# DAX rebalance flow: methods note

> Sample construction, return windows, and sensitivity checks for the DAX rebalance study. The results describe relative returns and do not establish trading profitability.

- Published: 2026-09-07
- Author: PIER20
- Tags: index-effect, dax, event-study, methodology
- Canonical: https://pier20.com/reports/dax-rebalance-methods-note

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This note supports [“DAX additions lost ground before rebalancing. Deletions gained.”](https://pier20.com/reports/dax-rebalance-study). The study describes stock returns relative to the DAX around membership changes from January 2015 to March 2023.

The main window starts at the next Xetra open after announcement. It ends at the rebalancing close, before the new composition takes effect. The study does not test statistical significance, causality, or trading profitability.

## Sample construction

The final return sample contains 38 security-event observations: 24 additions and 14 deletions. An observation represents one stock entering or leaving the index. Repeated changes in the same stock count as separate observations when the evidence confirms each change.

The event reconstruction covers 16 membership-change events. Several stocks share an event, so the observations are not independent. Ten additions share the September 2021 expansion announcement.

The study uses archived Deutsche Börse records to confirm membership before and after each change. These records comprise 25 index composition reports and 17 monthly ranking lists. The ranking lists provide membership snapshots through their current-membership column. Four archived iShares DAX ETF holdings snapshots provide additional evidence of absence.

The study uses International Securities Identification Numbers (ISINs) to identify securities. Announcement text supplies company names and dates. The membership records supply the security identifiers.

### Membership confirmation

Each accepted change must meet four conditions:

1. The last membership record before the effective date shows the old membership state.
2. The first membership record on or after that date shows the new membership state.
3. Each record contains the expected number of index members.
4. No other declared change in the same security makes the interval ambiguous.

The expected count is 30 before the September 20, 2021 expansion and 40 from that date. The ambiguity check includes share-class changes, issuer successions, and temporary spin-off inclusions.

The membership evidence confirms 39 observations before the price checks. The intervals between supporting records range from 73 to 903 calendar days, with a median of 364 days. These intervals describe the evidence gaps, not the return windows.

Three Beiersdorf changes remain ambiguous because the company left and reentered the index within one evidence interval. The study excludes those changes. It retains the separately confirmed March 2021 deletion.

Additional ETF snapshots support the Siemens Energy and Daimler Truck additions after earlier temporary inclusions. Those snapshots show absence between the temporary inclusion and the later addition. This test can support an addition, but it cannot confirm a deletion through evidence of presence.

### Coverage limits

A comparison of consecutive membership records found no unexplained net membership changes. One declared Beiersdorf change remained unattributed to a specific event.

This check cannot detect a departure and return that leave the same membership at both endpoints. The sample therefore does not establish complete coverage of every DAX change. Archive availability determines which changes the study can confirm.

The search also found some share-class changes, issuer successions, temporary inclusions, and free-float changes. It did not establish a complete sample of those actions.

## Prices and security checks

EODHD supplies the Xetra stock prices and the DAX performance-index series. The vendor identifies the benchmark as GDAXI.INDX. The study uses the index directly, without an ETF proxy.

Stock returns use the vendor's dividend- and split-adjusted closes. The study adjusts each stock's opening price by that day's ratio of adjusted close to unadjusted close. This places the opening price on the same adjustment basis as the closing price.

The DAX benchmark includes reinvested dividends. The calculation relies on the vendor's supplied series and adjustment conventions.

The study uses dates with benchmark observations as its trading calendar. It requires stock observations throughout the main and subsequent return windows.

The price checks reject missing sessions, adjusted-close jumps above five times, and runs of at least five identical closes. Vendor identifiers match the membership-record identifiers for 37 of the 39 confirmed observations.

Two observations require separate treatment:

| Observation | Issue | Treatment |
|---|---|---|
| Qiagen addition, September 2021 | Vendor and membership-record ISINs differ | Include with unconfirmed identity status. All 34 required sessions are present, with no disqualifying price pattern. |
| Linde deletion, February 2023 | ISIN mismatch and two missing sessions after the change | Exclude from the return sample. |

The Qiagen price checks support continuity but do not resolve the identifier mismatch. Linde's exclusion reduces the return sample from 39 to 38 observations.

## Return calculation

For each session, the study subtracts the DAX return from the stock return. It then adds these daily differences across the measurement window. This sum is the cumulative abnormal return, or CAR.

