Many (fundamental) investors generally have little faith in seasonal anomalies like the Monday effect or the January effect, but perhaps it is worthwhile to inspect the phenomenon of year-end rallies on stocks. There might be rational (tax?) or behavioral (holidays?) explanations for year-end rallies. As there seems to be some empirical evidence supporting the saying: "Sell in May, and go away, but remember to come back in September", why not consider other conventional investment wisdom?

So let us have a look at historical data first. To do this, we need to define "year-end". While some consider it to be only the period between Christmas and New Year, others look at the month of December or even a longer period. I focus on the months of December and November combined, since monthly data allows us to use longer time periods. If the year-end rally is driven by the last week of December, the effect should still pop up using monthly data.

Table 1 shows some evidence for year-end rallies for the S&P500, the Nasdaq100, FTSE100, and XETRA-DAX. The S&P500 provides the longest historical time-series, but the post-war sample of 64 years is used here (since 1950). We see that the average return for buying November 1st and selling December 1st yields a return of 1.71%, and buying December 1st and selling January 1st yields a return of 1.08% on average. The fourth entry in the first column shows what the combined return would be for buying November 1st and selling January 1st; this yielded 2.8% return on average. The bottom entry of the first column shows the average return overall, i.e. any given month, which equals 0.70% on average for the S&P500. We see that both November and December have performed better on average.

Since it is hard to compare two-month returns with one-month returns, all figures are annualized in the second column. It shows that December yields a 50% (14% vs. 9%) higher return on average, and November and December combined even show a 100% higher return (18% vs. 9%). For the Nasdaq100 the effect is even stronger. Both the December returns and the November+December returns are almost triple the size of an average monthly return.

Is this just a U.S. phenomenon? Let us look at the U.K. and Germany. For the FTSE100 and XETRA-DAX, the December returns are about as large as any other month, however, we can see once more that a holding period of November and December combined yields returns more than twice the size of "ordinary" months. In sum, average returns exhibit some evidence for year-end rallies.

Then again, average returns can be misleading; outliers can have a huge effect on this statistic. A historical accident (Lehman crash?) may have favored the year-end returns, especially since these markets are quite connected.

So let us look to some other metric. Let us simply count the number of Novembers, Decembers, and Novembers-Decembers combined that ended in a positive return. Since it does not matter in this case whether the return was 1% or a 100%, this statistic should be somewhat less sensitive to outliers.

The first thing that stands out in Table 2 is the rather robust result that any given month has about a 59% chance of ending up in a positive return for all markets. Regarding the year-end effect, we see that both Novembers and Decembers, and the periods November-December combined result at least as often in positive returns. For the period November-December combined, it is around 70% for every market. So empirically we cannot reject the conventional wisdom of year-end rallies.

As such, betting on a year-end rally has historically paid off. Then again, these numbers only say something about what happened, on average, in the past. Can we do a little better? Can we be a little bit more specific about this year?

Perhaps. It is known that certain fundamental indicators such as dividend-price (D/P) and earnings-price (E/P) ratios have some predictive power for stock returns. So let us use one of these indicators (a proxy for leverage in the market is used here) to predict returns. *(see Footnote 1)*

Table 3 shows the results of using a fundamental indicator to predict 3 month returns. This table therefore shows the expected returns for the holding period between October 1st and January 1st. Again, for all markets we expect a positive return. However, the second row in the table shows the range of returns that are statistically likely. Only for the FTSE100 is this interval strictly positive; its predictions range between 1.71% and 3.44% for the three-month period.

Based on the historical evidence, and the prediction exercise, the final row in Table 3 concludes how likely it is for each market to expect a year-end rally. Personally, I believe it is likely to happen for all markets, but less so for the S&P500, and more so for the FTSE100.

*Footnotes:*

1. The analysis consists of running a regression of 3-month returns on a measure for leverage in the market, and using the statistical fit to extrapolate the results into a prediction. If you want to do these kinds of predictions yourself for individual stocks, you can download the app "Tealeaf Stocks Prediction", available for Android and IOS. Further background information on the App and its prediction model can be found at www.adgillus.com.

This article was written by Professor Dr. Lammertjan Dam for *Foresight Investor. Lammertjan Dam, PhD, is an Associate Professor of Finance at the University of Groningen, the Netherlands. He has published in peer-reviewed journals such as the Review of Financial Studies, the Journal of Sustainable Finance and Investment, and the Journal of Economic Dynamics and Control. In addition, he is co-founder of Adgillus, V.O.F., a company that creates financial applications for mobile devices.*

**Disclosure:** The author has no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

The author wrote this article themselves, and it expresses their own opinions. The author is not receiving compensation for it. The author has no business relationship with any company whose stock is mentioned in this article.