Stock Market Earnings Yield and Inflation Over the Long Run

Is there a reasonably stable relationship between the stock market earnings yield and the inflation rate hold for “ancient” data? To answer this question, we turn to the very long run dataset of Robert Shiller. Using monthly data for the S&P Composite Stock Index, aggregate earnings for the stocks in this index, the consumer price index and the long-term interest rate over the period January 1871 through March 2008 (1,647 months), we find that:

The following chart shows the monthly behavior of the earnings yield (E/P) for the S&P Composite Stock Index minus the 12-month trailing inflation rate (I) over the entire sample period, along with a best-fit trend line. Based on this dataset, the real earnings yield (E/P-I) is far more volatile before than after 1961.

What does the real earnings yield look like since 1961?

The next chart shows the monthly behavior of the real earnings yield for the S&P Composite Stock Index since 1961. The average real earnings yield over this “quiet” recent subperiod is 2.38%. Relatively low data quality in “ancient” times may account for some of the apparent regime shift of the 1960s, as might changes in regulations, investing vehicles and the speed of information flow.

Does the level of variability in the real earnings yield affect the average real earnings yield demanded by investors?

The next chart shows the the average monthly real earnings yield and the standard deviation of the monthly real earnings yield for the S&P Composite Stock Index by decade over the entire sample period. It suggests a positive relationship between the variability of the real earnings yield and the yield demanded by investors. It also confirms the impression of a regime change about 1961.

For a different perspective on this mean-variance relationship, we use a scatter plot.

The following scatter plot relates the average monthly real earnings yield to the standard deviation of the monthly real earnings yield for the S&P Composite Stock Index by decade over the entire sample period. The R-squared statistic for a best-fit power law curve is 0.56, indicating that the level of variability in the yield explains over half its average value. (The R-squared statistic for a best-fit line is 0.50.)

Does the long-term interest (bond) rate work more reliably than the inflation rate as a hurdle for the nominal earnings yield?

The next chart shows the monthly behavior of the earnings yield (E/P) for the S&P Composite Stock Index minus the long-term interest rate (R) over the entire sample period, along with a best-fit trend line. It shows that R (representing a long-term bond yield) was often higher than the equity earnings yield in “ancient” times, but has been consistently lower since the mid-1950s.

How does the average of (E/P-R) compare to the average (E/P-I) in subperiods?

The next chart compares the average real earnings yield (E/P-I) to the nominal earnings yield minus the bond yield (E/P-R) for the S&P Composite Stock Index by decade over the entire sample period. The latter is is negative in four decades early in the sample and is not as “calm” as the real earnings yield since 1961.

Does variability help explain the variation in the average (E/P-R)?

The final chart compares the ratio of average to standard deviation for both (E/P-I) and (E/P-R) for the S&P Composite Stock Index by decade over the entire sample period. This ratio is fairly regular for the former and highly irregular for the latter. In fact, average (E/P-R) very weakly tends to be lower when variability in (E/P-R) is higher, with variability explaining less than 10% of the change in the average.

In summary, long-run data offers stronger evidence for a stock market model based on the real earnings yield than for a model that compares the earnings yield to the long-term bond yield. It also suggests: (1) a substantial structural break in the relationship between earnings yield and inflation about 1960; and, (2) the possibility of using real earnings yield variability in estimating an expected real earnings yield.

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