Ex-dividend day price and volume: the case of cum-ex trading

ABSTRACT In this paper, we analyse the extent of cum-ex trading in European markets. We document that the abnormal trading activity around the dividend day of a stock can be attributed to cum-ex trading, in addition to existing tax clientele hypotheses. Cum-ex trading is positively associated with dividend yield, which is consistent with maximizing returns from this strategy. Based on abnormal trading volume, we estimate a substantial loss to treasuries due to illicit tax refunds of withholding tax on dividends. Our results are robust, controlling for confounding effects and investors’ tax preference and heterogeneity.


I. Introduction
Prior research argues that the abnormal trading activity and stock price behaviour around exdividend days mainly result from tax heterogeneity among investors. For example, the dividend clientele hypothesis from Elton and Gruber (1970) suggests that the usual price drop ratio (PDR) on the ex-dividend day is less than one since the tax rate on dividend income is generally higher than on capital gains (e.g. see Bell and Jenkinson 2002;Graham, Michaely, and Roberts 2003;Elton, Gruber, and Blake 2005;Jeff and Rao 2010;Eminli 2018). Furthermore, the dynamic dividend clientele model from Michaely and Vila (1995) suggests that the PDR is determined by the average preference of all investors for dividends relative to capital gains and that the trading volume around the ex-dividend day is affected by tax heterogeneity together with dividend yield, risk and transaction costs (e.g. Michaely, Vila, and Wang 1996;Zhang, Farrell, and Brown 2008;Rantapuska 2008;Chen, Chow, and Shiu 2013;Le, Yin and Zhao, 2020). However, one factor that can also lead to abnormal trading activity around ex-dividend days but has not been considered so far is cum-ex trading, which has allowed a large network of banks, brokers, hedge funds and law firms to obtain multiple refunds of withholding tax on dividends that had only been paid once or not at all. This practice involves trading stocks quickly around the exdividend day with (cum) and without (ex) dividend rights to obscure who the actual owner of the stocks is. Tax authorities are unable to follow the change in ownership due to the underlying market microstructure and settlement process in place.
This paper examines the incidence and extent of cum-ex trading in European countries, which largely evolved from how withholding tax is collected. Typically, the dividend paying company withholds the tax on dividends and remits it to the treasury, while the shareholder's depository bank issues the tax certificate for a refund (if applicable). Intuitively, a tax system where the remitter and bearer of the tax differ should improve tax compliance, since the remitter does not directly benefit from any wrongdoing. However, Slemrod (2008) highlights the problems of such a tax system and shows that enforcement and the cost to administer taxation varies with the identity of who actually pays the tax. More generally, he argues that the standard economic view that states who remits a tax liability is irrelevant for the efficiency of a modern tax system does not hold in the presence of tax avoidance or evasion. 1 Buettner et al. (2020) build on the same economics of tax remittance and examine the rationale of withholding tax noncompliance. They find that cum-ex trading is mainly directed at exploiting existing tax laws as opposed to the arbitrage of the price drop on exdividend days. The ramifications from cum-ex trading are obvious: It provides an opportunity for some investors to earn short-term profits at virtually no extra risk to the detriment of all other investors and the society as a whole. Reported losses from this practice vary widely. References are often made without providing a reliable or legal basis. Apart from the insightful discussions by Dutt, Spengel, and Vay (2018) and Buettner et al. (2020), there are not many academic studies addressing the context of illicit dividend withholding tax refunds. 2 Our paper contributes to the literature on investors' abnormal trading activities around exdividend days by investigating the role of cum-ex trading in several ways. We shed light on this practice enabled by gaps in the tax system that have been well-known and ignored by law makers for many years. We first explain the rather complex transactions required to implement cum-ex trading. We then use actual market data to test the existence of cum-ex trading, complement the literature by providing estimates of the amount of trading volume accounted for by this strategy and corresponding losses based on an expanded sample of 4,295 firms and 34,564 dividend events. To the best of our knowledge, this is the first study that formally estimates the tax loss from cum-ex trading across different countries. For this, we develop a two-stage regression approach to disentangle the effect of cum-ex trading from alternative explanations for the increase in trading volume, including tax preference and heterogeneity among investors (e.g. see Lakonishok and Vermaelen 1986;Michaely and Murgia 1995;Michaely and Vila 1995;Koski and Scruggs 1998;Henry and Koski 2017). Using a regulation change on dividend withholding tax in Germany that bans cumex trading as a natural experiment, we show our two-stage approach effectively tests for cum-ex trading. We find a positive association between abnormal volume that is unrelated to general tax-induced trading and dividend yield in six out of eleven European countries, which could imply the existence of cum-ex trading since it is consistent with maximizing returns from this strategy. Our results suggest a total loss to treasuries from cumex trading between January 2002 and August 2018 of €10.3bn and €13.2bn based on mean-adjusted and market model excess volume. The average loss of the withholding tax per dividend event varies between 0.40% and 1.82%. Overall, we demonstrate why cum-ex trading has been so widespread and why it is likely to continue as long as inefficiencies in tax laws and administration exist. The results are robust controlling for confounding effects on abnormal volume, including risk, transaction costs as well as firm size, and provide an alternative but important intuitive explanation for the increased trading activity around the exdividend day.
