AgPa #27: Forecasting DAX Index Changes

Forecasting index changes in the German DAX family (2020)
Friedrich‑Carl Franz
Journal of Asset Management 21, 135-153, URL

Is it possible to forecast and exploit changes in the composition of equity indices? This is the central question of this week’s AGNOSTIC Paper and the author introduces a quite interesting trading strategy for the German DAX family indices…

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

Setup and Idea

The paper builds on the so called index effect. According to the author, this effect refers to the unsettled question whether abnormal returns exist around index additions and deletions. Why should there be such an effect? Well, a lot of the world’s assets are nowadays managed in passive index funds or ETFs. These funds commit themselves to track an index as close as possible. So whenever there is a change in the underlying index composition (additions or deletions), this should trigger massive trading volume.

It is completely reasonable to expect positive returns for index additions as these stocks may experience buying pressure from index funds. Similarly, selling pressure may lead to negative returns for index deletions. In addition to that, it is also important to distinguish between the announcement- and the rebalancing date. The rebalancing date is the day the index provider implements the changes. For example, Twitter left the S&P 500 as of November 1, 2022 because Elon Musk finally closed his deal.1More information about that here. The replacement for Twitter, Arch Capital Group performed quite strong after the announcement. So this seems to be (thankfully) in line with the idea of buying pressure. The announcement date, in contrast, is the day the index provider informs the public about changes in the index composition. Unsurprisingly, the announcement date is much more important because that’s the day when the information becomes publicly available.

In an efficient stock market we should therefore see most of the return reaction on the announcement date. Why? Because once some smart (and fast) investors figure out that index funds are going to buy or sell certain stocks, they will position themselves to exploit this already on the announcement day.2Or even before, if they can reliably forecast index changes. In addition to that, the author explains that some index funds also adjust their portfolio before the official announcement date. So overall, the more relevant day is definitely the announcement date!

The author contributes to this literature and empirically establishes an index effect for the German DAX family (DAX, MDAX, SDAX, and TecDAX), the most common indices for German equities. Apart from the scientific contribution, the results of the paper suggest a quite interesting trading strategy…

Data and Methodology

Stock indices usually follow certain rules that are at least to some extent publicly known. In case of the DAX family, the critical variables are free-float adjusted market capitalization and turnover rate.3More information and details about the methodology here. So if you know the index methodology and have the same data as Deutsche Börse (the index provider of the DAX family), you could exactly predict the index composition at each of the four quarterly rebalancing dates. In practice, unfortunately, this is a bit more difficult. The author explains that he couldn’t replicate the official data from Deutsche Börse with well-known data providers like Bloomberg or Compustat.4Of course, this doesn’t mean that Deutsche Börse cheats or anything like that. Minor deviations across databases are (unfortunately!) quite common in practice… So he develops another approach to forecast the index changes.

Each month, Deutsche Börse publishes a ranking list that includes all eligible German stocks with respect to the critical variables.5You can find the ranking lists here. The author uses these lists to forecast future changes. First, he takes the ranking list from t-1 to obtain the eligible universe. Second, he updates the variables with current data from Bloomberg or Compustat, and computes the rank-difference to the previous month. Finally, he adds this rank-difference to the ranking list of t-1 to estimate the ranking list of t. In theory, we should be able to perfectly predict index changes with those estimated ranking lists. In practice, however, there are of course some exceptions or data deviations and there is a risk of false predictions. But even with those minor weaknesses, the forecasting procedure was empirically quite successful…

Important Results and Takeaways

Index changes in the DAX family are predictable

During the sample period between 2010 and 2019, the simple forecasting model worked quite well. The model correctly identified 108 out of 228 index changes, a true positive rate of 45%. The false positive rate is 27% (40 out of 228). You might criticize that the true positive rate is below 50%, but this mainly comes from small caps in the SDAX. For the DAX and MDAX, the true positive rates are with 71% and 63% quite strong.

