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According to its creator, economist Robert Shiller, the relatively high December 2016 cyclically adjusted price-to-earnings (CAPE) ratio of 27.8 signifies an overvalued stock market and predicts a 10-year annualized real return of only 1.5%. But Jeremy Siegel asserts that it incorporates time-inconsistent data, and the failure to correct for changes in accounting methodology led to a substantial under-prediction of realized stock returns in recent decades. He recalculated the CAPE ratio using adjusted-NIPA profits and found much higher forward returns than the CAPE predicts.
To address this problem, I developed a methodology that uses valuations based on a 35-year moving-average of the CAPE ratio instead of its long-term mean.[1] The current value of this ratio predicts a 10-year annualized real (inflation-adjusted) return of 5.8%, similar to the long-term market trend expected value of 5.4%.
The historic long-term market trend
I used the historical data from Shiller’s S&P series to estimate future returns. The best-fit line for the real price of the S&P-composite with dividends re-invested (S&P-real) from 1871 onward is a straight line when plotted on a semi-log scale. There is no evidence to suggest that this long-term trend, which shows an average compound annual real return of 6.7%, will be interrupted. S&P-real and the best-fit line together with its 95% prediction band are shown in Figure-1. (For the equation of the trendline see Appendix A in this Aug-2012 article.)
The historical trend forecast obtained by extending the best fit line indicates a probable annualized real return of 2.8% over the next three years, and 5.4% over the next 10 years.
The Shiller CAPE ratio
Also shown in Figure 1 is the CAPE ratio, which is the real price of the S&P 500 index, divided by the arithmetic average of the last 10 years of real reported 12-month earnings per share of the Index. The CAPE ratio is currently at a level of 27.8. This is 11.1 higher than its 1881-2016 long-term mean of 16.7.
According to Shiller the elevated CAPE ratio level signifies substantial overvaluation of stocks. However, Siegel believes that the failure to correct for changes in accounting methodologies leads to a significant overstatement of the CAPE ratio and the model’s substantial under-prediction of realized stock returns in recent decades. (See The Shiller CAPE Ratio: A New Look and comments by Shiller and Siegel in the Appendix.)
In order to alleviate this problem of time-inconsistent data in the CAPE ratio, an alternative approach to assess stock market valuation would be to use a moving average of the CAPE ratio, rather than referencing the valuation to the 1881-2016 fixed long-term average. This will smooth or eliminate effects on the CAPE ratio from changes in accounting practices, dividend policies, etc.
In my analysis, a 35-year moving average of the CAPE ratio is calculated, currently having a level of 22.3, which is significantly higher than the long-term average of 16.7. The CAPE ratio is therefore only 5.5 above its current 35-year moving average, and the last deltaMA35 is (27.8 / 22.3 – 1) = 25%. This indicates that stocks are not nearly as overvalued as the current level of the CAPE ratio relative to its long-term average would suggest.
What gains (if any) can we expect?
Figure 2 shows the historic 10-year real annualized returns that followed various values of deltaMA35 from Jan-1916 to Dec-2006. The 10-year annualized return diminishes as deltaMA35 increases. The historic 10-year annualized returns that followed for a current deltaMA35 of 25% +/-2% ranged from -2.6% to +11.6%, and the forward 10-year real stock return is 5.8% when calculated from the regression equation.
Figure 3 shows the actual returns together with the forecast returns calculated from the deltaMA35 and the CAPE ratio’s regression equations. From 1999 to the end of 2006 the deltaMA35 predicted- and actual 10-year returns were almost identical (shown in greater detail in Figure 4).
Until 2003 the CAPE ratio’s predicted returns matched closely those calculated from deltaMA35. From then until the end of 2006, the CAPE ratio’s forecast returns were much less than the predicted deltaMA35 returns, and also much less than the actual returns.
For consistency the Shiller CAPE ratio forecast equation was determined over the same period as the deltaMA35 was determined, January 1916 to December 2006.
From Figure 4 above it is evident that the forecast decline of the CAPE ratio since 2003 is not reflected in the forecast returns from the deltaMA35 model.
Comparing the deltaMA35 and the Shiller-Siegel methodologies:
Siegel replaced Standard & Poor’s reported earnings with adjusted national income and product accounts (NIPA) profits in the calculation of the CAPE ratio to forecast a significantly higher forward stock return from January 2015 than what Shiller’s CAPE methodology produced. His results are summarized in Table 3 of his article – The Shiller CAPE Ratio: A New Look – and reproduced here for easy reference.