The remainder of the paper is organized as follows. In Section II, we provide background information on cum-ex trading. Section III describes the data and reports summary statistics. Section IV discusses the methodology. Section V presents empirical findings and we conclude in Section VI.

II. Institutional background
Cum-ex trading usually requires several parties involved. This includes the original owner of the stocks, banks or brokers that borrow and short sale the stocks and another investor who buys the stocks just before the ex-dividend day (often using loan facilities provided by banks for leverage). The settlement period for most security transactions is two or three business days commonly referred to in the industry as T + 2 or T + 3. 3 On the settlement day, payment must be received and the stocks delivered to the buyer. If a transaction occurs for instance two days before the exdividend day, the settlement might overlap with the ex-dividend day resulting in stocks being bought cum dividend but delivered ex-dividend. The standard clearing process ensures that the buyer receives (i) the stocks at the ex-dividend price, (ii) a corresponding dividend compensation net of withholding taxes from the seller and (iii) a tax certificate issued by her depository bank. 4 In the case of cum-ex trading though, the seller does not actually own the stocks. Rather, the seller is short selling the stocks. This form of short selling is allowed provided the seller has arranged to borrow the stocks or has entered into an agreement with a third party confirming that the stocks are available for settlement when it is due. 5 However, since the short sale is not recognized as such by the seller's (or original owner's) depository bank it also issues a tax certificate, resulting in double tax refunds. 6 In a final step, the buyer sells the stocks back to the original owner. The proceeds from the additional tax refunds are then shared among the parties. Figure 1 illustrates the institutional arrangements of a typical cum-ex transaction based on a €0.40 cash dividend paid by Telefonica S.A. on 12 May 2015. The overall statutory tax rate on dividend income in Spain at this time was 24%. We consider three investors, A, who owns 1,000 shares worth €13,310 (based on a closing price of €13.31) and investor C who short-sells 1,000 shares cum-dividend to investor B two days before the exdividend day. Following the settlement process described above, A still receives the dividend net of withholding tax €304.00, D(1-t w ), and a tax certificate from his depository bank that entitles A to a tax credit or refund of €96.00 withheld as tax, t w D. B receives the shares ex-dividend on the exdividend day plus a dividend compensation equal to the net dividend from investor C. In addition, B's depository bank also issues a tax certificate worth €96.00 ignoring that the shares are bought from a short-seller and that the original owner of the shares has already received a tax certificate. B then sells the shares back to C who transfers the shares to A. The resulting second certificate entitles the buyer for a refund of withholding tax that are only paid once.