This difference between large- and small caps is in line with expectations because data quality and availability tends to be poorer for smaller companies. In addition to that, IPOs and delistings are more relevant in the small cap universe. The previous month’s ranking list typically doesn’t include such events and the model has thus no chance to predict the corresponding index changes.

Despite the problems with small caps, the author concludes that index changes are indeed predictable from publicly available information. This is consistent with other results from the academic literature and also in line with the opinion of various practitioners.6For example, the author quotes BlackRock’s Head of Portfoliomanagement in Germany who “states that index changes are no surprise anymore […]”. Also note that the model is free from look-ahead- or survivorship bias. The following results are therefore quite robust with respect to practical implementation.

Buying index additions and shorting deletions generated strong risk-adjusted returns

Having a model that forecasts index changes is of course not only a fulfilling theoretical achievement but also a potential tool to generate excess returns. In fact, a simple strategy that goes long (short) predicted index additions (deletions) on the announcement date and holds them for one day produced quite attractive returns. And the coolest part: the strategy is only invested 4 times per year because the DAX family rebalances quarterly.

The following chart shows cumulative returns of the strategy. The left chart plots the performance of a theoretical benchmark that went long (short) actual index additions (deletions). So this is backward-looking and assumes that you predicted all index changes correctly. The right chart, in contrast, shows the performance of predicted index changes. Both portfolios are equal-weighted, so the strategy summarizes the average performance of index changes in the DAX family between 2010 and 2019.

Figures 3 and 4 of Franz (2020).

The strategy based on the predictions of the forecasting model generated average annual returns of 5.61% and a Sharpe ratio of 0.83. Note however, that these are statistics for being invested only four times per year. If investors would have access to such a strategy on every day of the year, the annualized Sharpe ratio becomes 6.59. This number is insanely high and impressively shows the attractive risk-return profile from trading on index changes.

Finally, I have to mention one important outlier. In March 2014 the strategy earned a 10.71% return which in part came from a false positive (the model falsely predicted the addition of Software AG to the TecDAX and went long). As clearly observable in the chart, this had a strong impact on the overall performance of the long-short portfolio. However, the author transparently explains that the performance pattern of the strategy was quite consistent except for this day. I believe it is important to highlight this outlier even though (or especially because!) it was actually beneficial in this case.

Conclusions and Further Ideas

In my opinion, the key takeaway is of course the trading strategy and the fact that index changes in the DAX family are predictable. But the idea to forecast and exploit index changes is obviously not new and sophisticated investors have been doing this for years. Against this background it is quite surprising that index additions (deletions) still generate positive (negative) returns and have not yet been arbitraged away. The author also discusses this issue and argues that some of the returns come from small- and mid caps. So this might explain some of the returns by frictions like illiquidity and a higher risk of false positives. But although of smaller magnitude, he still finds a significant index effect for DAX large caps.

I picked the paper because I really like the trading strategy. It sounds very appealing to make 6% per year at a high Sharpe ratio while only working 4 days per year.7I already imagine myself running such a fund from a beautiful tropical island… All jokes aside, this remains of course hard-earned money. Nevertheless, I still find event-driven strategies very interesting even beyond the index effect.

At least in my imagination, it should be easier to build successful strategies around events because the relevant return-drivers are much clearer. Either the stock is added to the index or not. If your forecast was wrong you will recognize it within a day and can exit the position accordingly. This is quite different from buying a stock at an arbitrary date. Anything can happen and it is really hard to understand what actually caused the price movement. For this reason, I will probably explore the event-driven world somewhat further…

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1 More information about that here. The replacement for Twitter, Arch Capital Group performed quite strong after the announcement. So this seems to be (thankfully) in line with the idea of buying pressure.
2 Or even before, if they can reliably forecast index changes.
3 More information and details about the methodology here.
4 Of course, this doesn’t mean that Deutsche Börse cheats or anything like that. Minor deviations across databases are (unfortunately!) quite common in practice…
5 You can find the ranking lists here.
6 For example, the author quotes BlackRock’s Head of Portfoliomanagement in Germany who “states that index changes are no surprise anymore […]”.
7 I already imagine myself running such a fund from a beautiful tropical island…