CAR = sum of (stock return − DAX return).

The first session of the main window uses the opening price as its starting price. Later sessions use the previous closing price. Windows after rebalancing start from the rebalancing close.

This is an arithmetic sum of relative returns. It is not a compounded portfolio return or a beta-adjusted estimate. The study does not estimate a market model.

Tables report the arithmetic mean across observations unless they specify another statistic. Each observation receives equal weight. Additions and deletions remain separate, and deletion returns retain their original signs.

A positive deletion return means the deleted stock outperformed the DAX. It does not represent the profit from a short position.

## Announcement and rebalancing dates

The study starts measurement at the first Xetra open after the announcement date. Archived announcements provide dates without reliable machine-readable publication times. This convention excludes the overnight announcement reaction from the main window.

Each stock uses its own announcement date when separate releases announce different parts of a replacement. The study does not assign both stocks the later release date.

The rebalancing close is the Xetra close on the chaining date. The old composition applies through that session. The new composition applies from the next trading session, called the effective session here.

| Window | Start | End |
|---|---|---|
| Main article window | Next Xetra open after announcement | Rebalancing close |
| Next 5 sessions | Rebalancing close | Close 5 trading sessions later |
| Next 20 sessions | Rebalancing close | Close 20 trading sessions later |
| Announcement reaction | Last close before the entry open | Entry open |
| Pre-announcement history | Start of the specified historical window | Last close before the entry open |

The effective session is the first session in each post-rebalancing window.

### Rulebook basis and historical caveat

The August 2019 DAX guide defines quarterly chaining on the third Friday of March, June, September, and December. It uses Xetra closing prices as the rebalancing basis. New weights apply from the next trading day.

The event reconstruction records 13 quarterly events and three extraordinary events. Its calendar check reports no mismatches. Extraordinary changes use unscheduled chaining rather than the quarterly calendar.

The study checked the convention against these rulebook references:

| Document | Edition | Relevant section |
|---|---|---|
| Guide to the DAX Equity Indices | Version 10.1, August 28, 2019 | Section 7, page 45. Section 7.1.2 covers unscheduled chaining. |
| DAX Equity Index Calculation Guide | July 2025 | Section 5.7, quarterly implementation day |

The study did not retrieve a rulebook edition in force during 2015–2018. Applying the convention to those years remains an assumption supported by the event-calendar checks. Those checks do not replace a contemporaneous rulebook.

## Main results: rebalancing-close windows

All figures below are arithmetic returns relative to the DAX.

| Cohort | Observations | To rebalancing close | Next 5 sessions | Next 20 sessions |
|---|---:|---:|---:|---:|
| Additions | 24 | −3.98% | +0.74% | −3.00% |
| Deletions | 14 | +3.04% | −4.02% | −3.12% |

Before rebalancing, 5 of 24 additions and 11 of 14 deletions outperformed the DAX.

### September 2021 expansion

| Addition subset | Observations | To rebalancing close |
|---|---:|---:|
| All additions | 24 | −3.98% |
| September 2021 expansion | 10 | −1.00% |
| Other additions | 14 | −6.11% |

Both subsets underperformed before rebalancing. The expansion reduces the size of the overall loss. Its ten observations share an announcement and market conditions, which limits their value as independent evidence.

The expansion had no deletions, so this exclusion does not change the deletion sample.

### Wirecard exclusion

| Deletion subset | Observations | To rebalancing close | Next 5 sessions | Next 20 sessions |
|---|---:|---:|---:|---:|
| All deletions | 14 | +3.04% | −4.02% | −3.12% |
| Excluding Wirecard | 13 | +3.43% | −1.18% | −1.85% |

Wirecard's August 2020 removal followed insolvency. The main results retain that observation. Its exclusion leaves the pre-rebalancing direction unchanged but reduces the losses after rebalancing.

## Pre-announcement history

Historical windows end at the last close before the entry open. Longer windows contain fewer observations because some stocks had only recently listed.

| Historical window | Additions: mean | Observations | Positive share | Deletions: mean | Observations | Positive share |
|---|---:|---:|---:|---:|---:|---:|
| 20 sessions | +2.60% | 24 | 50% | +0.39% | 14 | 64% |
| 60 sessions | +12.64% | 21 | 90% | −19.41% | 13 | 15% |
| 120 sessions | +15.22% | 18 | 89% | −33.27% | 11 | 27% |

Positive shares round to whole percentages. In the 60-session addition sample, 19 of 21 observations had positive relative returns.

