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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 and trades.
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.
We intend that this model offer visualization rather than a proof or rigorous test.
We will update this discussion every few weeks as new inputs accumulate.
Rationale for Model - Constructing the Model - Using the Model to Project S&P 500
The following chart shows the behaviors from 1/2/90 through 5/13/08 of the S&P 500 index (daily closes) and the the S&P 500 aggregate operating earnings (trailing 12-month operating earnings from Standard and Poor's, with each quarterly increment spread evenly over the next subsequent quarter to reflect the gradual release of actual earnings). The two series generally move up and down together, with the Internet bubble appearing to be an exceptional interval.
The next chart depicts the S&P 500 index and P/E for this index over the same period. It suggests that buying when P/E is relatively low and selling when P/E is relatively high may be effective in timing the stock market. In other words, the P/E relative to its historical average may be a useful indicator of undervaluation and overvaluation.
The above period includes the Internet bubble, unusual by many financial market measures. We therefore repeat the analysis for the recent post-bubble period of 4/1/05 through 5/13/08. The following chart shows the S&P 500 index and the the S&P 500 aggregate operating earnings over this shorter interval. Both series generally move upward across this recent subperiod.
The next chart plots the S&P 500 index and P/E for this index over the shorter period. It suggests that reversion of P/E to an historical average is a slow process, occurring over years rather than weeks or months.
In summary, operating earnings drive stock prices, and movement of P/E with respect to its average value may indicate overvaluation or undervaluation.
Our next step is to develop a model of stock market behavior by focusing on the behavior of P/E compared to its historical average.
The following chart focuses on the behaviors of P/E from 1/2/90 through 5/13/08. The average P/E for this period is 20.1 with standard deviation 4.2. The Internet Bubble stands out as a period of extraordinarily high P/Es, from which the market has retreated considerably. The period 1992-1998 may represent a more "normal" period within a modern investment risk environment, during which the average P/E is 19.6 with standard deviation 3.0.
The next chart is a close-up of recent P/E behavior, covering the interval 4/1/05-5/13/08. The average P/E for this interval is 16.6 with standard deviation 0.5. The P/E as of 5/13/08 is about 16.0, about one standard deviation below the average.
The above above charts show a fairly reliable relationship between operating earnings and stock prices, and they suggest long-term reversion of P/E toward its mean value over relatively long periods. Inferring a general investor requirement for a level of value, we define the following model:
This model has the advantage of simplicity, and testing it using historical data and earnings projections is straightforward. We can make it adaptive to persistent fluctuations in P/E by dropping old data as new data accrues to capture a current value environment.
In summary, stock investors/traders apparently require a somewhat constant level of value (P/E) from stocks over the long term.
USING THE RTV MODEL TO ESTIMATE S&P 500
Our next step is to construct both long-term and short-term mockups of the S&P 500 index using the above model (including projections through 3/31/09), and compare them to actual S&P 500 index behavior.
The following chart shows the long-term (1/2/90-3/31/09) mockup of the S&P 500 index and the actual S&P 500 index using the average P/E for the period (20.1) as the prediction engine. The average daily difference between them is 4.1%, and the standard deviation of daily differences is 20.2%. As noted above, we spread each quarterly earnings update evenly across the subsequent quarter, reflecting the gradual public release of information about actual earnings.
The following log version of the above chart depicts more clearly the percentage difference between these two series, accentuating the difference for low values and dampening the difference for high values.
As shown by the above charts, the underlying model does not explain the Internet Bubble; pre-Bubble and post-Bubble modeled values are therefore likely higher than they should be. This Bubble effect argues for using only more recent data for stock market prediction. The next chart shows a recent short-term (4/1/05-3/31/09) model of the S&P 500 index and the actual S&P 500 index using the same raw data as above, but applying the average P/E for this shorter period (16.6) as the prediction engine. The average daily difference between them is 0.1%, and the standard deviation of daily differences is 3.2%. Quarterly operating earnings growth drives the general rise in mockup values. The projection to 3/31/09 is sensitive to errors in earnings forecasts.
In summary, using the average P/E to calculate a value-supported level for stock prices generates a reasonably good fit between modeled and actual behaviors of the S&P 500 index over long periods.
