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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.

**by Georg Vrba, read the full article here.**