Stress testing the equity home bias: A turnover analysis of Eurozone markets

Stress testing the equity home bias: A turnover analysis of Eurozone markets

Journal of International Money and Finance 97 (2019) 70–85 Contents lists available at ScienceDirect Journal of International Money and Finance jour...

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Journal of International Money and Finance 97 (2019) 70–85

Contents lists available at ScienceDirect

Journal of International Money and Finance journal homepage: www.elsevier.com/locate/jimf

Stress testing the equity home bias: A turnover analysis of Eurozone markets Manuela Geranio a, Valter Lazzari b,c,⇑ a

Università Bocconi, Finance Department, Via Rontgen 1, 20136 Milano, Italy Università Cattaneo LIUC, Corso G. Matteotti, 22, 21053 Castellanza (VA), Italy c SDA Bocconi School of Management, Via Bocconi 8, 20136 Milano, Italy b

a r t i c l e

i n f o

Article history: Available online 20 June 2019 JEL codes: G12 G41 F36 Keywords: Home bias Equity markets Trading volumes Holiday effect Eurozone exchanges

a b s t r a c t Shifts in equity turnover happen on and around holidays because rationally bounded investors become distracted. Their pattern reveals a persistent equity home bias even in the Eurozone, a stress test case for the survival of this bias given the high level of economic and financial development and integration in this area. The bias is greater for small caps because investors are reluctant to hold this class of foreign asset. Our study corroborates calendar anomalies in trading volumes, but refutes the hypothesis regarding turnover sensitivity to stock returns common in the empirical and theoretical literature based on investor heterogeneity and short sale constraints. Our results reveal vanishing cost asymmetries in taking long rather than short positions. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Investors’ home equity bias remains a major puzzle in international macroeconomics thirty years after the French and Poterba (1991) seminal contribution. However, some recent evidence does suggest that such bias has declined, if not disappeared altogether among developed and integrated countries (De Santis and Gèrard, 2006; Baele et al., 2007; Schoenmaker and Bosch, 2008; Cooper et al., 2018). The resilience of equity home bias to growing financial integration may be due either to international portfolio diversification counterbalancing costs faced by fully rational investors or to a heterogeneity of bounded rational investors. In the first case, investment models based on the representative agent framework would be appropriate. To preserve their assumptions of perfect rationality and common priors, home bias must arise from frictions that lessen the benefits of international diversification, such as currency and domestic inflation risk, higher trading costs and any type of foreign country institutional risk (Stulz, 1981; Glassman and Riddick, 2001; Aggarwal et al., 2005, Levy and Levy, 2014). In the latter case, the bias could spring from factors undermining perfect rationality and common priors, such as selective dissemination of price sensitive news, bounded rational decision rules, and presence of noise investors. Social proximity and slow moving news may cause information advantages (Bodnaruk, 2009; Baik et al. 2010; Coval and Moskowitz, 2001). Moreover, investors may

⇑ Corresponding author. E-mail addresses: [email protected] (M. Geranio), [email protected], [email protected] (V. Lazzari). https://doi.org/10.1016/j.jimonfin.2019.06.002 0261-5606/Ó 2019 Elsevier Ltd. All rights reserved.

