## Fun with statistics

This post was provocative about the “January Effect” – whether January is a good indicator of the performance of the rest of the year.

There have been 72 Januaries since 1940, and of those, when January is positive, the year is positive in all but 7 years. so that implies that a positive January has a correlation to positive overall years.

But not so fast! says Ritholtz, who points out that in the years that January was negative, the year was positive in 14 years – in other words, a “false negative”.

He then adds those two sums together to point out that as a barometer, January sucks – the stock market goes up 72% of the years, and if January is wrong 29% of the time, that means that it’s no better a barometer than just assuming the market will go up.

And if we were still in December, and making a ‘hedge’ bet or some other fancy financial gamble that based our year’s portfolio on what happens in January, then I would definitely agree.

But the fact is, we are in February, and we now *know* what happened in January. And January was up. And in the years that January was up, the year was up 87% of the time. We can safely discard the other years.

Let me put it to you another way. Let’s say the average resale value of an average 2012 car is 30% of its purchase price in 5 years. If you chose a car at random, you’re likely to get one that’s worth close to 30% of its value in 5 years. Having said that, when you dig further, you find that the import cars have an average 36% resale value in 5 years, and the average domestic car has a 28% resale value in 5 years.

So if you randomly choose an import car, you can expect that your average resale value would be closer to 36%. You’re drawing from a smaller population, with a different set of probabilities than the larger population.

I’m just a statistical neophyte, so it’s possible my interpretation is totally off. But I feel pretty strongly that knowing more information changes your probabilities.

Honestly, I hope I’m not right. Because either Ritholtz *doesn’t* know this, and is really bad at his field, or he *does* know this, and is deliberately trying to mislead his readers for some agenda of his own.