Real Earnings Yield (REY) Model Details
The following discussion provides the rationale, design and projections of the Real Earnings Yield (REY) stock market model, constructed by the CXO Advisory Group LLC as a potential decision aid for timing equities investments and trades. The REY model is kin to the Fed Model , but: (1) it uses the inflation rate (a wealth discount rate) rather than Treasury instrument yields (competitors to stocks) as a benchmark for the aggregate stock operating earnings yield; and, (2) it allows for variation in the margin investors require between the aggregate earnings yield and the benchmark rate.
Blog Synthesis: Valuation Based on Fundamentals and Blog Synthesis: The Economy and the Stock Market compile some other research on the earnings-inflation rate valuation approach. Blog Synthesis: Gunning for the Fed Model? offers some pros and cons on the Fed Model.
This revision is tentative, especially with regard to the length of the regression interval as discussed below, pending further testing. We will update this discussion whenever we change the model, and as new data accumulate.
Rationale for Model - Constructing the Model - Using the Model - Testing the Model
Key guiding beliefs for development of this model are:
- Investors require the current (12-month trailing) earnings yield to exceed the current (12-month trailing) inflation rate as evidence that an equity investment has the potential to generate a positive real return. They also want the future earnings yield to exceed the future inflation rate.
- The margin that equity investors require between the earnings yield and the inflation rate may vary as they are more or less confident in future trends for these variables.
Relevant to the first belief, the following table presents statistics for historical (1990-2008) relationships between pairs of the following variables:
- The monthly S&P 500 operating earnings yield (E/P) calculated using monthly closes of the S&P 500 index and trailing 12-month operating earnings as compiled by Standard and Poor's. We spread each quarterly earnings increment over the next subsequent quarter to reflect the gradual release of actual earnings, as follows: one half the first month, two fifths the second month and one tenth the third month.
- The monthly closes of the yield on 90-day Treasury bills (T-bill).
- The monthly closes of the yield on 10-year Treasury notes (T-note).
- The monthly total and core inflation rates based on the 12-month trailing change in the non-seasonally adjusted Consumer Price Index (all items and all items excluding food and energy) as compiled by the Bureau of Labor Statistics (BLS). Since BLS releases data for each month about the middle of the following month, we introduce new inflation rate data with a one-month lag (for example, we insert the inflation rate for January into the model in February).
Results indicate that E/P is more closely related to the inflation rates than to the yields of Treasury instruments over this period, with both higher correlations and smaller variations in gap.
Relevant to the second belief, the following chart is a visualization of the gaps between E/P and the total and core inflation rates during January 1990 through January 2009 based on monthly data. While the gaps generally remain positive over this period, they vary in magnitude (especially for the relatively volatile total inflation rate). The average gap between E/P and total (core) inflation is 2.30% (2.51%), with standard deviation 1.01% (1.09%).
See our blog entry of 12/18/08 for a look at the E/P-inflation relationship over the very long term (January 1871 through March 2008). That analysis also shows a generally persistent positive gap between E/P and the total inflation rate, with a fairly abrupt and persistent decrease in the gap occurring about 1960.
In summary, equity investors appear to require positive but variable margins between the current stock market earnings yield and current inflation rates.
To develop a model of stock market behavior based on the gap between E/P and the inflation rates, we apply a rolling regression of historical relationships. Specifically, using data as described above, each month we calculate the slope and intercept of the relationship between E/P and the total inflation rate and between E/P and the core inflation rate over some historical interval. We then apply that slope and intercept to the earnings and inflation rates for the next month to model the S&P 500 index for that month. For projections of the S&P 500 index beyond available actuals, we apply the last available slope and intercept to an Earnings Forecast and an Inflation Forecast to estimate the future trajectory of the S&P 500 index.
The results of this approach suggest the possibility that investors vacillate between two states: (1) requiring only a small margin of safety between E/P and the inflation rate but very sensitive to changes in the earnings yield-inflation rate gap; or, (2) requiring a large margin of safety between E/P and the inflation rate and relatively insensitive (or inversely sensitive) to changes in the earnings yield-inflation rate gap. These states may relate to inflation rate and earnings volatilities.
What is a reasonable length for the rolling regression interval? A long interval picks up a large and thereby, ostensibly, more reliable historical subsample. A short interval is sensitive to abrupt shifts (regime changes) in relationships among variables.
The following chart explores the sensitivity of the model over the past four years to regression intervals of one, two, three and four years for the relationship between E/P and the total inflation rate. In general, the shorter the regression interval, the better the fit for historical data, but perhaps the greater the doubt that the derived relationship will be stable over an extended forecast period.
The next chart explores the sensitivity of the model over the past four years to regression intervals of one, two, three and four years for the relationship between E/P and the core inflation rate. Again, the shorter the regression interval, the better the fit for historical data, although the outputs from a two-year rolling regression are little different from those of a one-year rolling regression.
In summary, the rolling regression approach with short regression intervals enables tight fitting of the REY model with historical data, quickly incorporating any abrupt shifts in investor behavior. However, the derived fit is fairly unstable.
USING THE REY MODEL TO FORECAST THE S&P 500 INDEX
Pending some further testing, we focus on one-year rolling regressions.
The following chart compares the values generated by the REY Model based on one-year rolling regressions for both total and core inflation rates with actual S&P 500 index. Through December 2008, the model relies entirely on historical actuals. The average monthly difference between actual and modeled data for the total (core) inflation rate is 0.7% (-0.5%), and the standard deviation of monthly differences is 7.8% (7.6%).
The Earnings Forecast starts to affect model outputs starting in January 2009, and the Inflation Forecast begins to affect model outputs starting in February 2009. The trade-off for this look-ahead bias is currency of information. The projection through January 2010 is sensitive to the instability of the underlying regression and to errors in the inputs of the separate earnings and inflation rate forecasts. See Stock Market Status for current models projections.
In summary, the REY model in combination with the separate earnings and inflation rate forecasts offers a way to project the S&P 500 index over the next few quarters.
Does a current mismatch between modeled and actual values of the S&P 500 index predict future returns? Mismatches generally relate positively to future S&P 500 index returns, with correlations strongest four to five months out. Correlations are stronger for core inflation than for total inflation. However, all correlations are modest (below 0.20) and, for total inflation, inconsistent. The following chart summarizes average three-month S&P 500 index future returns for various ranges of mismatch between the same-month modeled and actual values of the index over the entire sample period. Except for the glaring instances of the "tails" (< -10% and > 10%, both involving relatively small subsamples) for total inflation, results suggest that positive mismatches (modeled > actual) indicate larger future returns than do negative mismatches (modeled < actual). Subsamples are small.
We will perform additional tests to assess the usefulness of the S&P 500 index projections.
For past versions of the REY Model, we found that:
Inflation rates based on inputs that are seasonally adjusted generate almost identical statistics with respect to stock prices as do inflation rates based on non-seasonally adjusted inputs.
Other measures of the inflation rate do not outperform the total and core inflation rates from BLS as stock market indicators. (See our blog entries of 7/6/06, 12/15/06 and1/20/07 for details.)
The Producer Price Index produces a very erratic relationship between E/P and inflation.
Incorporation of second order inflation effects (volatility) in the model, but every attempt has degraded backtest statistics. (See our blog entry of 6/21/07.)
