#### The January barometer

The January barometer is the claim, often mentioned in financial circles, that the performance of the stock market in January is a reliable portend of its performance for the full year — as January goes, so goes the year. The term was first coined by Yale Hirsch in 1972.

Many market analysts take it quite seriously. For example, a BofA-Merrill Lynch Global Research Report asserts “Based on S&P 500 data going back to 1928, January is a good predictor of the year.”

As another example, CNBC reports

The January barometer has been right in 62 of the last 85 years, or 73 percent of the time. Since 1929, the index followed January’s direction 80 percent of the time when it finished positive, and 60 percent of the time, when it finished negative. More recently, in the past 35 years, the S&P 500 followed January’s direction 25 times, or 71 percent of the time.

#### Analysis

However, there is one major problem with these analyses — whether or not the S&P500, for example, goes up in a given year is not a 50-50 coin flip; instead, the S&P500 has risen for 63 out of the 85 years, and down only 22 years, i.e., it is up 74.12% of the time.

Thus consider this “rule” instead: At the first of January, toss a weighted “coin” (a pseudorandom number generator will do) with head-weight = 74.12% (this is, after all, an entirely reasonable predictor). As it turns out, this rule correctly predicts the outcome of the S&P500 for the year, positive or negative, 61.7% of the time over the past 85 years (based 1000 pseudorandom trials) — not quite as good as the January barometer, but not that much different either.

However, most would agree that the history of the stock market in the early 20th century is hardly relevant today. So let’s take just the 35-year period from 1981 through 2015. Here the market was up 29 times out of 35, or 82.86%. So let’s toss a weighted “coin” with head-weight = 82.86%. Then this rule is correct 71.8% of the time over the past 35 years (again based on 1000 pseudorandom trials), which is identical to the January barometer performance.

Actually, one can deduce these performance figures mathematically, simply by noting that the probability of a correct prediction is p^{2} + (1-p)^{2}, where p is the probability of “heads” in the coin toss. So when we plug in p = 63/85, we obtain 61.6%, and when we plug in p = 29/35, we obtain 71.6%, in each case agreeing very well with the empirical results above.

#### Conclusion

While the January barometer performs slightly better than a weighted coin toss for the 85 year period 1931-2015, it is not any better than a weighted coin toss for the more recent period 1981-2015. It is reminiscent of the Halloween Indicator, which as we showed in an earlier Math Drudge blog, has little if any substance.

All widely circulated “rules” of this sort have a fundamental flaw: Insomuch as they rely on, say, S&P500 year-end averages or other coarse annual data, they are statistically overfit — there is not nearly enough such data in, say, the past 35 years, to produce rules with solid, non-random statistical significance.

Data over a longer time horizon, even going back to the Great Depression or before, is certainly available, but it is of highly questionable relevance today. This is especially true given the rise of computerized trading in recent years, which means that any trends or patterns that may exist in data are spotted (and neutralized) by sophisticated computer programs long before human analysts see them.

In short, it is folly to think that a simple rule of thumb such as the “January barometer” has any effectiveness in today’s highly mathematical, computerized market. There are no slick tricks to wealth, and no substitute for patient, long-term, low-cost investing.