## 1. Introduction

## 2. Tax and Accounting Background of Tax-Free Dividend Payments

## 3. Returns and Trading Volume on Ex-Dates—Taxes and Alternative Explanations

#### 3.1. Taxes

#### 3.2. Alternative Explanations

## 4. Data and Summary Statistics

## 5. Price Analysis

#### 5.1. Methodology

#### 5.2. Results

_{t}) in the five days prior to the ex-date and insignificant or significant and negative AAR

_{t}after the ex-date. On the ex-date itself, we find significant and positive AAR

_{t}since 2009. This result stands in contrast to the PDR estimation of one. There is no obvious reason from a tax point of view. The literature on the German stock market by Lasfer (2008) and Haesner and Schanz (2013) among others, reports comparable outcomes for the ex-date. Stale prices, as suggested by McDonald (2001), are not a valid explanation, as we control for this. Our analysis based on bid or ask prices reveals economically identical results for the ex-date. However, the estimation of the AAR differs from the methodology of the PDR estimation, because we implicitly consider transaction costs with the $\alpha $ in Equation (3).

_{t}prior to the ex-date indicate that short-term arbitrage does not significantly affect prices of German stocks with tax-free dividend either. The significant and negative AAR

_{t}after the ex-date are consistent with the declining price pressure of dividend-seeking investors. Dividend-seeking investors can purchase stocks before our event window, so we do not necessarily expect positive AAR

_{t}over the five days in advance of the ex-date (Kreidl and Scholz 2020). However, the AAR

_{t}on the ex-date do contrast with the otherwise consistent outcomes of our price analysis.

## 6. Volume Analysis

#### 6.1. Methodology

#### 6.2. Results

_{t}) for the days t − 2 and t − 5, respectively. The figures for OTC reveal an opposite result indicating that OTC trading is more prevalent on regular trading days without ex-dates. During the days after the ex-date, the MTFs show significant AAV

_{t}on days t + 2 and t + 3 compared to insignificant results for XETRA and the local exchanges. OTC trading is significantly increased on days t + 1 and t + 5 and significantly decreased on day t + 4. All venues show significant and positive average cumulative abnormal number of stocks traded (ACAV) over the event window. The ACAV varies between 0.3556 for the MTFs and 2.9314 for the local exchanges. Local shows the highest relative increase, but note that the level of daily number of stocks traded in the estimation period is considerably lower for Local and OTC. An additional analysis of XETRA and Local, where we neglect the years before 2008 to align the underlying data sets, produces almost identical results.18 This indicates a stable behavior of the AAV around the ex-date over time.

_{t}in advance of the ex-date and on the ex-date itself may indicate short-term arbitrage. However, considering the insignificant AAR

_{t−}

_{1}makes systematic short-term trading implausible. Our results after the ex-date do not indicate significant and negative abnormal numbers of stocks traded either.

_{t−}

_{1}. We are not going into further detail with this particular issue. Nevertheless, it seems to be a plausible explanation considering the fact that our analysis covers 456 dividend events of 128 individual stocks over almost 18 years.

_{t}on day t − 1, which makes the annual general meeting the most likely explanation for the significant and positive AAV

_{t}on this day.

_{i}. In contrast, the MTFs show significant and positive coefficients for DY and Cap. Thus, all else being equal, stocks with a higher dividend yield show a higher cumulative abnormal number of stocks traded, and stocks with a higher market capitalization, indicating lower transaction costs, show a higher cumulative abnormal number of stocks traded. The $\delta $ estimates are not significantly different from zero.