The deltaMa35 was 24.1% for January 2015. The projected stock return from the deltaMA35 methodology for January 2015 was 5.90%, which exceeds that from the Siegel Total Return CAPE with NIPA profits, the highest value in the Table 3.
As I stated before, deltaMA35 is calculated from the reported earnings, same as Shiller’s CAPE ratio, and can easily be reproduced by using the standard Shiller CAPE excel spreadsheet. The deltaMA35 model does not need replacing Standard & Poor’s reported earnings with adjusted NIPA profits to forecast significantly higher stock returns than the CAPE ratio from 2003 onward.
Conclusion
The current level of the CAPE ratio relative to its 35-year moving average does not suggest that stocks are highly overvalued. From deltaMA35 and the historic long-term market trend the 10-year forecast returns are 5.8% and 5.4%, respectively. Thus, the most likely forward 10-year real annualized return would be about 5.5%.
However, this should not be interpreted to mean that stocks will actually produce a 5.5% return over the next 10 years. From deltaMA35 and the historic long-term market trend the minimum and maximum 10-year forecast returns are -2.6% and 11.2% and -1.3% and 12.6%, respectively. Thus it is possible, but not very likely, that the market could show a small loss over the next 10 years.
Large drawdowns are always possible during a 10-year period. Investments can be protected by following signals from low frequency market-timing models, such as the CAPE Cycle-ID market timer. It is also important to know when a recession is looming, because stocks usually do poorly during recession periods. My Business Cycle Index should provide early warning of an oncoming recession.
Appendix
In this Sep-2014 article Shiller was quoted as follows:
As of yesterday my price earnings ratio was 26.3. There's only three major occasions in US history back to 1881 when it was higher than that. One is 1929, the year of the crash. The other is 2000, which I call the peak of the millennium bubble, and it was also followed by a crash. And then 2007, which was also followed by a crash. But that's only three observations so I don't say that it necessarily has to do the same thing, ...but it is cause for concern.
According to a June 13, 2015 commentary published in The Economist, Jeremy Siegel, a professor of finance at the Wharton School, does not share Shiller’s view on market valuation:
My point is that the earnings series that Mr. Shiller uses has changed substantially since he developed the model some 20 years ago. The mandates of the Financial Accounting Standards Board in the 1990s required firms for the first time to employ “mark-to-market” accounting, a procedure which greatly increased the volatility of reported earnings. Such volatility was particularly evident in the recession that followed the financial crisis when reported earnings fell by a much greater percentage than they had during the Depression of the 1930s, a slump that was five times as great.
The failure to correct for the change in accounting methodology leads to a significant overstatement of the CAPE ratio and the model’s substantial under-prediction of realized stock returns in recent decades. There have been only nine months since January 1991 when the CAPE ratio has been below its mean (signaling undervaluation), while in all but six months since 1981 the realized ten-year returns from stocks have exceeded forecasts using the CAPE model. In fact, the CAPE methodology signaled the stock market “overvalued” in May 2009 when the S&P 500 Index was 920, far less than one-half its current level.
These prediction failures are a result of time-inconsistent data, not a defect in the CAPE model. The Shiller CAPE ratio remains the best tool for predicting long-term real stock returns.
When a time-consistent series of corporate earnings, such as those published in the national income accounts are used instead of GAAP earnings, not only does the predictive power of the CAPE ratio improve, but the current stock market does not appear nearly as overvalued.
Georg Vrba is a professional engineer who has been a consulting engineer for many years. In his opinion, mathematical models provide better guidance to market direction than financial "experts." He has developed financial models for the stock market, the bond market, yield curve, gold, silver and recession prediction, which are updated weekly or monthly at http://imarketsignals.com/. Georg can be reached at [email protected].
[1] I obtained a ratio by dividing the CAPE ratio by its 35-year moving-average from which 1.00 is subtracted, termed deltaMA35. I then calculated a forecasting equation by regressing the forward 10-year annualized stock returns on the corresponding values of deltaMA35. The moving average over 35 years was chosen so that it would cover at least three business cycles based on the longest recent expansion and contraction period from March 1991 to November 2001 of 128 months.
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