What P/E Will the U.S. Stock Market Support?

Abstract

The purpose of the study reported here was to determine the earnings multiple of the U.S. stock market (proxied by the S&P 500 Index) that can be justified by economic fundamentals at any given time. When price to earnings or earnings to price was used as the dependent variable, several regression models were found to be significant. The final E/P model had eight significant variables and explained more than 88 percent of P/E variation. This model indicates that today's multiples of 30 to 35 are not justified by current or expected economic conditions.

Since 1926, the market P/E has ranged from a low of 5.9 (in 1949) to a high of about 35 (in 1999) and has averaged 14.4. Depending on conditions, $1 per share of earnings could be worth less than $6 or more than $30. How do investors know what price is fair, and what factors can be used to help predict a fair price? The study reported here attempted to develop a tool for estimating a fair P/E in given economic conditions. The article addresses, in particular, what earnings multiple can be justified for the S&P 500 Index given today's economic fundamentals.

Several authors have written about the determinants of stock prices, returns, and P/Es. I used these works, together with theory and logic, as a basis for this study. Given the advantage of knowing which independent variables have been significantly related to P/E in past studies, I expected to be able to develop a model that explains a large portion of variation in P/E. To construct the model, I used significant independent variables from prior studies (inflation, the dividend payout ratio, dividend yield, T-bill rates, growth in the money supply, GDP growth, trailing earnings growth, long-term T-bond rates, and trailing volatility) plus two variables that no previous paper appears to have studied—the U.S. Federal Reserve P/E index and trailing S&P 500 returns. The Federal Reserve P/E index is the P/E that the Fed purportedly believes is justified by the current 10-year Treasury yield. The rationale for using trailing S&P 500 returns is that investors appear more likely to accept high prices (and high P/Es) following several years of superior returns.

For this study (completed in mid–1999), I used quarterly time-series data from 1926 through 1997 for each variable. I chose this period because it includes the volatile 1930s and 1940s and because 1926 is as far back as comprehensive records are available for some variables. I used numerous independent variables in an effort to take into account everything that could help justify a high market P/E in economic conditions like those of today. The original 11 independent variables were reduced to 10 when I eliminated T-bills because of this factor's multicollinearity with bonds.

The first model used P/E as the dependent variable and resulted in seven significant predictor variables (adjusted R² of 83.0 percent). This model yielded a predicted P/E of 18.23 when early 1999 values were used for each variable. Then, because several previous studies surmised that earnings to price might produce a more linear relationship with various macroeconomic variables than price to earnings produces, I ran regressions with E/P as the dependent variable. I next applied various lags to obtain a still better fit. The final model used only eight significant variables (including lagged variables) to explain E/P and achieved an adjusted R² of 88.5 percent. Only money supply and standard deviation of S&P 500 returns were not significant.

Note that the use of ex post information and the addition of new variables probably caused this regression model to overstate the explanatory ability of the predictor variables on the earnings multiple. Nevertheless, when the same early 1999 values were used as were used for the P/E models, the justifiable E/P was found to be 0.0437. So, the estimated P/E would be 22.86, which is well below the 30–35 trailing earnings multiple experienced during much of 1998 and early 1999. The current market P/E thus appears to be an outlier even in relation to my most optimistic model. Investors should be very cautious.

I thank R. Peter DeWitt, Pam Kirby, Robert Kirby, Junsoo Lee, and James Xander for their guidance and editorial comments.