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An empirical analysis of mean reversion of the S&P 500’s P/E ratios

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Abstract

Numerous authors have suggested that the price-earnings (P/E) ratio can be used to predict the future movement of stock prices. Such arguments are based on the belief that P/E ratios are mean-reverting. However, are the S&P P/E ratios really mean reverting? A review of the literature finds arguments on both sides, but the issue of mean reversion has not been tested adequately. Using unit roots and multiple structural breaks, we explicitly show that the P/E ratio is stationary around multiple breaks, which means that it will eventually revert to some long-run means. This result supports evidence that high P/E ratios relative to the current long-run mean will be followed by slow growth in stock prices and/or high earnings growth.

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Notes

  1. Although not discussed here, the P/E ratio can be derived from the Gordon (1962) basic stock valuation model where the price of a stock reflects present value of expected dividends.

  2. Our results are consistent with the finding of Carlson et al. (2002) who examined the pattern of structural changes in price earning ratios. However, our analysis differs from their analysis. The mean reverting property is assumed in their analysis, while we examine the basic underlying question of whether price earning ratios are mean-reverting or not.

  3. GAAP Net Income excluding discontinued operations and extraordinary items.

  4. See the Appendix.

  5. Carlson et al. (2002) provide strong evidence of structural change by using the tests that assume stationarity of the series.

  6. More complex regime-switching models have been proposed in the literature. However, it is not the purpose of this paper to find the best fitting nonlinear model for the P/E ratio, but rather to reconcile the statistical evidence with our theoretical prior of mean reversion. As it turns out, this rather simple regime-switching model is sufficient for this purpose.

  7. http://www.econ.yale.edu/∼shiller/data.htm

  8. We used p = 2 for all regime switching models estimated in this paper. It also appeared reasonable to restrict the analysis to two regimes. As it is not the purpose of this paper to find the best regime switching models no further discussion on these choices is provided.

  9. As the sampling frequency decreases, the same transition probability indicates a longer time for which the process is expected to stay in Regime 1.

  10. Note that the probability of being in Regime 1 is 1 minus the probability of being in Regime 2, with the latter being displayed in Fig. 5.

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Correspondence to Junsoo Lee.

Appendix

Appendix

Table 4 ADF and enders-granger threshold AR unit root tests

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Becker, R., Lee, J. & Gup, B.E. An empirical analysis of mean reversion of the S&P 500’s P/E ratios. J Econ Finan 36, 675–690 (2012). https://doi.org/10.1007/s12197-010-9145-8

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