# A Twist on the 'January Effect'

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by: Justin Bynum

Given the incredible number of bogus market timing "strategies" in existence, I was initially skeptical of the January Effect. However, much to my surprise, there is strong statistical evidence that the stock market’s performance in January is a reasonable proxy for market performance over the entire year. In fact, a simple regression suggests that, on average, a negative January will result in zero subsequent annual returns. Regression results for the stock market (as measured by the S&P 500 employing Robert Schiller’s data) since 1900 are listed immediately below:

Observations: 107
Intercept Coefficient 0.0%
Positive January Coefficient 15.9%
Positive January Coefficient P Value 1.1-4
F 16.1

*Assumes all dividends reinvested

Clearly, with only 10% of annual returns explained by positive returns during January, there are a number of other factors at work. However, it should be noted that the January Effect is not only more statistically robust but also more predictive of subsequent market returns than other, more popular metrics such as PE ratios, Interest Rates, and The Fed Model.

In light of the above results, a thought occurred to me: how could I go about increasing the explanatory power of the January Effect? For starters, rather than using simple dummy variables (1 for a positive January, 0 for a negative), I could use the actual returns during January. Doing so produced the following results:

Observations: 107
Intercept Coefficient 6.7%
Actual January Return Coefficient 2.4
Actual January Coefficient P Value 1.8-4
F 15.1

Going backwards is frustrating to say the least. Fortunately, another thought came to mind: what if January is not the only month useful in predicting future returns. I knew from past experience that the stock market experiences seasonality (however small); why not test other months?

I started by including the prior year’s November and December returns with the January return. Using dummy variables, I assigned positive returns from those three months a 1 and negative returns a 0. Again, all dividends are assumed to be reinvested. The output:

Observations: 107
Intercept Coefficient -1.7%
Positive January Coefficient 18.6%
Positive January Coefficient P Value 2.8-6
F 24.5

Now we’re getting somewhere!

I wondered if adding even more prior months might help. My hypothesis was no – the market exhibits seasonal tendencies, so adding October, September, etc. would probably harm my analysis – but what a big no it turned out to be. Adding the prior October produced the following:

Observations: 107
Intercept Coefficient -3.7%
Actual January Return Coefficient 11.3%
Positive January Coefficient P Value .9-3
F 7.2

Adding even more summer/fall months only made things worse. Finally, in terms of preceding months, I thought of adding January through April. Without getting into it, that was also a dead end.

I could have stopped here with the satisfaction of knowing that I had improved upon the January Effect, but a seven percent bump in explanatory power wouldn’t make my investigative efforts worth publishing. I needed more.

Culling through my various other analyses I’ve performed was exhausting. Even more frustrating, most of the variables that assist in explaining long-term stock market performance are all but worthless given a one year time frame. In the end, and ironically enough, PE ratios proved to be the charm. Using the same parameters as those for the November-January time period, I simply plugged PE ratios in and stood back. My results were pretty fantastic for a two-variable regression:

Observations: 107
Intercept Coefficient 10.2%
PE Coefficient -.95%
Positive January Return Coefficient 21.9%%
PE Coefficient P Value 6.7-4
Positive January Coefficient P Value 3 .9-8
F 19.7

Yes, F went down from my best single regression model, but the drop is due to a decrease in the degrees of freedom. Notice that the P Value increases substantially for the Positive January Coefficient.

Now that I had an equation, I needed to decide how to use it. My strategy was simple: if the predicted return of the stock market was less than the treasury rate at the end of January, I would switch from stocks to bonds for the balance of the year. The drawback, of course, was that I would be at the mercy of the market throughout January. But, as previously mentioned, January is one of the most innocuous months of the year for stocks, so the risk appeared reasonable. Finally, I like this model because it’s about as no-frills as strategies come. High P/E, Negative January, High Interest Rates? Bonds it is. Here’s how my hypothetical strategy would have performed.

Buy and Hold PE+Modified January Effect
Average Annual Return 11.7% 13.8%
Standard Deviation 19.2% 15.0%

Lower volatility and higher returns: what’s not to like? One thing I didn’t test for but would probably boost returns even higher is staying in nascent bull markets rather than bailing simply because the January indicator is negative. However, overall, a very simple, mechanical strategy worth over 2% more than buy and hold is impressive, and possibly worth exploring further to assess the impact of taxes and other factors.