Despite warnings and testimonies from whistleblowers as early as 1992, 7 the practice continued and was so widespread that some banks setup Figure 1. Cum-ex trading. The figure illustrates the transfer of shares for a typical cum-ex trade between the original owner of the shares (investor A), the cum-ex seller (investor C) and cum-ex buyer (investor B) based on a standard dividend clearing process. D is the dividend paid and t w is the corresponding withholding tax rate. entire divisions specifically offering cum-ex trading to high net-worth or institutional investors. A consortium of international media outlets eventually helped to bring this practice into the spotlight in 2018. 8 Ongoing investigations have since identified hundreds of companies allegedly involved with numerous suspicious transactions, while assets have been frozen around the world and several trials either have started or are pending at the time of writing. 9 Tax authorities and lawmakers have failed to act upon numerous warnings or taken measures too slowly. For example, Germany has changed and updated its laws not until 2007. The new rules required that depository banks withhold and remit dividend taxes instead of the dividend-paying companies. 10 However, this only applied to domestic depository banks. Consequently, only investors with domestic bank accounts were precluded from obtaining illegitimate tax certificates. After that (at the latest), cumex trading went international. In Germany, cum-ex trading continued at least until 2012 when the government finally changed the rules for dividend withholding tax again (some 20 years after the first warnings). Since then, all banks (domestic and foreign) are responsible for withholding and remitting dividend taxes as well as issuing related tax refund certificates. However, somewhat surprising no EU-wide coordinated or joint efforts have been undertaken, even though several reports that similar short-comings of the withholding tax systems exist in various other European countries including Austria, Switzerland, France, Italy, Spain, Belgium and the Netherlands. 11 Albeit, we recognize that harmonizing tax systems to eliminate loopholes and opportunities for tax-motivated trading across different countries is inherently difficult, particularly if market participants collude. If cum-ex trading is indeed widespread, we would expect to see an increase in trading volume around the ex-dividend day. This follows from the normal settlement cycle, requiring short sales to be conducted two or three days before the ex-dividend day. 12 Figure 2 shows that in most countries, the average number of stocks traded increases sharply in the days right before the ex-dividend day and reverses shortly afterwards. 13 Bialkowski and Jakubowski (2012) report a similar pattern in a related dividend stripping trading practice with the sole purpose to reduce tax on dividend income. Buettner et al. (2020) examine the effect of cum-ex trading using a market equilibrium model and show that consistent with theoretical predictions, trading volume of stocks increases right before the ex-dividend day. While they focus on Germany, where a tax reform took place in 2012, we are not aware of other empirical studies that analyse the effect of cum-ex trading. An interesting question that naturally arises is how cum-ex trading contributes to the abnormal trading activities around ex-dividend days in addition to other well-established factors, such as tax preference and heterogeneity among investors. If it does result in abnormal trading volume, what is the extent of it and the tax loss associated with cum-ex trading across different countries? In this study, we attempt to provide answers to the above questions.

III. Data
We obtain information from Compustat Global on daily prices, returns, the number of shares traded and dividends of all publicly listed companies in the following countries: Austria, Belgium, Switzerland, Germany, Denmark, Spain, Finland, France, Italy, the Netherlands and Norway. These countries are the developed markets in Europe that have been identified by investigations to be (allegedly) affected by cumex trading. 14 In addition, we obtain foreign exchange rates from Datastream to convert all stock data to one currency (euro). Due to better data quality, we restrict our sample to common and preferred stocks (issue type code 0 and 1) in each country. Our sample comprises 4,295 firms and 34,564 firm-dividend observations over the period January 2002 to August 2018.  Table 1 provides an overview of taxable dividends in each country. Firms in Belgium and Switzerland pay on average the highest annual dividends in nominal terms (€12.9 and €12.7 respectively), while firms in Spain (€0.53) and Finland (€0.49) pay the lowest dividends on average. The standard deviation of individual dividends is highest in Switzerland (€58.63) and lowest in Spain (€0.35), while the average dividend yield varies between 3.29% in France and 5.08% in Norway. Because dividends can be paid quarterly, semi-annually or only once per year, annual dividend yield is calculated as the sum of dividends paid in a given year divided by the average price during the same year. The total dividends paid over the sample period also varies substantially across countries, ranging from €51.0bn in Austria to €1,140bn in France. To calculate the corresponding maximum amount of withholding tax revenue (assuming no refunds are credited to individuals and corporates), we use the relevant tax rates on dividend income in each year from the OECD Tax Database. Column 7 shows that withholding tax on dividends are a considerable source of revenue for treasuries, highlighting the importance of an effective and unassailable withholding tax system. On the other hand, it might represent a strong incentive for some investors to stretch legal limits beyond simply minimizing associated tax obligations.

