The U.S. stock market’s odds of rising this year did not go up because it rose over the first five trading days of the year.

I had thought my column on this subject from three weeks ago would have been enough to prevent the bulls from making such claims about this so-called “First 5 days of January” indicator. But I was wrong.

One analysis that made the rounds on Wall Street this week argued that whenever the stock market rises by more than 1.5% over the first five trading sessions of January, it’s higher for the full year more than 90% of the time. That certainly appears to be good news, since the Dow Jones Industrial Average
DJIA,
-0.40%

rose 1.6% over the first five sessions of this month and the S&P 500
SPX,
-0.58%

gained 1.8%.

Unfortunately, this happy conclusion is based on a statistical sleight of hand which, when corrected, makes the alleged pattern disappear.

This doesn’t mean the U.S. market won’t rise this year. The best bet is that it will, since it rises far more often than it falls. My point is that the odds of an “up” year don’t change because of how the market performed in the first five days of this month.

The sleight of hand traces to years in which the stock market rose over the first five trading sessions of January and then fell from then until the end of the year — but still finished higher than it was on Jan. 1. So while these years appear to be a success for the ‘First Five Days’ indicator, they actually are a failure. When correcting for this sleight of hand, the indicator does not have a statistically significant success rate.

The chart below reports the odds based on the Dow back to its creation in 1896. The Dow has risen in 67% of the calendar years since then, so if we assume the future is like the past, there’s a two-out-of-three chance it will rise this year too. If we focus on just those past years in which the market rose over the first five days, the odds of it rising thereafter through the end of the year increase modestly to 70%. That increase from 67% to 70% is not significant at the 95% confidence level that statisticians often use when determining if a pattern is real.

The same conclusion applies if we focus on just those years in which the market rose by more than 1.5% over the first five trading sessions. Though in 75% of those years the market rose from then until the end of December, the difference between those odds and those that exist in all years is not statistically significant.

Does the full month of January have any forecasting significance?

Bulls who are disappointed by my analysis may decide to shift their attention to the so-called January Barometer, according to which the full month of January foretells the direction of the market for the subsequent 11 months. It’s too early to know if the market will register a gain for all of this month, but as of mid-month this looks likely.

So let me pre-emptively focus on this indicator, in anticipation that you will be reading a lot more about it in coming days. As you can see from the chart, its historical odds of success are no better than those that exist for the other indicators based on the market’s early-year performance.

The bottom line: It’s the rare seasonal pattern that satisfies even minimal levels of statistical significance. Those based on January are not the exception.

Mark Hulbert is a regular contributor to MarketWatch. His Hulbert Ratings tracks investment newsletters that pay a flat fee to be audited. He can be reached at mark@hulbertratings.com

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