## 7. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A. Additional Tables and Figures

Full Sample | HI-System | FT-System | |
---|---|---|---|

2002–2019 | 2002–2008 | 2009–2019 | |

D | 0.8719 | 0.8035 | 0.9158 |

t-statistic | 7.68 | 3.34 | 14.00 |

$\alpha $ | −0.0398 | 0.0284 | −0.0616 |

t-statistic | −0.93 | 0.34 | −2.28 |

t-statistic (D ≠ 1) | −1.13 | −0.82 | −1.29 |

N | 456 | 70 | 386 |

Full Sample | HI-System | FT-System | |
---|---|---|---|

2002–2019 | 2002–2008 | 2009–2019 | |

Panel A: Closing prices—bid | |||

D | 0.9392 | 0.8744 | 0.9770 |

t-statistic | 9.97 | 4.29 | 18.01 |

$\alpha $ | −0.0689 | 0.0103 | −0.0898 |

t-statistic | −1.75 | 0.12 | −3.31 |

t-statistic (D ≠ 1) | −0.64 | −0.62 | −0.42 |

N | 450 | 65 | 385 |

Panel B: Closing prices—ask | |||

D | 0.8795 | 0.8237 | 0.9206 |

t-statistic | 9.01 | 4.10 | 14.73 |

$\alpha $ | −0.0425 | −0.0081 | −0.0584 |

t-statistic | −1.21 | −0.11 | −2.47 |

t-statistic (D ≠ 1) | −1.23 | −0.88 | −1.27 |

N | 447 | 67 | 380 |

**Figure A1.**Kernel-density estimate of price-drop-ratio distribution (bid). This figure depicts a kernel-based estimate of the distribution of price-drop ratios (PDRs) based on closing bid prices. The PDR is defined as the adjusted drop from the closing bid price on the dividend date to the closing bid price on the ex-date over the dividend payment of a stock. The sample includes all constituents with tax-free dividends of the German CDAX index between January 2002 and September 2019. Due to missing bid prices, only 450 of all 456 dividend events in the data are included. Epanechnikov kernel density. Data source: Refinitiv EIKON.

**Figure A2.**Kernel-density estimate of price-drop-ratio distribution (ask). This figure depicts a kernel-based estimate of the distribution of price-drop ratios (PDRs) based on closing ask prices. The PDR is defined as the adjusted drop from the closing ask price on the dividend date to the closing ask price on the ex-date over the dividend payment of a stock. The sample includes all constituentswith tax-free dividends of the German CDAX index between January 2002 and September 2019. Due to missing ask prices, only 447 of all 456 dividend events in the data are included. Epanechnikov kernel density. Data source: Refinitiv EIKON.

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1 | The withholding tax burden of 26.375% consists of a 25% dividend tax plus 5.5% solidarity surcharge. |

2 | The gross dividend is the distribution to the shareholders after corporate taxes. |

3 | |

4 | See, among others, Lakonishok and Vermaelen (1986) and Michaely and Vila (1996) showing a significantly negative relationship between transaction costs and trading volume around ex-dates. |

5 | Michaely and Vila (1996) document that both market risk and idiosyncratic risk reduce trading volume. |

6 | See Buettner et al. (2020) for a detailed discussion. In Germany, cum-ex trades were possible in the years from 1999 to 2011 (Spengel 2016). |

7 | Investors may benefit from a tax deferral. However, this advantage is negligible and will not be considered in the following. |

8 | Elton and Gruber (1970) derive Equation (1) in an equilibrium model, where risk-neutral investors, with no restriction on short sales, are indifferent between selling or buying the stock before the ex-date or after the stock is traded ex-dividend if the after-tax wealth is identical. |

9 | See, for instance, “XETRA Release 15.0—Marktmodell Aktien” or previous releases. |

10 | See “https://eur-lex.europa.eu/legalcontent/EN/TXT/PDF/?uri=CELEX:32004L0039&qid=1575473833940&from=EN” for a detailed definition. |

11 | BATS and CHI-X merged in November 2011. In the following analysis, we aggregate the number of stocks traded over all MTFs in the sample. |

12 | There is no data available for number of stocks traded OTC in Stuttgart and XETRA prior to 2014 and after 2018. |

13 | We apply the methodology of trimming as winsorizing would bias the price analysis on ex-dates. |

14 | For event i, we adjust the stock’s closing cum price by the respective expected return. See Equations (3) and (4) for the methodology. |

