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Reader Wes Williams of Stafford TX conjectured that our Real Earnings Yield (REY) Model and Reversion-to-Value Model, both of which use actual and projected S&P earnings, might be improved using results from "Stock Returns, Aggregate Earnings Surprises, and Behavioral Finance" by Jonathan Lewellen, S. P. Kothari and Jerold Warner (LKW). He notes that this research finds that stock market returns are generally low when aggregate corporate earnings are highest, and that returns are greatest (28% annualized) when earnings decline by 10-15% from the same quarter in the previous year.
This February 2003 paper explores the relationship between overall stock market behavior and aggregate corporate earnings, looking for parallels with firm-level price-earnings behavior. Using quarterly data for 1970-2000, they conclude that:
To evaluate this research, we first look at raw data over the period covered by our REY Model, which is driven by corporate operating earnings and the inflation rate (arguably a proxy for the discount rate).
The following chart depicts the relationship between quarterly returns for the S&P 500 index (representing the overall stock market) and the concurrent quarterly year-over-year (YOY) changes in aggregate operating earnings for the same companies since 1990. Data inside (outside) the LKW sample is show in blue (red). No relationship is apparent visually. The Pearson correlation between these two variables over the entire period is .03, further indicating no relationship. For the out-of-sample data alone, the correlation is .09. This result does not confirm LKW's conclusion that "overall stock market returns are negatively correlated with concurrent aggregate earnings." It may be that discount rate shocks (inflation rate) dominate cash flow shocks (earnings growth) for LKW, who include data from the inflation-volatile 1970s and 1980s. For our analysis, covering a more tame period of inflation, discount rate shocks and cash flow shocks may be more in balance.
Note that earnings are, in fact, not released until the quarter after the concurrent quarter. However, lagging the returns by one quarter produces about the same correlation.
The above chart looks at the earnings (cash flow shock) side of the REY Model. The next chart looks at the inflation rate (discount rate shock) aspect of the model. It depicts the relationship between quarterly returns for the S&P 500 index and the concurrent average quarterly inflation rate since 1990. Data inside (outside) the LKW sample is show in blue (red). Again, no relationship is apparent visually. The Pearson correlation between these two variables over the entire period is -.01, further indicating no relationship. For the out-of-sample data alone, the correlation is .11.
LKW suggest that earnings and discount rates move together over time, so the next chart depicts the relationship between the average quarterly inflation rate and the concurrent quarterly YOY change in aggregate operating earnings since 1990. Data inside (outside) the LKW sample is show in blue (red). The Pearson correlation between these two variables over the entire period is -.34, indicating that there may be a relationship, though not the one perhaps expected. When we lag the inflation data by four quarters, the correlation flips to a positive .16, so perhaps high earnings growth stimulates future inflation. This results tends to confirm the LKW suggestion that "earnings and discount rates move together over time." For the out-of-sample data alone, the concurrent correlation is -.23. When we lag the inflation data by four quarters, the correlation flips to a positive .61.
In summary, neither change in aggregate earnings nor the inflation rate alone is a good concurrent indicator for the overall stock market returns on a quarterly basis. However, because earnings growth and inflation are interrelated, they may together help forecast stock market behavior.
Note that the samples used here, especially the out-of-LKW-sample subset, are small and the results therefore tentative.
These results are analogous to those described in our blog entry of 4/21/06, which describes recent research by Hui Guo and Robert Savickas finding that:
Used together, overall stock market volatility and average idiosyncratic volatility reliably forecast stock market returns during 1927-2005. Neither overall stock market volatility nor average idiosyncratic volatility alone reliably forecasts stock market returns. Overall stock market volatility reflects the volatilities of both cash flow shocks and discount rate shocks, but overstates discount rate shock volatility. Average idiosyncratic volatility, which reflects the volatility of discount rate shocks only, corrects this overstatement.
It seems that LKW, by finding that past aggregate earnings do not relate to stock market returns, back into a conclusion similar to that reached by Guo and Savickas -- that the relationship between aggregate earnings and the discount rate interferes with the ability of either alone to predict stock market behavior. In the REY Model, we account for both cash flow shocks (changes in aggregate earnings) and discount rate shocks (changes in the inflation rate). In contrast, the RTV Model uses only aggregate earnings as the driver of returns.
For related research, see Blog Synthesis: Valuation Based on Fundamentals and Blog Synthesis: The Economy and the Stock Market.
