January Barometer Over the Long Run

Does long term data support belief that “as goes January, so goes the rest of the year” (January is the barometer) for the the U.S. stock market? Could this conventional wisdom be an artifact of data snooping or a victim of market adaptation? Robert Shiller’s long run sample, which calculates monthly levels of the S&P Composite Stock Index since 1871 as average daily closes during calendar months, offers data for testing. Using monthly levels of the S&P Composite Stock Index for 1871-2011 (141 years) and monthly closes of the S&P 500 Index for 1950-2011 (62 years), we find that:

The following scatter plot relates the return for the S&P Composite Stock Index during February-December to the return for the immediately preceding January over the period 1872-2011. The Pearson correlation between the two series is 0.23 and the R-squared statistic is 0.05, indicating that January returns explain 5% of returns for the balance of the year. Something else (or randomness) explains the other 95% of February-December returns.

Is this (weak) relationship reliable across subperiods?

The next chart compares Pearson correlations between the S&P Composite Stock Index return for January and the return for February-December of the same year over the entire sample period and three approximately equal subperiods (46-47 years each). Correlations are consistently positive but varying in magnitude for subperiods. The inconsistency suggests that investors operating in real time may draw different conclusions about the January barometer at different times.

Is there an important non-linearity in barometer readings?

The next chart summarizes average S&P Composite Stock Index February-December returns by quintile of same-year January returns over the entire sample period. Quintile size is a fairly small 27-28 observations. While there is some indication that the most negative (positive) January returns relate to poor (good) returns the rest of the year, the progression is not systematic, undermining belief in a reliable relationship.

Is the return for January more predictive of the return for the next 11 months than are returns for other individual months?

The next chart summarizes the correlations between the return for each of the 12 calendar months and the return for the immediately following 11-month intervals. Since the Shiller data calculates monthly index levels as average daily closes during months (perhaps representing typical investor experience) rather than monthly closes, we compare results for the Shiller sample to those derived from monthly closes of the S&P 500 Index during 1950-2011. Since there is no December 1949 closing value for the index, we calculate the January 1950 return using the open for the month.

For the long run Shiller data, January is no better than April, May, August or December as a predictor of subsequent 11-month returns. For S&P 500 Index data, January is the best predictor (though still not a strong one). This inconsistency, indicating that results are sensitive to sample period and/or return calculation method, undermines belief in a useful January barometer.

As a further robustness test, we repeat for S&P 500 Index subperiods.

The next chart summarizes the correlations between the return for each of the 12 calendar months and the return for the immediately following 11-month intervals for the S&P 500 Index during two equal subperiods (31 years each). Results are not very consistent across subperiods. During the older (more recent) subperiod, January is the best (fifth best) predictor of subsequent 11-month returns. In the recent subperiod, January returns explain less than 1% of subsequent 11-month returns.

The inconsistency suggests that investors operating in real time may draw different conclusions about the January barometer at different times. The inconsistency further suggests that belief in this barometer derives from old randomness or that the market has adapted to its recognition.

What about the first five days of January, sometimes encountered as an alternative January barometer?

The following scatter plot relates the return for the S&P Index during 1951-2011 to the return for the first five trading days of January during the same year. The Pearson correlation between the two series is 0.25 and the R-squared statistic is 0.05, indicating that the return for the first five trading days of January explain 5% of the return for the balance of the year.

However, the Pearson correlation is 0.55 for the first half of the sample and 0.00 for the second half, further suggesting that belief in this barometer derives from old randomness or that the market has adapted to its recognition.

In summary, evidence from long-run data indicates that U.S. stock market behavior in January is not a reliable indicator of its behavior for the following February-December.

Cautions regarding findings include:

• S&P 500 Index subsamples are small for inference.
• To the extent return distributions are wild rather than normal, usefulness of linear correlations as predictors breaks down.

You May Also Enjoy...

• Optimally Exploiting the January Barometer
• The January Barometer Retested
• January Effect Over the Long Run
• Persistence of the January Effect
• January Effect Alive and Well?