15 | Panel A of Table A2 in Appendix A provides the results for bid prices and Panel B shows the results for ask prices. All point estimates for D are larger compared to the results in Table 2. Especially the results for the bid prices in Panel A are clearly closer to one. The PDRs estimated on the basis of bid or ask prices are also not significantly different from one. Hence, the results are as expected and the PDRs are not statistically different from our results in Table 2. The Figure A1 and Figure A2 in Appendix A provide kernel-density estimates of the PDR distribution based on bid or ask prices. |

16 | A Hausman test (p-value of 0.3728) cannot reject the null, thus the random-effects estimator is consistent and efficient. |

17 | Results available for t-statistics following a Student’s t-distribution are upon request. |

18 | Results available are upon request. |

19 | Hausman tests cannot reject the null, thus the random-effects estimators are consistent and efficient. The respective p-values are 0.399 (XETRA), 0.854 (Local) and 0.189 (MTFs). |

20 | An additional price analysis would provide further insights. To our best knowledge, there is no information available for daily MTF closing prices of German stocks with tax-free dividend. |

21 | We do not suppose a significant shift to OTC trading, as reasoned by Gomber et al. (2016), because we do not expect systematic large-in-scale trades around ex-dates for our sample. |

**Figure 1.**Distribution of ex-dates with tax-free dividends. This figure illustrates the distribution of ex-dates with tax-free dividend payments between January 2002 and September 2019. The left graph reports the ex-dates over time, the right graph shows the average distribution of ex-dates within a year. The data sample includes 456 ex-dates with tax-free dividend payments. Data source: Refinitiv EIKON.

**Figure 2.**Total number of stocks traded around ex-dates. This figure shows the total number of stocks traded for the days [−65, 65] relative to the ex-date. It reports XETRA (

**upper left**), the sum over all local exchanges (Local) Frankfurt, Stuttgart, Munich, Hamburg, Hannover, Düsseldorf, Berlin and Tradegate (

**upper right**), the sum over the multilateral trading facilities (MTFs) CHI-X, BATS and Turquoise (

**lower left**) and the aggregated total number of stocks traded of the over-the-counter (OTC) trading in Stuttgart and XETRA (

**lower right**). XETRA and Local include the years 2002 to 2019, the MTFs cover the years 2008 to 2019 and OTC is available between 2014 and 2018. Data source: Refinitiv EIKON.

**Figure 3.**Kernel-density estimate of price-drop-ratio distribution. This figure depicts a kernel-based estimate of the distribution of price-drop ratios (PDRs) based on XETRA closing prices. The PDR is defined as the adjusted drop from closing cum price to closing ex price over the dividend payment of a stock. The sample includes all constituents with tax-free dividends of the German CDAX index between January 2002 and September 2019. Epanechnikov kernel density. Data source: Refinitiv EIKON.

