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In our Real Earnings Yield Model, we argue that inflation at the consumer level is fundamentally a wealth discount rate important in determining the value of equities to investors. Do investors therefore reliably react over the intermediate term to changes in CPI as a measure of the wealth discount rate? Using monthly historical CPI data (for all items, not seasonally adjusted) from the Bureau of Labor Statistics (BLS) and contemporaneous S&P 500 index data for the period January 1994 (the earliest for which release dates are available) through May 2008 (173 months), we find that:
The following chart shows CPI and the S&P 500 index over the entire sample period, with axes truncated to enhance overlay. S&P 500 index values are the opening levels on (pre-market) CPI release dates. Both indexes tend to rise over time, with stock prices more volatile than consumer prices. Visual inspection suggests there may be a negative correlation between them, with aggregate stock prices tending to advance (decline) when CPI falls or rises slowly (rises quickly).
For a closer look at the relationship between the two series, we compare monthly changes in CPI to monthly changes in the S&P 500 index.
The following scatter plot relates the monthly change in the S&P 500 index (between CPI releases) to the prior-month change in CPI. There is a weak negative relationship between the the two series, with a Pearson correlation of -0.12, suggesting that stocks do tend to advance (decline) as CPI falls (rises). However, the R-squared statistic is 0.00, indicating that the relationship is so dispersed that monthly changes in CPI explain nothing about stock market movements over the next month.
Is there any significant lead-lag relationship between monthly changes in CPI and monthly stock behavior?
The next chart shows the Pearson correlations for various lead-lag relationships between monthly changes in CPI and monthly changes in the S&P 500 index (between CPI release dates). Offsetting the two series such that changes in CPI lead and lag changes in the S&P 500 index by 0-6 months produces waves of small correlations, perhaps due to reversals in CPI every few months. There is not much of a signal for monthly trading. It seems that the stock market has already incorporated any discount rate changes implied by CPI releases.
What if the relationship is cumulative, significant not for monthly changes but perhaps for quarterly changes?
The next scatter plot compares the quarterly change in the S&P 500 index to the prior-quarter change in CPI for the entire sample period (60 quarters). There is a slight positive relationship between the the two series, with Pearson correlation 0.09. However, the R-squared statistic is just 0.01, implying that quarterly CPI changes explain only 1% of next-quarter stock market movements. The relationship is again too dispersed to motivate trading.
Is there any significant lead-lag relationship between quarterly changes in CPI and quarterly stock behavior?
The final chart shows the Pearson correlations for various lead-lag relationships between quarterly changes in CPI and quarterly changes in the S&P 500 index. Offsetting the two series such that changes in CPI lead and lag changes in the S&P 500 index by 0-4 quarters suggests that the relationship between CPI and stock prices is most likely negative/coincident. Again, it seems that the stock market has already incorporated any discount rate changes implied by CPI releases.
In summary, CPI data alone is not useful for intermediate-term trading of the broad stock market. A good three-month inflation forecast is apparently needed to exploit any intermediate-term relationship between CPI and stock prices.
Note that this analysis may contain a small amount of revision bias because BLS occasionally adjusts old data.
For analysis of other macroeconomic indicators, see Blog Synthesis: The Economy and the Stock Market.
