Reversion-to-Value (RTV) Model Details

The following discussion provides the rationale, design and outputs of the Reversion-to-Value (RTV) stock market model, constructed by the CXO Advisory Group LLC as a potential decision aid for timing equities investments.

The RTV model is based on the expected stock market earnings yield, defined as aggregate expected corporate operating earnings divided by stock index level. Earnings yield is the inverse of price-earnings ratio. The Fundamental Valuation category identifies some formal research on the validity of such a valuation approach.

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

Rationale –  Construction and Backtesting –  Use

RATIONALE FOR RTV MODEL

The key guiding belief for development of this model is:

Investors require a predictably substantial expected (12-month forward) stock market earnings yield. The larger (smaller) the expected earnings yield, the better (worse) the prospect for stocks as investors bid prices up (down) to restore a normal expected yield.

The following chart compares the behaviors of the S&P 500 Index and the S&P 500 forward earnings yield 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 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 average forward earnings yield over the entire sample period is 5.37%, with monthly standard deviation 1.07%.

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 RTV MODEL

The following scatter plot relates the 6-month future return for the S&P 500 Index to the forward earnings yield over the available sample based on monthly data. The Pearson correlation between the two series is 0.23 and the R-squared statistic is 0.05, indicating that the forward real earnings yield explains 5% of the variation in 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 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 0.16 (0.32) and the R-squared statistic is 0.03 (0.10).

To check robustness of the relationship, we segment future returns by ranges of the forward 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 earnings yield over the available sample period. For all three future return intervals, average returns increase somewhat consistently across forward real earnings yield quintiles. The imperfect consistencies are cautionary regarding model reliability. 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 0.00 and 0.29. The disparity in correlations and the lack of correlation for the early subperiod are cautionary regarding model reliability. The overall sample period is fairly short (compared to return intervals) for subperiod tests.

How can these results translate into forecasts?

USING THE RTV 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 earnings yield are 2.53 and -0.10, respectively. The forward earnings yield as of the end of January 2010 is about 6.59%. The projected return for the S&P 500 Index from the end of March 2010 through the end of September 2010 is therefore 2.53 * 6.59% – 0.10% = +6.8%.

Similar calculations indicate returns of +3.3% from the end of March 2010 through the end of June 2010 and +14% 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 that differ materially from the Earnings Forecast used here.
• The U.S. stock market is not a closed system. Other, substantially uncorrelated earnings yields may compete.
• Decision factors other than real earnings yield (such as the inflation rate, as applied in the Real Earnings Yield Model) may be important to investors.
• There may be considerable randomness in market behavior.

In summary, the RTV Model appears to offer perhaps a little information about S&P 500 Index returns over the next few quarters, but it is not very reliable. 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 earnings yield may not persist.
• Non-normality of the stock market returns disrupts interpretation of “normal” statistics.