Tax-Free Dividend Stocks in CDAX | ||||

Years | 18 | |||

Constituents | 128 | |||

Ex-dates | 456 | |||

Min. | Mean | Median | Max. | |

Dividend per stock (EUR) | 0.03 | 0.46 | 0.25 | 6.00 |

Dividend yield (%) | 0.07 | 1.26 | 0.86 | 10.36 |

Risk | 0.56 | 1.95 | 1.76 | 8.17 |

Spread (%) | 0.00 | 1.54 | 1.12 | 11.26 |

Market Capitalization (Mio. EUR) | 2 | 2,551 | 114 | 55,970 |

Full Sample | HI-System | FT-System | |
---|---|---|---|

2002–2019 | 2002–2008 | 2009–2019 | |

D | 0.8698 | 0.7937 | 0.9166 |

t-statistic | 7.29 | 3.11 | 14.57 |

$\alpha $ | −0.0380 | 0.0469 | −0.0630 |

t-statistic | −0.86 | 0.52 | −2.39 |

t-statistic (D ≠ 1) | −1.09 | −0.81 | −1.33 |

N | 456 | 70 | 386 |

Low DY | Medium DY | High DY | |
---|---|---|---|

2002–2019 | 2002–2019 | 2002–2019 | |

D | 0.9854 | 1.0409 | 0.9678 |

t-statistic | 6.99 | 28.28 | 3.65 |

$\alpha $ | −0.1660 | −0.0988 | −0.0217 |

t-statistic | −1.25 | −3.55 | −0.65 |

t-statistic (D ≠ 1) | −0.10 | 1.11 | −0.12 |

Full Sample 2002–2019 | ||
---|---|---|

(1) | (2) | |

$\omega $ | 0.6008 | 0.9304 |

t-statistic | 2.05 | 2.73 |

DY | −2.8005 | −4.675 |

t-statistic | −0.48 | −0.72 |

Risk | −0.0459 | −0.0381 |

t-statistic | −0.46 | −0.36 |

Spread | 2.8976 | 3.1018 |

t-statistic | 0.63 | 0.71 |

Cap | 0.0318 | −0.0293 |

t-statistic | 1.03 | −0.78 |

N | 436 | 436 |

Adj. R^{2} | 0.005 | 0.014 |

Full Sample 2002–2019 | HI-System 2002–2008 | FT-System 2009–2019 | ||||
---|---|---|---|---|---|---|

AAR_{t} | t-Statistic | AAR_{t} | t-Statistic | AAR_{t} | t-Statistic | |

t − 5 | 0.0012 | 0.84 | 0.0033 | 0.88 | 0.0008 | 0.56 |

t − 4 | −0.0004 | −0.30 | −0.0041 | −0.07 | 0.0003 | 0.36 |

t − 3 | −0.0011 | −1.28 | 0.0016 | 0.41 | −0.0016 | −1.61 |

t − 2 | 0.0012 | 0.94 | −0.0037 | −0.97 | 0.0021 | 1.45 |

t − 1 | −0.0007 | −0.18 | 0.0068 | 1.93 | −0.0020 | −1.02 |

t0 | 0.0064 | 5.02 | 0.0013 | 0.88 | 0.0073 | 5.22 |

t + 1 | −0.0049 | −3.37 | −0.0102 | −2.44 | −0.0040 | −2.73 |

t + 2 | −0.0050 | −2.61 | −0.0020 | −0.66 | −0.0055 | −2.62 |

t + 3 | 0.0005 | 0.06 | 0.0030 | 0.79 | 0.0001 | −0.40 |

t + 4 | −0.0022 | −1.49 | −0.0015 | −0.24 | −0.0023 | −1.56 |

t + 5 | −0.0030 | −1.71 | −0.0015 | −0.17 | −0.0033 | −1.83 |

N | 456 | 70 | 386 |

_{t}, for the days [−5, 5] relative to the ex-date in the event window. A stock’s daily abnormal return for the days [−5, 5] is defined as the daily excess return minus the stock’s daily expected return. The daily expected return for the days [−5, 5] is estimated using a market-model specification with estimation period [−65, −6] and [6, 65]. The daily CDAX return is used as market-portfolio return. The table shows the results for the full sample, 2002 to 2019, for the HI-system between 2002 and 2008 and for the FT-system since 2009. The sample includes all constituents with tax-free dividends of the German CDAX index between January 2002 and September 2019. We apply t-statistics by Kolari and Pynnönen (2010). Data source: Refinitiv EIKON.

XETRA 2002–2019 | Local 2002–2019 | MTFs 2008–2019 | OTC 2014–2018 | |||||
---|---|---|---|---|---|---|---|---|

