Extrapolating Multiples to Forecast Returns

There are less rigorous methods for predicting the direction of stock prices. Look, for example, at the price level of an equity index like the Standard & Poor's 500. At the depths of the recent market decline in March of 2009, Robert Shiller estimated the p/e ratio for the S&P 500 at about 13.3. The price of the index was measured relative to the trailing 10-year average of the index's quarterly earnings.

See Shiller's site for details.

http://www.econ.yale.edu/shiller/data.htm

Looking back historically, every time the p/e was in this range, the subsequent average 10-year return to the S&P 500 was approximately 8.5 percent since 1926 and 10.5 percent since World War II. At the time this chapter was written, the S&P was trading at about 12× earnings. Historically, when the p/e multiple is within 11× and 13×, subsequent 10-year returns have been 11.8 percent since 1871. These numbers are not meant to be precise, but rather, to illustrate how one could extrapolate from the historical record to forecast forward returns. Thus, one could appeal to the historical record and forecast equity returns moving up into this range over the next decade. While convenient, we must keep in mind that these are long-run return forecasts grounded completely in the belief that history repeats itself, that is, that the market mean-reverts to its historical average performance level. The implication here is that fundamentals in the future will behave much as they have historically.

Looked at differently, if the historic average p/e is 16 and we believe that the stock market is mean-reverting, then for any current level of earnings, we can extrapolate the change in the price of the index required to get us back to the long-term average. To illustrate, the S&P 500 fell to a closing low of 757 at the end of March 2009. For argument's sake, suppose that the analyst consensus forecast for forward earnings was $70 per share over the next year. If we believe in mean reversion (strictly speaking, mean reversion is a trend stationary process whereby the trend is a constant growth rate), then a multiple of 16 would imply that the index level would rise to 16∗$70, or 1120, to support the consensus earnings forecast. The S&P was trading a little above 1100 by year's end. The growth in the index value exceeded 65 percent over this period.

The foremost problem with extrapolation of multiples—or any trend reversion model for that matter—is timing, or rather, the lack thereof. These models provide no guidance as to when the predicted reversion will occur. It could occur in the next month or the next decade. Another weakness is that the multiple itself has two random components and no descriptive model governing the dynamics of either. In the case of the p/e, it is price and earnings, neither one of which has a forward model going forward. Hence, mean reversion, as it were, is not just a function of one or the other but both components of the multiple. Does the p/e multiple revert due to changes in price (reflecting fundamentals or merely noise) or changes in expected earnings (reflecting economic fundamentals)? We don't know. Moreover, particularly stressful periods may reflect structural changes to economic fundamentals, which will manifest in prices and cash flows, and these may suggest that multiples are quite independent of what's really going on in the economy. Yet, multiples are quiet on these developments in the sense that they do not inform us about the structure of their respective markets.