# January Barometer Over the Long Run

February 14, 2018 • **Posted in** Calendar Effects

Does long term data support the belief that “as goes January, so goes the rest of the year” (January is the barometer) for the the U.S. stock market? 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. Because average monthly levels differ from monthly closes, we run all tests also on the S&P 500 Index. Using monthly levels of the S&P Composite Stock Index for 1871-2017 (147 years) and monthly and daily closes of the S&P 500 Index for 1950-2017 (68 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 1872-2017. The Pearson correlation between the two series is 0.21 and the R-squared statistic is 0.04, indicating that January returns explain 4% of the variation in returns for the balance of the year. Something else (or randomness) explains the other 96% of variation in February-December returns.

For the subperiod during which S&P 500 Index data are available (1950-2017), the correlation is 0.30 and the R-squared 0.09. January is a better barometer in recent data.

Is there an important non-linearity in barometer readings?

The next chart summarizes average S&P Composite Stock Index February-December returns by ranked fifth (quintile) of same-year January returns over the entire sample period. Quintile size is a fairly small 29 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.

Since the Shiller data calculates the monthly index level as the average daily close during a month rather than monthly closes, we compare the above results to those for monthly closes of the S&P 500 Index.

The following scatter plot relates the return for the S&P 500 Index during February-December to the return for the immediately preceding January over the period 1950-2017. For this calculation, we approximate the January 1950 return using the opening level for that month (no December 1949 close is available). The Pearson correlation between the two series is 0.26 and the R-squared statistic is 0.07, indicating that January returns explain 7% of the variation in returns for the balance of the year. Something else (or randomness) explains the other 93% of variation in February-December returns.

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 from three sets of data:

- Shiller since 1872.
- Shiller since 1950.
- S&P 500 Index since 1950.

For the entire Shiller data series, January is no better than April, May, August or December as a predictor of subsequent 11-month returns. For the Shiller and S&P 500 Index data since 1950, January is the best predictor of returns over the next 11 months. These results indicate that barometer power is sensitive to sample period, undermining belief in a reliable January barometer.

As a further robustness test, we repeat for two 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 (34 years each). Results are not consistent across subperiods. During the older (more recent) subperiod, January is the best (tied for fourth best, or fifth best including contrarian indications) predictor of subsequent 11-month returns. In the recent subperiod, January return explains only 0.6% of the variation in subsequent 11-month return.

The inconsistency suggests that: (1) investors operating in real time may draw different conclusions about the January barometer at different times; and, (2) belief in the January barometer derives from mid-20th century data.

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

The following scatter plot relates the annual return for the S&P Index during 1950-2017 to the return for the first five trading days of the same year. The Pearson correlation between the two series is 0.26 and the R-squared statistic is 0.07, indicating that the return for the first five trading days of January explain 7% of the variation in return for the same entire year.

However, the Pearson correlation is 0.49 for the first half of the sample and 0.03 for the second half, suggesting that belief in this barometer derives from old data.

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.*

In other words, belief in the January barometer based on mid-20th century data did not help investors in recent decades.

Cautions regarding findings include:

- As noted, the monthly stock index level in the Shiller data is the average daily close during the month, and not the monthly close, thereby blurring monthly return calculations.
- S&P 500 Index subsamples are modest for inference.
- Market behaviors (including seasonality) may change as the market environment changes, such that seasonality is real but dynamic.

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