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prioritize the stocks more visible to them due to their limited capacity for attention and their behavioral perception of lower risk or information advantage arising from familiarity (Bailey et al., 2008; Grinblatt and Keloharju, 2001; Huberman, 2001). Our work shows that within a heterogeneous population of bounded rational investors, home bias can emerge even when real frictions limiting the benefits of international diversification are minimal. We see this happening even in the Eurozone, among some of the most developed and interconnected economies in the world. This observation undermines the common belief that the preference for domestic stocks is set to disappear as the global integration of financial systems grows. Compared to the existing literature, we specialize our study in terms of the metrics, the geography, and the granularity of the investigation. As for the metrics, unlike most other contributions, we study trading volumes rather than holdings. Representative agent models are mute on turnover; their markets clear in terms of the stock of assets rather than trade flows. Prices adjust to news with no need for trading beyond random liquidity shocks. Even information asymmetries do not justify massive turnover if traders fully and rationally update their beliefs based on counterparty behavior (Kyle, 1985). These models do not explain trading patterns dictated by clientele effects and deviations from full rationality. Models with heterogeneous investors can account for such patterns since differences in beliefs and slow-moving news depart from common priors, while noise traders and investors’ attention constraints deviate from perfect rationality (Harris and Raviv, 1993; Hong and Stein, 2007; Shleifer and Summers, 1990). Rationally bounded investors manage their information overload allocating their time and skills between stocks (Hirshleifer and Teoh, 2003; Peng and Xiong, 2006). As the preference of investors goes to the stocks that are most visible to them, clientele effects arise. Combined with short sale constraints and investors’ overconfidence in their own information, heterogeneity produces a positive co-movement between returns and turnover, links high valuation with overtrading (Hong and Stein, 2007) and causes subdued trading volumes in low return summer months (Hong and Yu, 2009). In terms of geography, we focus on turnover in the major Eurozone public equity markets as a form of stress test for the home bias hypothesis. Frictions hampering foreign holdings are absent among these countries. The unprecedented integration achieved in this region leaves no room for investors’ distance aversion, making the geographic, economic, cultural and institutional distance insignificant. Coeteris paribus, any evidence of bias towards domestic stocks, if detected, would reveal a preference for local assets (strict home bias) rather than an aversion for those of remote countries (foreign bias), a distinction made by Chan et al. (2005) and Bekaert and Wang (2009). We add the UK and the US to benchmark the Eurozone and assess the role of the two main world financial centers, the former being proximate and the latter dominant in investment capacity (Yeandle and Wardle, 2019). As for the granularity of the analysis, we treat the home bias for stocks of different size separately to verify if bias inversely correlates with the stocks’ international visibility, size being its most common proxy. The literature on home bias relates to holdings at country level, at the most focusing on some investor types (Hau and Rey, 2008). Surprisingly, it has never approached the issue on a more granular level despite the fact that small caps might cater more to domestic investors than large caps. A world of bounded rational heterogeneous investors gives rise to three claims on which we leverage. First, turnover fluctuates because the attention capacity of investors varies over time. If they allocate their cognitive effort to more activities than stock trading, the turnover should drop when a common factor of distraction emerges, as investors lose focus and fail to adjust their portfolio promptly to the new information (Jacobs and Weber, 2012). Second, the investors’ recognition hypothesis suggests that investors deal with the stocks most visible to them, causing preferred trading habitats to emerge (Merton, 1987). In an international setting, this translates into investor bias towards local stocks, regardless of any real friction hampering diversification gains. Third, either the bias emerges from a spontaneous preference of domestic investors for national assets or it is imposed by the reluctance of foreign investors to deal with such assets. Thus, we have the both an ‘‘active” and a ‘‘passive” component of home bias (Cooper et al., 2018). If investors perceive foreign small caps as more remote than foreign large caps, or insist on extra liquidity to facilitate the exit from a foreign market in case of need, the bias would weigh more heavily on small caps because of such passive component. The interaction between the investor holiday distraction and the preferred trading habitats shapes particular crosscountry patterns of trading volumes that we exploit as a natural experiment. Holidays serve as exogenous shocks to the size and composition of the investor population useful for tracking cross-country trading activity. In this paper, we aim to assess if the pattern of turnover shifts during holidays is consistent with either the emergence of a common pool of liquidity in the Eurozone or the persistence of a home bias. If the latter, we also consider the possibility that even in such a highly integrated area the bias might be more pronounced in the case of less visible and liquid stocks. In pursuing our goal, we distinguish between the holidays when the domestic exchange is open for trading (open market holidays – OMH) from those when it is closed (closed market holidays – CMH). In our experiment, the three claims described result in a few testable hypotheses. OMHs should cause a significant turnover dip if festivities distract bounded rational investors from focusing on the stock market. In turn, if a strict home bias persists the turnover drop induced by OMHs in the Eurozone should be greater in the country on holiday, while no difference across countries should emerge in case a common Eurozone liquidity pool exists. Lastly, by considering stock size as a proxy for stock visibility, at a more granular level we test the hypotheses of a higher passive component of home bias for small caps and, conversely, of a lower active component for large caps. The dip in turnover in the country experiencing the OMH should weigh more on its small caps than large caps as local investors disproportionally own smaller stocks due to the greater reluctance of foreigner investors to hold them. Correspondingly, the trading dip caused by foreign CMHs and OMHs should weigh more on large than on small caps, if investors prefer foreign stocks with a larger capitalization.