IV. Methodology
This section describes the event study framework we use to test for cum-ex trading in European markets. Since the nature of this practice requires settlement to overlap with the ex-dividend date, we focus on the abnormal number of shares traded around the ex-dividend date. The standard settlement cycle for securities trading varies across European countries between two and three days referred to as T + 2 and T + 3. Therefore, the three days prior to the ex-dividend date are used as the event window. 15 We follow Ajinkya and Jain (1989) and use a log-transformation of raw trading volume before estimating abnormal volume based on the following two approaches, mean-adjusted volume and a market model. 16 For each event, the mean-adjusted abnormal volume is defined as the trading volume around ex-dividend date i on day t minus the average trading volume in the estimation period: where T is the number of days in the estimation period, for which we choose 100 trading days with f the first and l the last day of the estimation period (i.e. f = −110 and l = −11). 17 This period is long enough to avoid measurement errors and ensures estimators are not influenced by the volume around the event (see MacKinlay 1997).
The market model is defined as: where V it is the number of shares traded on day t during the same estimation period as above prior to ex-dividend date i, α i and β i are obtained with ordinary least squares estimation and ε it is the usual error term. The average market trading volume on day t, � V mt , is calculated as follows: where n is the number of shares in the market. The market model abnormal trading volume during the event window is then calculated as: For both approaches, a dividend event with missing trading volume on more than 40 days during the estimation period or with missing trading volume on any day during the event window is dropped. Table 2 reports daily abnormal trading volume relative to the average trading volume during the estimation window. Corresponding with Figure 2, the average number of shares traded during the event window increases substantially in most countries. The mean-adjusted abnormal trading volume ranges between 103% in Austria and 411% in Norway. Abnormal volume estimated by the market model is somewhat lower ranging between 85% in Austria and 328% in France. The difference between the estimation and event period is statistically significant in all countries.
Furthermore, since cum-ex trading is largely based on exploiting existing loopholes in the tax system, the question whether it might be illegal has always been present. For most investors, there is a definite answer, while for others it may seem more ambiguous. Therefore, we conjecture that investors mainly implement cum-ex trading in a way that maximizes the potential gains from the strategy, for example by focussing on high dividend yield stocks. In Table 3, we thus condition on the dividend yield as a possible refinement. If investors indeed maximise profits from cum-ex trading by focusing on high dividend yield stocks, we would expect to see higher abnormal trading volume for such stocks. Apart from a few exceptions, both mean-adjusted abnormal trading volume and market model estimates increase with dividend yield. The number of shares traded increase on average about twice as much in the first three quartiles and more than 300% in the top quartile. The difference between the quartiles is statistically significant in most of the countries. However, prior literature shows that tax preference and heterogeneity among investors also results in higher trading volume around the exdividend day (e.g. Lakonishok and Vermaelen 1986;Michaely and Murgia 1995;Michaely and Vila 1995;Michaely, Vila, and Wang 1996;Dhaliwal and Li 2006;Zhang, Farrel and Brown, 2008;Chen, Chow, and Shiu 2013;Le, Yin, and Zhao 2020). Investors with differing preferences for dividends versus capital gains will trade the relative tax burdens with each other. That is, high (low) tax bracket investors tend to sell (buy) shares cum-dividend then reverse and buy (sell) shares on or after the ex-dividend day. The drop in share price on the ex-dividend day in turn reflects the average tax preference of all investors for dividends relative to capital gains. Furthermore, Le, Yin, and Zhao (2020) document the higher the degree of tax heterogeneity among investors is, the greater dividends are valued, and the greater the price drop on the ex-dividend day. Therefore, in order to disentangle cum-ex from general tax-motivated trading, we use the drop in share prices on the ex-dividend day relative to dividends to capture the effect of tax preference and heterogeneity on excess volume. 