Stock market bias on quarterly expirations

Most people are familiar with stocks. Even those ones that are not interested in stock markets know that, somehow, you can buy shares from listed companies expecting their value to rise in the future and then taking profits. However, not so many people know that shares are not the only way to trade. There is a family of closely related trading products called derivatives that comprises a wide variety of trading products such as CFDs, ETFs, futures and options. Each of these products has their own peculiarities and it is out of the scope of this article to dip into their details. In this article, we are going to focus on options, which constitute itself a huge market and is the target of the study presented later.


When people buy stocks they know that they will make profit whenever the stock rises, and they will lose whenever the stock drops; price is the target. Although time is also considered, as people obviously prefer making profit in the shortest possible time, they know that they will make profit if the stock finally rises above the price they were bought, as long as they hold the stocks enough time.

Options are rather different; it is a complex product compared to stocks and their pricing behaves in a different manner. Suppose you are betting a given company value is rising and decide to buy shares. Your bet will be profitable as long as you hold them and their price rises, regardless of how long it takes. This is no longer true when trading with options because they expire, and, therefore, timing plays a key role.

Just with the purpose of illustrating the role of time, let me focus on a specific kind of operation on options. Long call options are a financial contract that gives you the option, but not the obligation, of buying an asset at a specific price (strike) until a specific date (expiration) by paying a price (premium).

The figure above depicts the different behavior of a trade made via buying shares and via long calls. In this example, we are buying shares and long calls of an asset at 4050, and long calls that have a premium of 50 at that time. We find different outcomes for each trade at expiration. Regarding the scenario of positive return, the trade made via shares yields profit if the asset price is above 4050, and this is true even beyond the expiration date. The trade made via long call yields profit only if the asset price is above 4100 at that time. In addition, the trade is forced to be closed at that time (expires). Regarding the negative return scenario, shares yields losses proportionally to how low the asset price is, i.e., price do matters to compute the losses. On the contrary, long calls have their maximum loss capped, i.e., prices below 4100 do not translate into a greater loss.

Market behavior on quarterly expirations

The market of derivatives offers a rich variety not only of products but also of expirations. Here, we focus on quarterly expirations because they are the most relevant. They take place in the third Friday of March, June, September and December. This applies to the stock markets both in USA and Europe, only differing in the precise time of expiration. This study reveals the influence of these events in the market, causing a well-defined behavior pre-expiration and post-expiration. It has been carried out over the EuroStoxx 50, which is an index that englobes fifty of the biggest companies of Europe, from 2010 to 2021.

For this study, two different trades are defined:

  • Pre-expiration: Long every quarterly expiration pre-expiration offset hours before the expiration precise time, where the trade is closed.
  • Post-expiration: Long every quarterly expiration at the expiration precise time. The trade is closed post-expiration offset hours later.

Hours refer to trading hours for the EuroStoxx 50 futures (8:00 – 22:00 CET). The chart below shows the gross cumulative return of this strategy in the last ten years. For instance, the cell where the pre-expiration offset is ’10h’ and the post-expiration offset is ’20h’ shows the cumulative return of buying ten trading hours before each quarterly expiration in this period and selling twenty trading hours after each expiration. The reader can see a clear bullish bias in the surroundings prior to expiration and a bearish bias once the quarterly options have expired.

Aiming for a richer visualization, you can find below two interactive charts. They depict the cumulative return at every single expiration throughout the last decade. In the first chart, trades are made before the expiration, and, in the second chart, trades are made after the expiration. You can use the sliders to explore the effect of trade timing.

The results shown may have some little inaccuracies due to data irregularities in the historical quotes (i.e., some trades might be simulated a few hours far from the offsets considered). The Python code written to collect all the simulation data used to create these charts is available at this repository of my GitHub.


  1. Bien Fran!

  2. ¡Muy interesante!

  3. ¿Está disponible la versión en español en algún vinculo?, me cuesta entender en ingles.

    • No lo tengo escrito en español, pero puedes utilizar la traducción automática del navegador. Aunque algunos términos los traduce mal, la traducción es de bastante calidad.

  4. Bien de nuevo Fran!

  5. Muy buen artículo, gracias.

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