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Our results support these hypotheses. Because of time varying investors’ attention capacity, turnover fluctuations reveal clientele effects due to the investors’ passive bias towards small local stocks, and a reduced active bias towards large stocks when trading abroad. This observation holds true even in the Eurozone where frictions hampering the international diversification benefits are almost nil, which makes this region a good stress test case for home bias. OMHs are a source of distraction, albeit to a different extent, for bounded rational investors everywhere, except in the UK. Thus, country specific cultural and institutional factors matter. To the best of our knowledge, this work is the first to investigate the interconnectedness of trading activity across countries, mapping the relevance and direction of cross-country trading sources. Such mapping reveals that both the size of each market and the proximity between markets matter. When the markets in the US (a large but distant one), or in the UK (a smaller but closer one), stop trading due to a CMH, the turnover drops significantly in the Eurozone. By introducing the control variables suggested by the literature, we derive further novel results regarding the rationale for trading dynamics around holidays and turnover sensitivity to stock returns. The turnover trend around CMHs, OMHs and weekends favors the hypothesis of bounded rational investors who are slow to refocus on trading after a festivity distraction rather than the alternative of fully rational investors who are quick to catch up with the liquidity shocks occurring during a holiday. Our results also question the long-held hypothesis of an unconditional positive correlation between turnover and returns. Karpoff (1987) shows that turnover surges with both the size and the absolute size of the rates of returns, which implies that trading is more sensitive to increases than to decreases in prices. By proving that this now holds for smaller stocks only, for large and mid caps we dispute a common theme in most trading models with heterogeneous investors, namely that short selling constraints make long positions less costly to hold than short position (Hong and Stein, 2003). Overall, our results suggest that even in highly integrated financial markets, where conditions provide a stress test scenario for the survival of a home bias, a noticeable preference towards trading domestic stocks still persists and is more pronounced for small caps. This conclusion runs counter to some recent evidence on a disappearing home bias based on metrics inferred from portfolio holdings as referenced in the opening paragraph. The second section outlines the research framework; the third sets up the models, describing variables and dataset. Results are in Section 4, divided into sub-sections the last of which covers the outcomes of the sensitivity checks aimed to ascertain the robustness of the findings. The fifth section concludes.

2. Theoretical framework We consider the daily volume traded in the exchanges of the three main Eurozone economies (EZ-3): Germany, France and Italy. Even though we focus on these three countries alone, our sample offers a comprehensive picture of the Eurozone public stock market accounting for two thirds of its overall market cap and turnover. These countries, along with the UK, are similar for development, financial sophistication and economic size (all data at end 2018 are in Table 1). Thus, the scope of the analysis facilitates the comparability and interpretation of the results. Among these countries, there is no rational reason for investors to entertain a significant home bias since the reciprocal barriers against profiting from cross-border diversification are close to nil. In the Eurozone all metrics of remoteness among countries used in the literature to motivate such bias are insignificant: geographic proximity, information intensity, openness of capital and trade flows, cultural links, common traits in terms of institutions and development (Bekaert and Wang, 2009). On a macro level, stocks listed on these exchanges benefit from being part of a common market with free movement of goods, services, capital and labor. They share a common monetary policy, and currency and respond to converging fiscal policies and economic cycles. On a micro level they trade, clear and settle through integrated processes, and rely on similar systems of investor protection and corporate governance as defined by the European Union regulation. Its pillars consist in shared transparency obligations, governance requirements, takeover discipline, trade execution policy rules, principles of open access and inter-operability of market infrastructures. Schoenmaker and Bosch (2008) find that the home bias has declined in Europe starting from the introduction of the Euro, with Euro area investors switching from domestic to euro area securities. Baele et al. (2007) claim that the globalization and regional integration have strongly eroded the determinants of home bias, with a sharp decrease of such bias especially in the Eurozone. Similar findings emerge from De Santis and Gèrard (2006), while Mishra (2015) draws a more conservative conclusion. According to the measure developed by Cooper et al. (2018), investors in Eurozone countries show a negative strict home bias (a preference to invest abroad, in countries similar to home, rather than domestically) and a minimal positive distance aversion, neither of which is significant. Yet, Eurozone stocks continue to trade mainly on their legacy national exchange. From January 2014, the earliest available data, to February 2019, the last date in our sample, these exchanges claimed a market share of domestic blue chip trading ranging from 62% in the UK to 75% in Italy (source: www.fidessa.com). Counterintuitively, this does not imply separate preferred domestic trading habitats that perpetuate a market fragmentation across borders (‘‘persisting home bias hypothesis”). Despite Eurozone integration, each legacy exchange might have retained an advantage in attracting order flows for its domestic stocks from everywhere, this having been their only available liquidity pool for over a century. Hysteresis would then explain why trading, even among home bias free investors, keeps gravitating toward legacy exchanges (‘‘hysteresis hypothesis”).