18 In untabulated tests, we re-estimate the results reported in Table 3 for quartile portfolios of abnormal trading volume first sorted based on the stocks' ex-dividend day price drop ratio and then on dividend yield. As before with the univariate sort, there is a distinct positive association between excess volume and dividend yield in most countries after controlling for investors' tax preference and heterogeneity. The two-dimensional sort highlights the separate role of dividend yield unrelated to general tax hypotheses. Investors trying to maximize the gains from obtaining dividend withholding tax refunds might partially drive this relation. The analysis that follows provides further support for this view. The table reports average abnormal trading volume based on dividend yield quartiles formed each year. Abnormal volume is defined as the ratio of estimated daily abnormal trading volume during the event window over the daily average trading volume during the estimation period. Panel A is based on mean-adjusted trading volume, whereas Panel B is based on abnormal volume estimated from a market model. ***, ** and * denotes statistical significance at the 1%, 5% and 10% level. The sample period is from January 2002 through August 2018. Elton and Gruber (1970) demonstrate that the ex-day price drop ratio reflects the relative value of dividends versus capital gains as following: where Price cum is the cum-dividend day closing price, Price ex is the ex-dividend day closing price, t d is the dividend tax rate and t g is the capital gains tax rate. We follow Chen, Chow, and Shiu (2013) and calculate the price drop ratio using the closing price on the ex-dividend day adjusted for market movements as: where P cum is the cum-dividend closing price, P ex is the ex-dividend closing price, b r i is the expected return of stock i. 19 We first regress abnormal trading volume on PDR and PDR 2 : where AVR it is the abnormal trading volume ratio for dividend event i calculated as the average daily abnormal volume over the three-day event window divided by the average daily volume over the estimation window. 20 We include PDR 2 since Le, Yin, and Zhao (2020) report that abnormal trading volume around ex-dividend days could be a concave function of tax heterogeneity. Equation (8) allows us to separate the part of abnormal volume that is related with short-term trading activities due to investors' tax preference and heterogeneity. We then employ the coefficients of PDR, PDR 2 and the constant term (θ 1 , θ 2 , and γ) to estimate abnormal volume, d AVR; and calculate the residual of AVR as: We use this estimate of excess volume as dependent variable and regress it on dividend yield and other firm-specific variables to account for important determinants of abnormal trading volume around the ex-dividend day identified in prior literature: Again, AVR_residual reflects volume unrelated to general tax-induced trading. Therefore, a statistically significant and positive coefficient estimate of DY indicates the likely existence of cum-ex trading, since stocks with higher dividend yields can be used to claim higher tax refunds. DY i is calculated as the euro amount of dividends per share divided by the cum-dividend stock price. Controls i,t is a vector that includes risk, Vola i , defined as the highlow range-based volatility for stock i during the estimation period, since risk decreases tax arbitrage activities (e.g. see Michaely and Vila 1995;Wang 1996, 1996). The risk measure also accounts for the market turmoil during the global financial crisis (2007)(2008)(2009) and the Eurozone debt crisis (2010-2012) in our sample period. Including risk further captures general limits to the profitability of cum-ex trading and avoids measurement errors from a model that only accounts for the upside. For example, large price changes between the time the stocks are sold short and bought back might affect the overall return from the illicit tax refund. The main results reported below are unaffected using other measures for risk including the estimated CAPM beta, β, from regressing individual stock returns on market returns based on the estimation period (days −110 to −11 before the exdividend date) as a measure of systematic risk and idiosyncratic risk calculated as the standard error of the CAPM residuals divided by the standard error of the market returns during the estimation window, σ ε /σ m , (e.g. see Dhaliwal and Li 2006). Since transaction costs reduce trading profits and likely trading volume (e.g. see Michaely and Vila 1995;Wang 1996, 1996;Chen, Chow, and Shiu 2013), we follow Karpoff and Walkling (1988), Naranjo, Nimalendran, and Ryngaert (2000) and Dhaliwal and Li (2006) and calculate transaction costs, TC i , as the inverse of the cum-dividend closing price. As a robustness test (untabulated), we estimate the average Amihud (2002) illiquidity ratio for each stock during the estimation period as an alternative proxy for transaction costs. The illiquidity ratio measures the price impact of trades, which inhibits short-term trading activities on the ex-dividend day. The results remain largely unchanged. We also consider other widely applied control variables including lagged dividend yield, L_DY i , cumulative market returns, R m as well as average daily market capitalization, ACAP i , during the estimation window to control for the effect of market performance and firm size, if any, on abnormal volume. Equation (10) is estimated as panel regression including firm and year fixed effects. To reduce the effect of outliers, the data is winsorized at the top and bottom 1%ile. We also exclude special dividends, since such dividends normally tie to specific large events with large abnormal trading volume.

