Blog - Investing Notes

March 21, 2005 – March Madness: Fed Model Upsets P/E Model

Conventional wisdom says that high market P/E ratios forecast negative future stock returns. In their March 2005 paper entitled "The Market P/E Ratio: Stock Returns, Earnings, and Mean Reversion," Robert Weigand and Robert Irons to test this conventional wisdom. Using data back to the 1880s, they pit the Fed Model against the P/E mean reversion model to determine which one better explains stock market behavior. They find that:

• There is a significant break in the stock return-P/E relationship at P/E ratios of 21, above which real earnings growth is well above average and 10-year real stock returns are at the historical average.
• The behavior of the market P/E changes abruptly about 1960, shifting from stationary to nonstationary as the market earnings yield (E/P) develops a strong correlation with the 10-year Treasury note (T-note) yield.
• Investor use of the Fed Model allows the market P/E to persist above trend indefinitely; it is no longer mean-reverting.
• Especially since 1960, changes in the market P/E, rather than the level of the market P/E, correlate closely with expected earnings growth.
• Both the Fed Model and the P/E reversion model predict declines in market P/E, the former because of rising interest rates during economic expansion and the latter because of mean reversion.
• Returns on U.S. equities over the next decade will be low (about 1.3% real or 3.8% nominal annual returns) but positive.
• The extremely high market P/Es of the 1990s, the duration of those high P/Es, the historically low stock dividend yield and persistently overoptimistic earnings forecasts of analysts justify investor wariness.
• As long as investors believe in the Fed Model, the market P/E is a slave to nominal interest rates. Investors have more to gain from equating E/P and interest rates when rates are falling. Since the Fed Model is likely driven more by cognitive error than economic fundamentals, investors may abandon the model as interest rates rise, negatively influencing equity returns.

This paper stimulated us to compare Fed Model outputs to our Reversion-to-Value Model, a P/E model, constraining the Fed Model to the same three-year horizon that we use. To construct the Fed Model prediction for the S&P 500 index, we divide the 12-month trailing operating earnings of the S&P 500 by the T-note yield over the period 2/1/02 through 12/31/05. We use the same estimates for future earnings and T-note yields that we use in our model. To inject reality, we adjust the fed model prediction curve (downward roughly 2%) so that overs equal unders when we compare Fed Model predicted values with actual values of the S&P 500 index over the period 2/1/02 through 3/18/05. This adjustment is similar to one we make in constructing our model. The following chart depicts results:

The adjusted Fed Model is volatile because it is very sensitive to changes in the T-note yield. Based on past actual yields, it is clearly wrong with respect to both level and direction of the market for 2002. Again based on past actual yields and earnings, the adjusted Fed Model generally agrees with our model in generating an upward trend for the market during 2003-2004. While both models indicate that the market is undervalued now, the Fed Model predicts that the market has peaked for 2005 due to significant projected increases in the T-note yield. The Pearson correlation between our model's estimation and the actual S&P 500 index is 80%. The Pearson correlation between the adjusted Fed Model's estimation and the actual S&P 500 index is 37%.

In summary, the Fed Model better describes the behavior of the market P/E over the past forty years than does a mean-reverting model. Expect stocks to provide low but positive returns over the next decade. Do not expect gloom and doom reversion to single-digit P/Es, unless the T-note yield rises to an extremely high level or investors abandon the Fed Model.

For a collection of recent research related to the Fed Model, see Blog Synthesis: Gunning for the Fed Model?.