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Table 1 Country Summary Statistics – December 2018. For each country, the table provides summary statistics on the size of: (i) the economy; (ii) the equity markets; (iii) the assets of equity funds assets; (iv) the investments in listed equity and mutual funds abroad. Data source: 1World Bank; 2,3World Federation of Exchanges, Euronext and Borsa Italiana; 4International Investment Funds Association; 5 Coordinated Portfolio Investment Survey data (CPIS), International Monetary Fund (30 June 2018). Germany

France

Italy

UK

US

World Total

Gross Domestic Product1 (m. USD) Share of the World Total Equity Market Capitalization2 (ml. USD) Share of Eurozone Total Share of World Total

4,000,386 4.72% 1,755,173 24.49% 2.35%

2,775,252 3.28% 2,373,366 33.11% 3.18%

2,072,201 2.45% 622,710 8.69% 0.83%

2,828,644 3.34% 3,015,286 – 4.04%

20,494,050 24.18% 30,436,313 – 40.77%

84,740,322 100.00% 74,662,848 – –

Turnover (Electronic Order Book)3 (ml. USD) Share of the Eurozone Total Share of the World Total

1,818,479 33.19% 1.87%

1,335,734 24.38% 1.37%

719,307 13.13% 0.74%

1,828,463 – 1.88%

36,130,733 – 37.11%

97,365,368 – 100.00%

Equity Funds’ Assets4 (ml. USD) Share of World Total

311,155 1.56%

333,502 1.67%

22,119 0.11%

807,942 4.06%

11,888,725 59.68%

19,921,574 100.00%

Assets held in investment funds and foreign equity5 (ml. USD) Share of the World Total

1,266,593 4.34%

931,712 3.19%

1,081,524 3.49%

2,075,842 7.11%

8,780,480 30.08%

29,190,167 100.00%

The major sources of international order flows are outside the Eurozone, in the US and the UK, home of the main global financial centers. EZ-3 accounts for 6.4% of the global market cap, slightly more than the UK (4.0%), but much less than the US (40.8%). Proportions are slightly lower for turnover: 4.0%, 1.9% and 37.1% of the world total. The assets of equity funds in the EZ-3 make up for 3.4% of the world total, against the 4.1% for the UK and 59.7% for the US. The EZ-3 tallies 11% of foreign portfolio investments, the UK and the US 7.1% and 30.1% respectively (Table 1). Including the US and the UK in the analysis provides a broader scope to our investigation. The extent to which these countries contribute to Eurozone trading is of great consequence in terms of liquidity and investor population. Whilst the US is the largest center for equity investments, the UK is closer to the Eurozone geographically (time zone), institutionally (in the EU) and economically (business cycle and trade flows). Thus, comparing the interconnectedness of the US and the UK with the Eurozone sheds light on the relative importance of size versus proximity in cross border trading. So far, there has been little attempt to understand the geography of trading flows, a limited exception being the analysis of the turnover in Europe when US exchanges are closed (Casado et al., 2013). To fill this gap, we leverage on the natural experiment provided by the divergent calendar of national holiday to test some hypotheses on the geography and time pattern of trading. The Eurozone exchanges agreed to run trading on all weekdays of the year, apart from six exceptions: Good Friday, Easter Monday, May Day, Christmas, December 26 and New Year’s Day, all closed market holidays (CMHs). Italy adds three days to this list, August 15, Christmas Eve and December 31; Germany only the last two, which come with shorter trading hours in France (morning only). On any other festivity, such as January 6 in Italy or July 14 in France, trading runs regularly, giving rise to open market holidays (OMHs). A CMH/OMH partition also applies to the US and the UK. They run shorter trading hours on selected days: the day before Independence Day, Black Friday and Christmas Eve in the US; the last trading day before Christmas and December 31 in the UK. Since OMHs provide a proxy for investor distraction (Jacobs and Weber, 2012), we exploit them to test some hypotheses on the pattern of stock trading. Days with shorter trading hours fall in between OMHs and CMHs. We consider the effect of these half-trading days (HTDs) on turnover separately. We start by testing H1) If distracted by a national festivity, attention capacity constrained investors will spend less effort to stock market activities, causing domestic turnover to drop on OMHs. If this holds, we then test H2) If an equity home bias persists among Eurozone investors, OMHs will depress domestic turnover the most. Instead, a combined presence of both a common Eurozone liquidity pool and hysteresis in the competition between exchanges will cause the OMH effect to spread more evenly over all the Eurozone markets. If the persisting home bias is due to a familiarity issue, it should affect stocks to a different extent in relation to their varying level of visibility. Small caps should appear less familiar to foreign investors and more difficult to evaluate in both economics and governance terms compared to large caps. Moreover, foreign investors’ fears of an adverse selection risk due to a slower dissemination process of price sensitive news might be exacerbated in the case of small caps. Investors may even demand extra liquidity when venturing abroad to facilitate a prompt exit as a risk-mitigating factor on foreign exposures. If so, small caps would become even less internationally attractive, passively catering mainly to domestic investors. Such a clientele effect suggests two further testable hypotheses: H3) During an OMH, domestic turnover will drop more for small caps than for large caps because of the induced passive form of home bias; H4) The effect of CMHs and possibly OMHs on foreign turnover will drag down mainly the turnover of large caps as they are less exposed to the active component of home bias than small stocks.