Effectiveness of the two-stage approach
Since our dependent variable is unrelated to tax preference and heterogeneity (orthogonal to PDR), dividend yield is no longer a necessary condition for excess trading around the ex-dividend day. 21 Although dividend yield is not a necessary condition for cum-ex trading either, we surmise that investors mainly trade stocks where the potential payoff from wrongfully obtained withholding tax refunds is highest. Therefore, conditioning on dividend yield biases against finding evidence of cum-ex trading. Before examining the extent of cum-ex trading in all countries in our sample, we use the case of Germany as a natural experiment to test the effectiveness of the proposed approach by including a dummy variable that equals one for all dividend events between 2013 and 2018, Post2012. This period accounts for changes in the administration of dividend withholding tax to ban cum-ex trading that came into effect in Germany in 2012. Yet, we are not aware of a European-wide joined action to halt this practice. Table 4 reports separate regression results for the mean-adjusted and market model abnormal trading volume respectively. The coefficient estimates on DY i are only positive and statistically significant in the sub-period before the change in legislation (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011). In the subsequent period the coefficients are indistinguishable from zero, i.e. DY i has no effect on excess trading after 2012. We also estimate Equation (10) for the entire sample period (2002)(2003)(2004)(2005)(2006)(2007)(2008)(2009)(2010)(2011)(2012)(2013)(2014)(2015)(2016)(2017)(2018) and add an interaction term between dividend yield and Post2012. While DY i has a positive and significant effect on (orthogonalized) abnormal volume, the coefficient on the interaction term is significantly negative. To the extent that dividend yield indeed captures activities from profit-maximizing cum-ex traders, the change in tax legislation appears to have helped to curb this practice in Germany. By contrast, clientele effects and other legitimate tax-induced trading that are positively related with DY should be unaffected by changing how withholding tax is administered (as opposed to the differential tax rates between dividend income and capital gains). These findings support our two-stage approach to test for cum-ex trading.

Cum-ex trading and tax loss in European markets
In this section, we examine the extent of cum-ex trading in ten European markets. Table 5 reports the corresponding results. For half of these countries the coefficient estimates on DY i are significantly positive. 22 The magnitude of the coefficients is somewhat misleading since the average dividend yield (particularly for interim dividends) tends to be rather small. To put it into perspective, the coefficient estimated for a mean sized dividend yield in Spain give a fitted daily abnormal volume ratio of 5.43% (1.19 × 4.56%), indicating a cum-ex trading associated volume of 16.28% over the three-day event window relative to the normal trading volume during the estimation period. Similarly, for a dividend event that is one standard deviation 21 Dividend yield is used as a measure of the tax-disadvantaged portion of stock returns and combined with tax heterogeneity among investors results in excess trading: investors with tax advantages (disadvantages) on dividends hold or buy (sell) stocks cum-dividend (before the ex-date and buy them back on the exdate or later) (see e.g. Vila 1995, 1996;Michaely, Vila, and Wang 1996;Dhaliwal and Li 2006). 22 The results are robust to different model specifications with and without control variables, including or excluding firm and time fixed effects (or using random effects), as well as estimating the panel regressions for a pooled sample of all observations across countries (including fixed effects). Somewhat surprising, the estimation results obtained for the independent variables appear to be largely indistinguishable from zero in some of the countries. Nonetheless, we report the results to ensure consistency with the prior literature on abnormal volume around ex-dividend days and our complementary analysis of cum-ex trading.
