Consistent with their bullish mood and histrionic reporting, CNBC talking heads are touting that the stock market’s performance in just ended January was the best in 15 years and that when it has been up, the rest of the year has been up 87% of the time.

The statistical truth is that January’s performance has no meaningful impact on the rest of the year, as the following analysis demonstrates. Especially note 1987, where that January was three times stronger than this January and during the next 11 months the stock market declined 9.9%, which even included a little rebound from the devastating 1987 Crash. Do you remember 1987 being characterized as a bullish year?

What we call the All-January Barometer* has had seven false positives since 1940, where January was up, but the rest of the year was down. If dividends are considered then there were six false positives, since from February through December of 1947 the U.S. stock market experienced a negative price-only return, but a positive total return for those following11 months.

BBBBBJanuary Rest of Year

1946 +7.0% -17.6%

1947 +2.4% -2.3%

1966 +0.5% -13.5%

1987 +13.2% -9.9%

1994 +3.3% -4.6%

2001 +3.5% -16.0%

2011 +2.3% -2.3%

Last year, 2010, the All-January Barometer was a false positive since it did not work: January was up 2.3% and the rest of the year declined 2.3%, The previous year, 2010, was by far the biggest of the 14 false negatives since 1940, since January was down 3.7%, but the rest of the year was up 17.1%.

In conclusion, January has failed to signal the direction for the rest of the year 20 to 21 out of the past 72 years, or about 29% of the time.*

And being correct 71% of the time** is statistically the same as betting that the stock market will be up every year, which it has been 52 out of the 72 years since 1940, or 72% of the time.

*. There are two other well-known January Barometers, which we call the “Jan5-Rest of Jan” and the “Jan5-Rest of Year,” each which use the stock market performance during of first five trading days to project the rest of January and the rest of the calendar year, respectively. They have even lower Bayesian probability (true and false positives and negatives) than the “All-January Barometer”, or what we prefer to less ambiguously call the “Jan-Rest of Year Barometer” as we analyze and present here.

** The historical trend of the Jan-Rest Barometer has been getting worse over time since 13, or 62-65% of the 20 to 21 failures, have occurred during the 34 years since 1978, or the most recent 47% of the 72 years since 1940, which is about a 35% higher rate of failure than the earlier 38 years.

*** This is using Bayesian (true/false) probability analysis with the S&P 500 index (on a price-only basis, or without dividends) since 1951, and the DJIA 30 before 1951. Regression analysis is much more useful since it also takes the magnitude into account, rather than just the positive or negative direction of the stock market’s performance. However, careful analysis of the scattergram chart below shows that the trivial r-squared of 7% is due to small January performances, since the ten largest ones actually have a negatively-slope regression line (red dashed) that has almost twice the r-squared of 13.5%.

*Click to enlarge:*

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