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OMH and CMH cross-country effects enable us to appreciate the contribution of the US and the UK to the EZ-3 turnover, the US being proxy for the ‘‘size” factor and the UK for the ‘‘proximity” factor. Since we cast our experiment in terms of holiday effects on daily turnover, our approach must account for high frequency shifts in trading volumes. The standard method for detecting abnormal volumes on specific dates employs the event study methodology, comparing the turnover on the event dates to a normal turnover estimated over a properly selected estimation window (Chae, 2005). The comprehensiveness of our experiment makes this option unsuitable in our case. Since we consider several event dates across five markets, it is impossible to build an event free estimation window for each one. To avoid unreliable and logically inconsistent estimates of ‘‘normal trading”, we have to frame our analysis in a regression setting. We build linear models to explain daily turnover changes using dummies that identify all relevant dates (OMH, CMH, HTD), plus other control variables which are also responsible for systematic patterns of high frequency turnover shifts. This approach requires extra care in interpreting the coefficients of the dummies related to back-to-back days, as in the case of OMHs or HTDs. If both parameters are significant, a sign reversal signals an abnormal shift in volume on the first day, with the turnover reverting to normal on the next day. On the other hand, the insignificance of the next day estimate implies a persisting turnover anomaly. To discriminate the home bias effect by type of stocks, we run models for large, mid and small caps. Our analysis includes year dummies to account for any time related shift in turnover, and some control variables for the known calendar anomalies. We start by including dummies for the days around the holiday (Meneu and Pardo, 2004), as well as for the days of the week (Chordia et al., 2001). The turnover around holidays or weekends allows us to test two competing hypotheses condensed in H5) If liquidity shocks drive the trading activity, turnover will rise after a CMH (weekend), as investors catch up on their trading plans. The same will occur the day before a CMH if investors can also anticipate this rebalancing. Instead turnover will drop on the day before and the day after a holiday if investors get distracted preparing for the holiday (weekend) and need time to refocus afterward. This second alternative is in line with the results of Dellavigna and Pollet (2009). They find a weak investor reaction to earnings disclosed on a Friday and no evidence of any ‘‘catching up” with the news on the following Monday. Meneu and Pardo (2004) find no anomalies in pre-holiday trading. The dummies for the days of the week also serve as control variables for events that may regularly affect turnover on a given weekday, independently of the arrival rate of price sensitive news flow. For instance, exchange traded derivatives expire on Friday. This could possibly drive a surge in stock trading on that day, as investors settle their positions. Our models also include two pairs of dummies to account for turnover anomalies due to the window dressing trading which takes place at the turn of the asset managers’ reporting cycles (Lakonishok et al., 1991). Such dummies single out the first and last trading day of the year and of remaining months. Confining the effects of the turn of the reporting cycle to a couple of days may be overly restrictive. However, our methodology serves to capture daily shifts in turnover. As such, it is not optimal to deal with slow moving turnover changes occurring over a fuzzily defined time horizon. A final type of control addresses the swings in turnover caused by a time-varying arrival rate of price sensitive news. We add the absolute value of both positive and negative stock returns to the model as separate instruments for news flow intensity. Coeteris paribus, richer updates of the information set, proxied by larger price movements in either direction, amplify the effect of investor heterogeneity on turnover. We use control variables in the form of two such pairs of returns, both contemporaneous and with a one-day lag, to account for delayed transmissions. This ensures that any holiday effect on turnover is not due to a changing intensity of the arrival of price sensitive news. The same holds for the day-of-the-week effects as monetary policy announcements always happen on the same weekday (Federal Reserve on Wednesday; European Central Bank and Bank of England on Thursday). The pair of same day return variables also offers the opportunity to test a claim delivered by models based on investors’ heterogeneity, short sales constraints and investors’ overconfidence in their own beliefs: the positive sign of the unconditional correlation between turnover and returns. Epps (1975), Karpoff (1986), as well as Hong and Stein (2003) with their endogenous revelation process of private information converge on the following hypothesis H6) Turnover will react more to increases than decreases in stock prices if short positions cost more to hold than long positions. Since advances in stock lending practices and the growth of the equity option market have made such cost asymmetry questionable, at least for large caps, we test if H6 still holds. 3. Empirical specification We run models of daily percentage turnover changes for stock size ‘‘k” (large, medium and small caps) and country ‘‘i” (Germany, France, Italy, UK and US), as follows: j j i i i i i i DV i;k t ¼ a þ Rj b1;j OMHt þ Rj–i b2;j CMHt þ ðb3;i HTDt þ b4;j HTDtþ1 Þ þ ðb5;i OMHt1 þ b6;i OMHtþ1 þ b7;i CMHt1 þ b8;i CMHtþ1 Þ  þ b9 Dmon þ b10 Dtue þ b11 Dthu þ b12 DfriÞ þ ðb13 DSY þ b14 DEY þ b15 DSM þ b16 DEM   i;k i;k þ b17 Rþi;k þ b18 Ri;k þ b19 Rþi;k t t t1 þ b20 Rt:1 þ Rt b21;t Y Dt þ Det