larger than the average dividend yield in Spain the fitted daily abnormal volume ratio equals 9.01% (or a cumulative abnormal volume of 27.03%). We next calculate the tax loss from cum-ex trading for each dividend event i in country j where the coefficient estimate on dividend yield in the previous table is significantly positive as: where CAV i is the cumulative abnormal volume during the event window, Div i is the gross dividend paid and τ j,y is the withholding tax rate in a given year. The total tax loss reported in Table 6 is then calculated as: The total loss in tax revenue for treasuries in Europe amounts to €10.3bn based on mean-adjusted abnormal volume (Equation. 11a) and €13.1bn based on the market model (Equation. 11b). 23 Denmark and Germany have been widely affected by cum-ex trading. 24 Yet, we also find considerable tax losses in countries that have received less attention including Finland, Norway and Spain. The loss per dividend event is also substantial and varies between €53,722 (Austria) and €602,462 (Spain) on average. Relative to the average withholding tax per dividend event, the loss varies between 0.40% (Austria) and 1.82% (Finland). Overall, our estimates are below Spengel, Dutt, and Vay (2017) who report a minimum loss in Germany of €7.2bn. However, this estimate is based on non-public data from Clearstream requested by  2002-20112012-20182002-20182002-20112012-20182002-2018 The table reports results from a panel regression of average daily abnormal trading volume orthogonal to tax heterogeneity (proxied by PDR and PDR 2 ) measured over a three-day event window. DY is the dividend yield, defined as the dividend per share divided by the stock price on the last cumdividend day. Post2012 is a time indicator, which equals 1 for all dividend events in the period 2013 to 2018 and 0 otherwise. Post2012*DY is an interaction term between dividend yield and the time indicator. Vola is the high-low volatility during the estimation period. TC is the inverse of the cum-dividend stock price as a proxy for transaction costs. L_DY is the lagged dividend yield from the previous dividend event. Return is the average stock return and Ln(ACAP) measures firm size as the average market capitalization over the estimation period. t-statistics are reported in parentheses. ***, ** and * denotes statistical significance at the 1%, 5% and 10% level. The sample period is from January 2002 through August 2018.
a special parliamentary inquiry, which is otherwise not available for research. Therefore, estimating the loss due to cum-ex trading using simple orthogonal abnormal volume measures appears to be rather conservative. We also do not account for multiple tax refunds where stocks are borrowed or sold short more than once via a series of OTC trades in combination with forward contracts (e.g. see Spengel 2016;Rau 2010). Our results are similar to Buettner et al. (2020) who report a tax loss for Germany of up to €1.01bn.
In any case, tax losses from cum-ex trading are an important issue for various reasons, (i) they affect the entire society since less public funding is available in all areas of government spending (including consumption, investment and transfer payments), (ii) most countries run long-term budget deficits and (iii) the practice of cum-ex trading has been known for many years. The importance of the issue is further highlighted in recent court rulings ending the previous legal limbo by confirming that cum-ex trading schemes are illegal. 25 Several banks, hedge funds and The table reports results from a panel regression of cumulative abnormal trading volume orthogonal to tax heterogeneity (proxied by PDR) measured over a three-day event window. Panel A reports results for mean-adjusted abnormal volume and Panel B for excess volume estimated from a market model. DY is the dividend yield, defined as the dividend per share divided by the stock price on the last cum-dividend day. Vola is the high-low volatility during the estimation period. TC is the inverse of the cum-dividend stock price as a proxy for transaction costs. L_DY is the lagged dividend yield from the previous dividend event. Return is the average stock return and Ln(ACAP) measures firm size as the average market capitalization over the estimation period. t-statistics are reported in parentheses. ***, ** and * denotes statistical significance at the 1%, 5% and 10% level. The sample period is from January 2002 through August 2018.
traders have been ordered to repay hundreds of millions of euros in wrongfully obtained tax refunds and to pay fines. 26

VI. Conclusion
Flaws in the tax systems and general inertia of lawmakers in European countries have allowed a network of investors, banks and law firms to obtain refunds of withholding tax on dividends that have not been paid before. We assume that the positive association between abnormal volume and dividend yield reflects (at least partially) a refinement of cum-ex trading to maximize profits. This view is supported when we control for alternative hypothesis for excess volume around the ex-dividend day, including investors' tax preference and heterogeneity, risk and transaction costs. Using abnormal trading volume around the ex-dividend day, we estimate a total loss of around €10bn to European treasuries from cum-ex trading. This estimate is based on market data and a widely used form of cumex trading that involves short selling shares and repurchasing them quickly around the exdividend day, but we will probably never know the full extent of this practice. The existence of cum-ex trading is disheartening, not only because it joins an already long list of wrongdoings in the financial sector, but in particular because it has been well-known and ignored by regulators and government officials for many years allowing the pilferage of public money.

Disclosure statement
No potential conflict of interest was reported by the authors. The table reports the total tax loss due to cum-ex trading, the average tax loss per dividend event using the regression coefficient reported in Table 5 and the average tax loss in percentage of the withholding tax amount per dividend. The estimates are based on both mean-adjusted abnormal trading volume and on abnormal volume derived from a market model. The sample period is from January 2002 through August 2018.