AAV_{t} | t-Statistic | AAV_{t} | t-Statistic | AAV_{t} | t-Statistic | AAV_{t} | t-Statistic | |

t − 5 | 0.1303 | 0.40 | 0.2317 | 0.43 | 0.0851 | 2.33 | 1.0553 | −0.28 |

t − 4 | 0.0768 | 1.08 | 0.3127 | 0.96 | 0.0321 | 0.86 | −0.2499 | −1.95 |

t − 3 | 0.2160 | 1.20 | 0.5525 | 1.59 | 0.0729 | 0.69 | 0.1594 | −0.56 |

t − 2 | 0.3285 | 1.51 | 0.6388 | 1.69 | 0.1305 | 2.84 | −0.1013 | −6.70 |

t − 1 | 0.4040 | 3.24 | 0.5421 | 1.92 | 0.1796 | 6.89 | −0.1435 | −7.82 |

t0 | 0.3490 | 2.45 | 0.5860 | 1.93 | 0.1968 | 5.94 | −0.0408 | −10.05 |

t + 1 | 0.1214 | 0.92 | 0.1908 | 0.56 | −0.0222 | −0.09 | 5.6195 | 2.51 |

t + 2 | 0.1126 | 0.96 | 0.0896 | 0.69 | 0.0725 | 2.24 | 0.2667 | 0.84 |

t + 3 | −0.0468 | 0.31 | 0.0043 | 0.13 | 0.0571 | 4.14 | 0.1491 | 0.28 |

t + 4 | −0.0244 | 0.13 | −0.0711 | 0.06 | 0.0005 | 0.95 | −0.2765 | −1.68 |

t + 5 | 0.0119 | 0.08 | 0.0098 | −0.02 | 0.0041 | 0.43 | 1.1061 | 2.51 |

ACAV | 1.6684 | 3.71 | 2.9314 | 2.99 | 0.3556 | 8.21 | 1.1642 | 9.09 |

_{t}, for the days [−5, 5] relative to the ex-date in the event window. A stock’s daily abnormal number of stocks traded is defined as the daily number of stocks traded for the days [−5, 5] minus the average number of stocks traded in the estimation period [−65, −6] and [6, 65] relative to the ex-date over the average number of stocks traded. ACAV represents the average cumulative abnormal number of stocks traded over the days [−5, 5] relative to the ex-date. This table provides results for the trading venues XETRA, the sum over all local exchanges (Local) Frankfurt, Stuttgart, Munich, Hamburg, Hannover, Düsseldorf, Berlin, and Tradegate, the sum over the multilateral trading facilities (MTFs) CHI-X, BATS and Turquoise and the sum over the over-the-counter (OTC) trading in Stuttgart and XETRA. XETRA and Local include the years 2002 to 2019, the MTFs cover the years 2008 to 2019 and OTC is available between 2014 and 2018. The sample includes all constituents with tax-free dividends of the German CDAX index between January 2002 and September 2019. The t-statistics are based on a nonparametric generalized sign test following Bartholdy et al. (2007). Data source: Refinitiv EIKON.

XETRA | Local | MTFs | ||||
---|---|---|---|---|---|---|

(1) | (2) | (1) | (2) | (1) | (2) | |

$\delta $ | 5.3155 | 4.9868 | 3.5429 | 3.3132 | 0.0256 | −0.6745 |

t-statistic | 2.88 | 2.14 | 1.94 | 1.68 | 0.02 | −0.48 |

DY | −12.1346 | −28.3522 | 7.7671 | 1.4437 | 39.9210 | 57.0001 |

t-statistic | −0.37 | −1.02 | 0.23 | 0.04 | 1.66 | 2.19 |

Risk | −0.5944 | −0.4877 | −0.7187 | −0.6094 | −0.6269 | −0.5403 |

t-statistic | −1.12 | −0.81 | −1.50 | −1.47 | −1.67 | −1.27 |

Spread | −31.2998 | −22.7293 | - | - | - | - |

t-statistic | −1.38 | −1.35 | - | - | - | - |

Cap | −0.3321 | −0.3334 | 0.1313 | 0.0960 | 0.2001 | 0.2740 |

t-statistic | −1.84 | −1.53 | 0.58 | −0.38 | 1.68 | 1.85 |

N | 436 | 436 | 436 | 436 | 246 | 246 |

Adj. R^{2} | 0.012 | 0.007 | 0.004 | 0.000 | 0.004 | 0.000 |

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