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M. Geranio, V. Lazzari / Journal of International Money and Finance 97 (2019) 70–85 Table 2 Total return stock indices used in the analysis. Source of data on trading volumes and indices values: Bloomberg. Country

Large caps

Medium caps

Small caps

Germany France Italy UK US

DAX 30 CAC40 FTSE MIB FTSE 100 S&P 500

MDAX Index CAC Mid 60 FTSE IT Mid Cap FTSE 250 S&P 400

SDAX Index CAC Small FTSE IT Small Cap FTSE Small Cap S&P 600

i,k i,k i,k i,k Our dependent variable is the daily percentage change in turnover, DVi,k t, = (Vt,  Vt1)/Vt1,, with Vt being the turnover of stocks included in the equity market index for stocks of size class k of country ‘‘i” on day ‘‘t” (source: Bloomberg). Table 2 provides the complete list of these indices. We divide our explanatory variables into seven groups. The first group contains the dummies for open market holidays in each country ‘‘j” (OMHj). They appear in all models, causing both same (i = j) and cross-country (i – j) effects. There is almost no cross-country overlap among OMHs, these being local holidays. As OMHj proxies for the distraction of country j investors, their sign should be negative if the investors’ attention capacity is constrained (H1). Under the local preferred habitat hypothesis, the OMHj own country effect dominates the cross-country effect (H2). According to the investors’ recognition hypothesis, the passive home bias is more relevant for small caps than for large caps, implying that OMHs must have the greatest effect on domestic small caps (H3). The second group of variables consists of dummies for closed market holidays in each country ‘‘j” (CMHj). They only appear in models of other countries’ turnover (i – j), causing cross-country effects. Due to an almost perfect overlap in CMHs of Eurozone countries, we use three dummies to identify CMHs, one each for the US, the UK and the Eurozone as a whole. This last variable captures any holiday with no trading in at least two of the three Eurozone member countries under consideration. Slight changes to the model are appropriate for the US due to its vastly larger scale as compared to the European domestic markets taken separately. We drop their OMH dummies and build the CMH dummies using a pyramidal approach to detect the level of aggregation where they reach sufficient critical mass to affect the US turnover. CMHEZ identifies holidays shared by at least two Eurozone countries, but not by the UK. CMHUK refers to UK holidays that fall on dates other than CMHEZ. CMHUK&EZ stands for days when exchanges close in both the UK and in any two Eurozone countries. Because of the recognition hypothesis and the higher propensity to invest abroad by professional investors who usually focus on large caps, CMH dummies should play a more prominent role in the regressions for large caps than for small caps (H4). Keeping the stock size constant, the CMHj parameters should be more significant if the international equity capacity of the investing country ‘‘j” is larger (capacity effect), the investable market ‘‘i” is closer to the investors of country ‘‘j” (proximity effect) and the international relevance of the former is higher (country visibility effect). The first effect should stress the relevance of US holidays for the Eurozone, whilst the second should favor the role of UK festivities. Because of country visibility, foreign holidays should weigh more on core markets (Germany) than on peripheral ones (Italy). The third group of variables consists of the dummies HTDit and HTDit+1 that indicate when the market of country ‘‘i” operates a shorter session (morning only) and the following day when trading hours are back to normal. HTDit coefficients should be negative. Even with a constant arrival of price sensitive news and no distraction, the shorter trading time shrinks the set of new daily information to which investors must adjust. If distraction plays a role, turnover would drop more than proportionally visà-vis the shorter trading session. On the contrary, if the liquidity trades of the day could be concentrated in the shorter session, the turnover would drop less than proportionally. In any case, HTDit+1 should be positive since the venue resumes normal operating hours. There is no HTDit and HTDit+1 in the regressions for Germany and Italy, as their public markets never schedule HTDs. For these variables, and any other discussed below, we only consider the own-country effect. By means of the fourth group of variables, we assess the competing hypothesis in H5 on possible pre- and post-holiday trading anomalies. Four series of dummies identify the trading day before and after an open market holiday (OMHit1 and OMHìt+1) and a closed market holiday (CMHit1 and CMHit+1). If random liquidity shocks were the motive for trading, CMHit+1 should have a positive sign. Investors would both catch up with their portfolio rebalancing after a full day of no trading and adjust their holdings in response to the richer update of the public information set that became available during the extra 24 h from close to opening. To a lesser extent, similar implications should hold for OMHit+1. Investors might prefer not to adjust their portfolio to a liquidity shock on OMHs because they are either distracted or afraid of trading in a low liquidity market. Should they have discretion on the timing of their response to liquidity shocks, they may even anticipate their trade. If so, coefficients for CMHit1 and, to a lesser extent, OMHit1 might be positive. Otherwise, if investors lose their trading focus on the eve of the holiday and need time to refocus once the festivity is over, both pre- and post-holiday dummies should have a negative sign. The fifth group of variables consists of dummies designed to control for calendar anomalies. We start by including four dummies that identify the day of the week, with Wednesday as the baseline case. In some countries (US, UK), holidays cluster on a specific day of the week, namely Monday, forcing to control for any potential day of the week effect.

