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 a price/earnings ratio (P/E) model driven by aggregate corporate operating earnings and stock index price. Blog Synthesis: Valuation Based on Fundamentals identifies some formal research on the validity of such a valuation approach.
This revision is tentative, 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 focus on earnings more than any other valuation parameter.
- Over intervals of a few years, investors tend to sustain a roughly stable relationship between current (12-month trailing) earnings yield and stock price. In other words, P/E generally varies only slowly (it is "sticky").
Relevant to the first belief, the following chart shows the behaviors since January 1990 of the S&P 500 index (monthly closes) and the the S&P 500 aggregate operating earnings (trailing 12 month) 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 two series generally move up and down together, although not perfectly, supporting a belief that earnings are a very important determinant of stock pr ices.
Relevant to the second belief, the next chart depicts the lagged S&P 500 operating P/E since 1990. While P/E does wander from about 13 to 30, it mostly varies slowly on a scale of years.
In summary, operating earnings is a principal driver of stock prices, and P/E usually varies slowly over intervals of a few years.
To develop a model of stock market behavior based on a slowly trending ("sticky") P/E, we employ a rolling linear fit. Specifically, using data as described above, each month we calculate the slope and intercept of the S&P 500 P/E over some historical interval and estimate the P/E for next month by extrapolating the line so defined by one additional month. We then use the estimated P/E and the 12-month trailing operating earnings to estimate the level of the S&P 500 index for that next month. For projections of the S&P 500 index beyond available actuals, we apply the last available estimated P/E to an Earnings Forecast to estimate the future trajectory of the S&P 500 index. (An alternative would be to continue the extrapolation of P/E using the last available calculated slope and intercept.)
What is a reasonable length for the rolling linear extrapolation interval? A long interval picks up a large and thereby more stable historical subsample. A short interval is sensitive to abrupt shifts (regime changes) in relationships among variables, and should be less affected by nonlinearities in P/E variation.
The following chart explores the sensitivity of the modeled S&P 500 index over the past four years to linear extrapolation intervals of one, two, three and four years for the trend in P/E. While the outputs based on shorter intervals fit more closely, differences across the four tested intervals are not dramatic.
In summary, the rolling linear extrapolation of P/E enables a pretty good fit between modeled and historical data across extrapolation intervals of one to four years, with the shortest interval adapting most quickly to an abrupt shift in investor behavior.
USING THE RTV MODEL TO ESTIMATE THE S&P 500 INDEX
Pending some further testing, we focus on one-year rolling linear extrapolations.
The following chart compares the values generated by the RTV Model based on one-year rolling linear extrapolations of P/E with the actual S&P 500 index. Through December 2008, the model relies entirely on historical actuals. The average monthly difference between actual and modeled data 0.3%, and the standard deviation of monthly differences is 6.8%.
The Earnings Forecast starts to affect model outputs starting in January 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 last generated value of P/E and to errors in the inputs of the separate earnings forecast. See Stock Market Status for the current models projection.
In summary, the RTV Model in combination with the separate earnings forecast 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? In general, a current mismatch is a very weak predictor of future returns in the expected direction, with inconsistencies across subperiods. 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. Results imperfectly suggest that positive mismatches (modeled > actual) indicate larger future returns than do negative mismatches (modeled < actual). Subsamples are relatively small.
We will perform additional tests to assess the usefulness of RTV Model S&P 500 index projections.