Excluding Wirecard reduces the 60-session deletion decline to 7.02%, across 12 observations. The earlier weakness remains, but Wirecard accounts for much of its average size.

The 60- and 120-session results show earlier strength in additions and weakness in deletions. The 20-session window does not show the same pattern. These windows use different samples and do not isolate a cause for the later returns.

## Announcement reaction and adjacent sessions

The overnight announcement reaction has the expected direction for index-related demand. Additions gain relative to the DAX, while deletions lose.

| Cohort | Mean announcement reaction | Median | Positive share |
|---|---:|---:|---:|
| Additions | +0.62% | +0.34% | 83% |
| Deletions | −0.25% | −0.03% | 43% |

Twenty of the 24 addition observations have positive announcement reactions. This reaction is outside the main window and does not offset the later average loss.

| Session | Additions: mean | Deletions: mean |
|---|---:|---:|
| Rebalancing session | −0.99% | +1.44% |
| Effective session | +1.04% | −0.97% |
| Both sessions combined | +0.05% | +0.47% |

The direction changes after the rebalancing session. The two sessions nearly offset for additions and leave deletions ahead by 0.47%. These daily observations do not identify tracker trades or measure their price impact.

## Comparison with the effective-close convention

The earlier analysis ended its main window at the effective-session close, one session after the rebalancing close. Its subsequent windows also started one session later.

The table below preserves those results for comparison. They use different endpoints from the article's main results.

| Cohort | Measure | Mean | Median | Interquartile range |
|---|---|---:|---:|---|
| Additions, 24 | Entry open to effective close | −2.94% | −2.78% | −6.10% to +0.89% |
| Additions, 24 | Next 5 sessions from effective close | −0.71% | +0.21% | −3.70% to +2.04% |
| Additions, 24 | Next 20 sessions from effective close | −3.54% | −2.32% | −6.38% to −0.30% |
| Additions, 24 | Entry open through effective close +5 sessions | −3.65% | −4.74% | −7.08% to +0.66% |
| Additions, 24 | Entry open through effective close +20 sessions | −6.49% | −7.00% | −10.32% to −2.22% |
| Deletions, 14 | Entry open to effective close | +2.07% | +3.77% | +0.05% to +7.52% |
| Deletions, 14 | Next 5 sessions from effective close | −4.95% | −1.46% | −5.58% to +3.49% |
| Deletions, 14 | Next 20 sessions from effective close | −1.66% | −2.92% | −4.02% to +3.57% |
| Deletions, 14 | Entry open through effective close +5 sessions | −2.88% | +0.24% | −3.61% to +6.13% |
| Deletions, 14 | Entry open through effective close +20 sessions | +0.41% | +1.27% | −5.66% to +7.58% |

The interquartile range describes the middle half of observations. It does not measure uncertainty around the mean.

Under this convention, expansion additions average −0.01% through the effective close. Other additions average −5.04%. The expansion's −1.00% rebalancing-close result therefore becomes nearly zero after the effective session.

Wirecard also affects the effective-close results:

| Deletion measure | All 14 observations | Excluding Wirecard, 13 observations |
|---|---:|---:|
| Entry open to effective close | +2.07% | +2.85% |
| Next 5 sessions from effective close | −4.95% | −0.55% |
| Next 20 sessions from effective close | −1.66% | −0.56% |
| Entry open through effective close +5 sessions | −2.88% | +2.31% |
| Entry open through effective close +20 sessions | +0.41% | +2.30% |

The five-session total changes sign when the sample excludes Wirecard. This sensitivity concerns that total window. The article's pre-rebalancing finding keeps the same direction.

## Interpretation and limits

The results describe a small sample that depends on surviving archive evidence. Shared announcements and repeated securities limit independence. The study does not report confidence intervals or statistical significance.

Earlier price movements could help explain the later relative returns. Anticipated index demand and other causes could also contribute. The study does not separate these explanations or establish a causal index effect.

The calculations exclude trading costs, market impact, borrow costs, borrow availability, and capacity constraints. They do not establish executable returns or show that the opposite trade would earn a profit.

This note reports aggregate results and methods. It does not supply the underlying vendor prices or reconstructed membership dataset. Readers cannot fully reproduce the calculations from this note alone.

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Read online: https://pier20.com/reports/dax-rebalance-methods-note

Disclaimer: research output, not investment advice.