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Mondays and Fridays are of primary importance as they bookend the weekend. In so doing, they mirror the case of CMHt1 and CMHt+1, however, with three differences: their weekly occurrence might make the risk of distraction less disruptive; the stop on trading on weekends lasts two days instead of one; trading stops at the same time in all markets. We also introduce dummies to identify the first and the last trading day of the year (DSY and DEY), as well as the first and last trading day of the remaining eleven months (DSM and DEM). In the asset management industry these days mark the turning point between different reporting cycles providing professional investors with an incentive for window dressing trading. Because of this, turnover might surge as managers liquidate and rebuild their portfolio positions. DSY and DEY do not appear in the regressions for France and the UK. Their markets run a morning only trading session on the last day of the year making it impossible to disentangle the turn of the year from the half-day trading effect. In these cases, we give priority to the HTD variables, dropping the turn of the year dummies. The sixth group of variables consists of the absolute size of the same day and previous day returns. Primarily, they serve as instrumental variables for the varying arrival rate of price sensitive news. However, Karpoff (1987) and Hong and Stein (2003) provide a different motivation for using these variables. They posit that diverging costs in holding long rather than short positions cause a discrepancy in the size of the immediate portfolio adjustment to positive and negative news. This, in turn, gives rise to the hypothesis of an asymmetric turnover reaction to positive and negative returns of similar size, the former being greater than the latter. We build the return series from the daily closing values of the total return indices shown in Table 2. Since turnover positively correlates with the same day returns, no matter what their sign is, we introduce R+i,k and R-i,k t t , the absolute value of the daily return in country ‘‘i” for stocks of size k when respectively positive or negative, and zero otherwise. Thus, we allow for -i,k varying turnover sensitivity to upward and downward price changes. We include prior day returns, R+i,k t1 and Rt1, to capture an expected negative lagged effect: turnover should revert to normal once the information content of the previous day’s return has been incorporated into the prices and the rebalancing executed. In the seventh group, we include the year dummies meant to capture time varying trends in turnover. Our analysis covers 11 years, from 17 December 2007 to 5 February 2019. We do not consider the Eurozone in its infancy stage, as during that period investors had to adjust to the new setting. Instead, we set our start date around the time when the Eurozone entered its 10th year (1 January 2008). We choose a slightly earlier start date (17 December 2007) to preserve turn of the year observations. For the same reason we postpone the end date (5 February 2019) compared to the typical year-end cutoff. Table 3 Bank holidays and half-day trading sessions. Number of days in which exchanges are: (i) open for trading despite a national holiday (OMH); (ii) closed because of a national holiday (CMH); iii) on a shorter trading session (HTD). There are 24 days when a CMH occurs in at least two of the three Eurozone countries, but not in the UK. Instead, 42 of the UK CMHs fall in days when a CMH occurs in no more than a single Eurozone country. Country or Economic Area involved

Open Market Holiday (OMH)

Closed Market Holiday (CMH)

Half Trading Day (HTD)

