# Is December Different for the Stock Market?

This post is motivated by a piece I read over at The Big Picture blog, by Barry RItholtz, who runs a blog I like very much. In that entry, he republishes Jim Bianco’s chart showing average monthly total return (i.e. price + dividends) by month and concludes that December has historically been a good month to be in the stock market, Santa Claus rally or not.

(*Source: Bianco Research via The Big Picture*)

To his credit, Ritholtz points out that the predictive value of a chart like this is very low, but the bars do very much make it seem like December is the best month to be invested. Like kids, we find ourselves wishing that it could be Christmas all year!

I have trouble with charts like these, because the averages need to be compared to the in order to get a sense of whether they are significant in either a statistical or substantive way. I took my own data – created from Robert Shiller’s data on US stock returns and created this chart:

This chart captures the full spread of monthly returns in the postwar period, some 60 years of data. Each point represents the return for one month over that period. Looking at the data like this, December really does not stand out in any particular way, except perhaps for a smaller range of returns – which we discuss further below.

The red and green lines show the highest and lowest mean returns across months (1.4% in January; -0.5% in September). The FULL range of monthly means fits within those lines. Bianco’s chart fits mostly this range, extending slightly beyond, because his range goes from -.75% to 2% rather than -0.5% to 1.4%. Given that this chart has twice as long a history as Bianco’s, it is not surprising that the averages contract towards the mean somewhat.

What does stand out is that the entire range of monthly averages is only a fraction of the possible scatter for each month, which tells us that these averages do not provide much market-timing information. Indeed, an ANOVA analysis says that this data offers little if any reliable timing information (F statistic=1.65, p-value=0.08, R^2 = 2.3%). Most statisticians would not consider this statistically significant, and most people would not consider it substantively tradable unless one can guarantee many, many repeated chances to invest (as opposed to once per year).

Traders perhaps will not demand 95% confidence that statisticians require and be willing to accept a 90% confidence, but even so, the expected differences are small, and the 90% probability is only that “at least one mean is different from at least one other mean” (that difference most likely being that September is different from January). Hardly a great vote of confidence. Even if it were, to profit from this difference reliably would require

- an exceedingly long time horizon, on the order of a human lifespan, while also
- assuming that the past is a reliable representation of the future, and
- running a strategy based on calendar performance alone

My numbers are slightly different from Bianco’s because 1) I use a data history going back to 1946, and 2) Shiller’s data uses the change in average monthly price, rather than the month-end price (I then add on the dividend yield). The main advantage of Shiller’s data is that it goes back further than 1957 and allows looking at a longer return history than Bianco.

If we chart the average total return by month, in the way that Bianco does, we do get a similarly sized and shaped return profile. The numbers are slightly different because of the data source and Shiller’s method, but the overall interpretation is the same (Y axis values are in %)

What is noteworthy about the December is that the month seems to be less volatile, on average, than most other months, as shown by the standard deviation of returns (excess returns i.e. returns minus the return on 90d T-bills).

So the advantage of December appears to be lower risk. Perhaps market participants are eager not to rock the boat too much in December.

The Sharpe Ratio compares the excess return with the standard deviation of those returns. The chart below calculates this risk-adjusted measure for each month and annualizes it (for comparability with other Sharpe Ratios) as an exercise for curiosity’s sake.

All of this does suggest that staying out of the market from June to October has been a good strategy historically, and that both December and January have tended to be good times to be exposed to equities.

We shouldn’t read too much into this chart, however, because the statistical reliability of these averages is still fairly low. At best, it suggest marginally higher exposure rates, or – better yet – permission to enjoy your holiday time with friends and family.