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Asset Management

Seasonality systems

J. González



Wouldn’t it be terrific if we knew that on a specific day of the month, a security is going to grow significantly? We could invest only on those days we know we are going to make money, and go to sleep under the palms the rest of the time.

Well, some anomalies do exist in the market that, to a certain extent, get us closer to this utopia. Under the term seasonality movements, we can include several unexpected behaviors of the security prices related with the “calendar”.

The last day of the month

Historically, bullish behavior is seen within the market around the days at the beginning and the end of every month.

From 1/1/1980 to 15/10/2014 we observe in the table the mean daily returns on the days before and after the end of the month in the S&P 500 index.


Obviously, these values are going to depend on the historical period selected. In the graphs you can see how the mean daily return of the first four days of the month varies year by year:


If we design a strategy that goes long when we reach the third day prior the end of the month, until the third day after the end of the month in S&P 500, (keeping disinvested the rest of the time), the results would be the following:


These results do not include return on cash or costs of any kind. Dividends, in the portfolios nor in S&P 500 index, are included either.

The portfolio that trades only at the end of the month shows quite appealing returns, with much less risk than the index. The portfolio below holds a long position in S&P 500 every day, but the ones of the turn-of-the-month portfolio (green line) shows a very poor behavior in the long run, with a high drawdown and very unstable returns.

Imagen4 Imagen5

In terms of risk, the end-of-the-month portfolio takes advantage of not being at the market most of the time, thus avoiding dramatic falls. On the other hand, the market shows stronger run ups most of the years – too bad! Did you think I was going to share the Holy Grail if I had it?

Anyhow, this strange market pattern is very interesting. It’s not enough to build a complete trading strategy, but perhaps it can be taken into account in a broader frame.

Here and here you can find very interesting posts about the subject.

Preholiday trading days

Empirical studies show that the day before a holiday in the stock exchange are usually bullish. Again, this takes us to a (very simple) seasonality strategy.

As previously, we use exclusively S&P 500 Index for our tests: Let’s design a portfolio that goes along 3 days before every exchange holiday (at the close) and ends the position at the close of the last day before the holiday:



Perhaps the results are not very spectacular, but we must keep in mind that most of the time our position is in cash, and that these numbers doesn’t include interest rate returns. This investment system can be included in a larger strategy. Or, at least, taken into account for an investment decision.

This system can be evolved to include other seasonality rules, such as avoiding closing a position the day after options expire, closing the position on a Friday when the holiday is on Thursday, etc. But, for this post I am not going to delve more into this.


I have presented two well-known market “biases” that perhaps are not strong enough to develop a stand-alone investment system, but are still worthwhile to know.

The last of the month strategy has shown quite interesting results, with an important reduction of risk. It does, however, fall behind the reference index in bullish periods.

I see the preholiday system only as a curiosity that could be taken into account in more ambitious systems.

There are other anomalies of this type – options expiration week, day-after options expiration, first day of the week, etc. – that I will try to explore in following posts, maybe mixing them to obtain a more robust strategy (see Fosback’s seasonality strategy).

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9 years ago

I think the noteworthy thing is how much this effect has disappeared over the past two years. It could be random/temporary, or it could be a genuine change in investor behavior that has eliminated the anomaly.

9 years ago
Reply to  evo34

Yes, now this system suffers a tough period in which it is difficult to know what to do. But it is nothing we haven’t seen before: in the annual returns graphic it is clear that you are not going to have outstanding results every year.
The key with this or any other strategies of this kind, with no correlation with the market, is how long I am willing to wait until I obtain nice returns.

9 years ago

I believe the only problem you could face to develop an adaptive seasonality algo. With adaptive I mean that it can detect changing in seasonalities.
What do you think about it? I’m really interested in your work.


9 years ago
Reply to  aimdal

I am not really sure that this kind of biases, anomalies or the name you prefer, are an anticipation of anything; I would have to develop a deeper statistical analisys. Nevertheless, the problem with this kind of systems is the adjustment in the backtesting, no matter if you use them to detect changing seasonalities, forecast movements or directly to trade. Another important drawback with this seasonality systems is the difficulty to give a reasonable explanation of why this works. This is specially problematic in periods where the system doesn’t work or just falls behind the market, since in those cases… Read more »