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The wealth discount (inflation) rate is arguably a critical decision input for investors, as it is for our Real Earnings Yield (REY) Model. Investors ought to demand that their stock holdings earn profits at a rate somewhere above the inflation rate. Because of the current misbehavior of that model (and belatedly following up on some reader suggestions), we review here alternative measures of the inflation rate and test their performances with respect to the S&P 500 operating earnings yield (E/P) and the REY Model. Using monthly data for December 1989 through November 2006 (203 months), we find that...
The different shades of the inflation rate that we consider are:
The following chart compares the various inflation rates to the earnings yield. We omit the seasonally adjusted inflation rate because it follows the non-seasonally adjusted rate almost exactly. We match earnings yield data to inflation rate data based on monthly release of the latter in the middle of the next month. The chart shows that the range among inflation rates is usually about 1% and sometimes as high as 2%. The total inflation rates are generally more volatile than the core/trimmed rates, and more volatile than the stock earnings yield. When we test correlations between the non-seasonally adjusted inflation rate and the stock earnings yield by shifting one series timewise, the highest correlation is for coincident data. This result suggests that the inflation rate and stock earnings yield neither lead nor lag each other.
The next chart shows the average inflation rates and average gaps between the S&P 500 operating earnings yield and the various inflation rates. It shows that the volatilities of total inflation rates in comparison with core/trimmed rates tend to cancel over time. It also shows that PCE-based inflation rates tend to be lower than BLS rates, with the real earnings yield of stocks consequently higher. Results suggest that investors require a real earnings yield of 2-3%.
The next chart compares the average gaps between the S&P 500 operating earnings yield and the various inflation rates for four subperiods across the entire sample. It shows that the gaps vary between about 1.5% and 3% for different subperiods. It also shows that the current set of gaps (as of 12/14/06) is generally large in comparison with past subperiod and overall averages, but less substantially for those derived from the core/trimmed inflation rates.
The next chart compares the standard deviations of gaps between the S&P 500 operating earnings yield and the various inflation rates for these same four subperiods. It shows that the variability of the inflation rate-stock earnings yield relationship changes over time, and inconsistently with respect to different measures of the inflation rate.
The following table summarizes the results of inserting the various monthly inflation rate series into the REY Model in terms of statistics for the fit between the model output and actual S&P 500 index. It shows that the total inflation rates provide slightly better general directions and short-term fits than do the core/trimmed rates. It also shows that the inflation rate based on PCEPI offers marginally better statistics than the non-seasonally adjusted inflation rate from BLS (the inflation rate currently used in the model).
The next two charts compare the behavior of the S&P 500 earnings yield to those of the non-seasonally adjusted BLS inflation rate and the PCEPI-based inflation rate. For both, we have ordered the inflation rate series from lowest to highest values over the entire sample period. The horizontal axes are therefore not time-sequential. The scales for the vertical axes are offset by roughly the average difference between the earnings yield and the inflation rate for the entire sample. This offset makes the graphs overlap for ease in seeing how much they do or do not vary together.
The charts show that the earnings yield generally tends to rise with the inflation rate, but the relationship is noisy. The degree to which the earnings yield graph bounces up and down across the inflation rate graph depicts the level of noise (as does the dispersion in a scatter plot). This format facilitates understanding whether the relationship and noisiness are stronger for some values of inflation than for others. The charts indicate that the stock earnings yield may not be sensitive to the inflation rate in the middle of the sample range. The relationship may be more reliable when the inflation rate approaches extremes of its distribution.
In summary, total (rather than core/trimmed) inflation rates produce slightly better outputs from the REY Model for the entire sample period. The PCE-based inflation rate may be a very slightly better indicator for the stock earnings yield than the total BLS inflation rates.
At this point, expecting the model will return to balance, we are making no changes in the REY Model.
It makes sense that the "risk-free"yields on Treasury instruments, such as the 90-day Treasury bill or the 10-year Treasury note, might influence (as a competitor for stocks) the relationship between the inflation rate and the stock earnings yield. However, our attempts to incorporate information from these rates substantially degrade the performance of the REY Model over the entire sample period. It seems that investors in Treasuries do not quickly/reliably respond to the real yields of these instruments.
For related research, see the REY Model.
