steady prices in the presence of strong earnings growth. Today’s demographics have reduced returns overall, as baby boomers compete for investment returns. But the emotional attractiveness of stocks is diminishing when compared to alternative investments. Disappointing returns are replacing the excitement of the late 1990s.

Have fun.

John Walter Russell
March 11, 2006