What January’s market decline means for stock returns in 2021

You’ll be seeing lots of references to this indicator in coming days, now that January is officially in the record books as a “down” month — with the S&P 500 SPX, +0.60% slipping 1.1%. I have written before that the January Predictor rests on a shaky statistical foundation. Financial headlines will nevertheless trumpet the allegedly negative implications of January’s decline for the remainder of 2021.

So let me point out a few other ways in which the Predictor is not worth following.

What’s so special about January?

A good place to start is to recall that January 2020 was also a down month (declining 0.2%) and yet the subsequent 11 months produced a well-above-average gain of 18.4% (assuming dividends were reinvested).

That’s just one data point. Another clue that there’s nothing particularly special about January is that other months have even greater predictive “powers” when forecasting the stock market’s direction over the subsequent 11 months. Since the S&P 500’s creation in 1954, in fact, June has the strongest forecasting ability, followed by February. January is in third place.

Why, then, don’t you read about a June Predictor, or a February Barometer? My hunch is that adherents are less motivated by statistical rigor than by stories and narratives that capture their attention. From a behavioral point of view, the calendar year is a more natural period on which to focus than the February-to-February or June-to-June periods. But psychological significance is different than statistical significance.

The importance of real-time tests

There’s another tell-tale sign that the January Indicator isn’t all that it is cracked up to be: It doesn’t pass real-time tests.

By this I mean tests conducted after it was initially “discovered.” If the January Predictor had been able pass these tests, we would have much greater confidence that it isn’t merely the result of a data-mining exercise in which the historical data are tortured long enough to make a pattern emerge.

But it wasn’t able to. As far as I can tell, the real-time test of the January Predictor begins in 1973. That’s the earliest mention of it on Wall Street, according to an academic study on the subject. Unfortunately, its record since is far less impressive. Since 1973, in fact, not only is it not significant at the 95% confidence level that statisticians often use when determining if a pattern is genuine, it is not significant at even the 85% level.

We shouldn’t be surprised; actually, the January Predictor is in good company. Consider a study that appeared last May in the Review of Financial Studies. It examined 452 supposed statistical patterns (or “anomalies”) that prior academic research had found to exist. The authors of this recent study were unable to replicate these results in 82% of the cases. The remaining 18% turned out to be much weaker than originally reported.

No correlation between the magnitude of January’s rise and return over next 11 months

Yet another clue that the January Predictor rests on a shaky statistical foundation is that there is no correlation between the strength of the market in January and its gain over the subsequent 11 months. If there were such a correlation, we might be able to concoct a plausible narrative about investor confidence at the beginning of the year carrying over for the rest of the year.

But there is no such correlation. Because of that absence, to believe in the efficacy of the January Predictor you’d have to believe that a S&P 500 gain of just 0.01 carries just as much predictive power as a gain of 13.2%. That strains credulity.

By the way, I chose this 13.2% in my illustration because it is the biggest January gain for the S&P 500 since its creation in the mid-1950s. That came in 1987. From Jan. 31 of that year through the end of 1987, the S&P 500 lost 9.9%.

To profit from a statistical pattern, you must follow it religiously for years

Finally, even if the January Predictor rested on a solid statistical foundation, you would need to act on it for many years in a row in order to rationally go about trying to profit from it. A good rule of thumb in statistics is that you need a sample of at least 30 before patterns become meaningful. In the case of the January Predictor, this means you would need to follow it for three decades. Furthermore, during those 30 years you would undertake no other transactions except shifting into a 100% equity allocation every Jan. 31 in which the stock market rises in January, and into a 0% allocation if the market in January is down.

Absent that patience and discipline, you are doing little to improve your odds above that of a coin flip.

The bottom line? For all intents and purposes, you can conclude nothing from the stock market’s January decline about where it will stand on Dec. 31.