Real Earnings Yield (REY) Model Details

The following discussion provides the rationale, construction and use of the Real Earnings Yield (REY) Model of the U.S. stock market, constructed by the CXO Advisory Group LLC as a potential decision aid for timing investments in equities.

The REY model is kin to the Fed Model, but it uses the expected inflation rate (a wealth discount rate) rather than Treasury instrument yields (competitors to stocks) as a benchmark for the expected stock market earnings yield, defined as aggregate expected corporate operating earnings divided by stock index level.

The Fundamental Valuation and Economic Indicators categories offer other research on earnings-inflation rate valuation approaches. The Fed Model category offers some pros and cons on the Fed Model.

We update this discussion whenever the model changes, and as new data accumulate.

Rationale –  Construction and Backtesting –  Use

RATIONALE FOR REY MODEL

The key guiding belief for development of this model is:

Investors require the expected (12-month forward) stock market earnings yield to exceed the expected (12-month forward) inflation rate as evidence that equities have the potential to generate a positive real return. The larger (smaller) the gap between the expected earnings yield and the expected inflation rate, the better (worse) the prospect for stocks as investors bid prices up (down) to restore a normal gap.

The following chart shows the gap between the S&P 500 forward earnings yield and the forward total inflation rate during March 1989 through March 2010 based on end-of-month data. The forward earnings yield is the 12-month forecasted operating earnings for the S&P 500 (from Earnings Forecast) divided by the level of the S&P 500 Index. To convert from the quarterly earnings cycle to a monthly frequency, we assume new earnings data for a quarter becomes known as follows: 50% during the first month after quarter end; 40% during the second month after quarter end; and, 10% during the third month after quarter end. Availability of S&P 500 lagged (trailing 12 month) operating earnings from Standard and Poor’s as an input to the Earnings Forecast limits the sample period. The forward total inflation rate comes from the Inflation Forecast.

The chart also shows for reference the S&P 500 lagged earnings yield and the lagged total inflation rate.

The gap between the forward earnings yield and the forward total inflation rate is the S&P 500 forward real earnings yield. The average forward real earnings yield over the entire sample period is 2.38%, with monthly standard deviation 0.96%.

How does the forward real earnings yield relate to S&P 500 Index behavior?

The next chart compares the behaviors of the S&P 500 Index and the S&P 500 forward real earnings yield over the available sample period. Visual inspection suggests some tendency for the stock market to be relatively strong (weak) after the forward real earnings yield is high (low).

For precision, we relate the forward real earnings yield to stock market returns over fixed future intervals.

CONSTRUCTION AND BACKTESTING OF THE REY MODEL

The following scatter plot relates the 6-month future return for the S&P 500 Index to the forward real earnings yield over the available sample based on monthly data. The Pearson correlation between the two series is 0.38 and the R-squared statistic is 0.14, indicating that the forward real earnings yield explains 14% of the variation in the 6-month future return. As hypothesized, the best-fit line slopes upward from left to right, indicating that future stock market returns tend to be higher (lower) when the forward real earnings yield is relatively high (low).

Because the future return measurement interval (six months) is longer than the sampling frequency (monthly), the number of points on the scatter plot overstates effective sample size.

For a future return measurement interval of three (12) months, the Pearson correlation is 0.28 (0.41) and the R-squared statistic is 0.07 (0.17).

To check robustness of the relationship, we segment future returns by ranges of the forward real earnings yield.

The next chart summarizes the average 3-month, 6-month and 12-month future returns for the S&P 500 Index by quintile of forward real earnings yield over the available sample period. For all three future return intervals, average returns mostly increase across forward real earnings yield quintiles. The overall sample size is fairly small (based on return intervals) for a quintile breakdown.

For an additional robustness test, we look at two subperiods.

The Pearson correlations for the relationship between the 6-month future return for the S&P 500 Index and the forward real earnings yield over two equal subperiods (3/89-6/99 and 7/99-9/09) are 0.26 and 0.58, indicating some consistency in the relationship over time. The overall sample period is fairly short (compared to return intervals) for subperiod tests.

How can these results translate into forecasts?

USING THE REY MODEL TO FORECAST U.S. STOCK MARKET RETURNS

The (messy) linear relationship implied by the scatter plot above offers a means to estimate S&P 500 Index future returns. For example, based on data available through March 2010, the slope and y-intercept for the relationship between the S&P 500 Index 6-month future return and the forward real earnings yield are 4.64 and -0.07, respectively. The forward real earnings yield as of the end of March 2010 is about 4.61%. The projected return for the S&P 500 Index from the end of March 2010 through the end of September 2010 is therefore 4.64 * 4.61% – 0.07% = +14%.

Similar calculations indicate returns of +7% from the end of March 2010 through the end of June 2010 and +24% from the end of March 2010 through the end of March 2011.

See Stock Market Status for a summary of current stock market projections.

Note that the fairly wide dispersion of data points around the best-fit line in the above scatter plot indicates considerable variability in actual future returns. What might drive the dispersion? Possibilities include:

• Investors may employ methods of estimating forward earnings and forward inflation rate that differ materially from the Earnings Forecast and Inflation Forecast used here.
• The U.S. stock market is not a closed system. Other, substantially uncorrelated real earnings yields may compete.
• Decision factors other than real earnings yield may be important to investors.
• There may be considerable randomness in market behavior.

In summary, the REY Model appears to offer some information about S&P 500 Index returns over the next few quarters. Longer-term projections are more reliable than shorter-term.

Some additional cautions regarding this conclusion are:

• As noted above, the effective sample size is fairly small for the tests employed.
• The available sample period may be unusual such that the indicated relationship between S&P 500 Index future returns and the forward real earnings yield may not persist.
• Non-normality of the stock market returns disrupts interpretation of “normal” statistics.