Comparing Lagged and Forward RTV and REY Models

The Reversion-to-Value (RTV) Model and the Real Earnings Yield (REY) Model are alternative ways of thinking about U.S. stock market (S&P 500) valuation. The former hypothesizes that the aggregate forward earnings yield (E/P) for the S&P 500 relates positively to future stock market returns, and the latter hypothesizes that the gap between the aggregate forward earnings yield and the forward total inflation rate (E/P – I) relates positively to future stock market returns. Both models use a technical Earnings Forecast based on short-term momentum/acceleration and long-term reversion to trend. The REY Model uses also a technical Inflation Forecast based on both persistence and momentum. Do these input earnings and inflation forecasts add value? Using forecast inputs and model outputs for March 1989 through August 2009 (246 months), we find that:

First, consider as a benchmark the outputs of the RTV and REY Models based on lagged actual aggregate S&P 500 operating earnings and lagged actual inflation rate over the sample period. The following chart compares correlations between:

• Lagged E/P, the lagged RTV Model, and future S&P 500 Index returns at horizons of three, six and 12 months.
• Lagged (E/P – I), the lagged REY Model, and future S&P 500 Index returns at the same horizons.
• Lagged (E/P – I – rf) and future S&P 500 Index returns at the same horizons, where rf is the risk-free rate represented by the yield on 3-month Treasury bills. This third set of correlations tests whether investors focus on raw or excess returns from stocks.

Results indicate that lagged E/P and lagged (E/P – I) contain some information about future stock market returns, with (E/P – I) more informative than E/P. There is some indication that predictive power grows with forecast horizon. Results do not support a belief that investors focus on excess, rather than raw, stock market returns.

Does the forward earnings outlook derived from the Earnings Forecast enhance the power of the models to anticipate stock market returns?

The next chart compares correlations between both Lagged E/P and Forward E/P (based on the Earnings Forecast) and future S&P 500 Index returns at horizons of three, six and 12 months. Results indicate that the Earnings Forecast adds value. In other words, the Earnings Forecast generates RTV Model inputs that appear to be closer to investor expectations than lagged earnings.

Does the Inflation Forecast enhance the power of the REY model to anticipate stock market returns?

The next chart compares correlations between both Lagged (E/P – I) and Forward (E/P – I) and future S&P 500 Index returns at horizons of three, six and 12 months. Forward (E/P – I) uses the outputs of both the Earnings Forecast and the Inflation Forecast. In this case the use of forward rather than lagged inputs to the REY Model does not improve power to anticipate stock market returns. Since the Earnings Forecast improved the RTV Model outputs, a possible interpretation of this failure is that the Inflation Forecast actually diminishes REY Model predictive power. In other words, the lagged inflation rate better represents investor expectations for the inflation rate than does the Inflation Forecast (even though the latter predicts the future inflation rate more accurately than the former over the sample period).

As a cross-check, we try the REY Model with the forward earnings yield but the lagged inflation rate.

The final chart adds to the previous one correlations between (Forward E/P – Lagged I) and future S&P 500 Index returns at horizons of three, six and 12 months. Correlations for this third alternative are the strongest of the three at all horizons, supporting beliefs that the Earnings Forecast enhances the power of the models to anticipate stock market returns and that the Inflation Forecast does not. Results also support an interpretation of these results is that the lagged inflation rate may better reflect investor expectations than does the Inflation Forecast.

Applying the method described in “USING THE REY MODEL TO FORECAST U.S. STOCK MARKET RETURNS” based on (Forward E/P – Lagged I) currently generates an REY Model outlook for the S&P 500 Index very similar to that generated by Forward (E/P – I).

In summary, evidence from simple tests on a fairly small sample indicates that the Earnings Forecast enhances the power of the RTV and REY Models to anticipate stock market returns, but that the Inflation Forecast does not enhance the REY Model.

Note that samples are fairly small in terms of completely independent observations, and consideration of multiple model alternatives increases the probability of discovering “lucky” results.

Based on these findings, we are adding an alternative REY-A Model to Stock Market Status based on forward earnings yield and lagged inflation rate, pending identification of a way to forecast the inflation rate that better reflects investor expectations.

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