Germany France Italy UK US

21 59 42 20 22

59 33 57 68 76

0 17 0 22 26

Table 4 Average change in daily returns and trading volumes for large, medium and small caps. Average Daily Return (%)

Average Daily Turnover Change (%)

Arithmetic Mean

Geometric Mean

Standard Deviation

Arithmetic Mean

Geometric Mean

Standard Deviation

GERMANY Large Cap Medium Cap Small Cap

0.02% 0.04% 0.02%

0.01% 0.03% 0.02%

1.42% 1.42% 1.12%

4.87% 3.25% 3.20%

0.42% 0.08% 0.01%

32.47% 27.39% 27.48%

FRANCE Large Cap Medium Cap Small Cap

0.01% 0.00% 0.02%

0.02% 0.01% 0.01%

1.45% 1.45% 1.18%

4.87% 3.45% 4.46%

0.12% 0.23% 0.06%

37.71% 30.92% 32.87%

ITALY Large Cap Medium Cap Small Cap

0.01% 0.15% 0.02%

0.02% 0.02% 0.03%

1.69% 4.05% 1.15%

3.09% 3.23% 2.94%

0.07% 0.03% 0.07%

26.53% 27.22% 26.02%

UK Large Cap Medium Cap Small Cap

0.01% 0.03% 0.02%

0.00% 0.02% 0.02%

1.20% 1.13% 0.75%

4.10% 4.28% 4.76%

0.02% 0.28% 0.07%

33.38% 33.38% 33.86%

US Large Cap Medium Cap Small Cap

0.03% 0.04% 0.04%

0.02% 0.03% 0.03%

1.27% 1.41% 1.52%

3.07% 3.05% 3.22%

0.03% 0.07% 0.07%

27.22% 27.65% 28.25%

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The number of observations is not the same in all countries due to diverse CMH schedules (Table 3). It also varies across stock classes, as we drop unreliable outliers (a daily turnover change above +200% or below 67% on otherwise ordinary dates). Missing data and outliers account for less than 0.4% of the sample, ranging from zero (Italy, mid cap) to 43 (US, small caps). The number of observations thus goes from 2,754 (US small caps) to 2,844 (French large caps). We build separate OMHs and CMHs schedules matching the calendars of the exchanges with corresponding national festivities retrieved from www.timeanddate.com. As Table 3 shows, OMHs are more common in the Eurozone, CMHs in the US and UK. In our sample there are 26 half-days of trading in the US, 22 in the UK, 17 in France, and none in Germany and Italy. Table 4 shows the average of the daily discrete returns and turnover rates of change of the stock indices, calculated as both arithmetic and geometric mean. The latter is interpretable as the arithmetic mean of the continuous returns and turnover rate of changes, a more suitable metric to use when having to aggregate them over time. However, since our analysis must center exclusively on a daily frequency, we work with discrete changes, as they are more intuitive and more commonly used. We confine the continuous changes to a sensitivity analysis. In the case of the turnover rate of change, there is a huge difference between the arithmetic and the geometric mean, with the former being positive for all series and the latter close to zero, often slightly negative. This wide gap is due to the extremely high volatility of such series, a drastic case of the well-known volatility drag phenomenon. A preliminary data analysis reveals the presence of heteroscedasticity, but no autocorrelation. Thus, we apply a robust standard errors procedure in the estimation. Tables 5–7 show the results for each of the five countries, with respect to large, mid and small caps. Each table consists of six segments. One to four show the first four groups of variables. To enhance readability, the display of the results for the

Table 5 Turnover models for large cap indices (17 December 2007–5 February 2019). Results for linear regression models of turnover in the stocks included in the large cap indices of the countries in Table 2 (Germany, France, Italy, UK and US). Each segment of the Table covers estimates and p-values for a different set of variables. Open Market Holiday (OMH) dummies are in the first segment; Closed Market Holiday (CMH) dummies in the second; half trading day (HTD) dummies in the third; the dummies for the day before and after the holiday in the fourth (subscripts ‘‘t  1” and ‘‘t + 1”). For clarity, results for the remaining variables are in Tables 8–10 (dummies for the days of the week, turn of the year and of the month effects and local index daily returns). Headings refer to the country of reference, or wider geographical area. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level.

OMHGER OMHFRA OMHITA OMHUK OMH

US

CMHUS CMHUK*

Germany

France

Italy

UK

US

0.295^^^ 0.000 0.055^ 0.090 0.091^^^ 0.002 0.041 0.540 0.115^^^ 0.001

0.152^^^ 0.000 0.173^^^ 0.000 0.041 0.129 0.045 0.524 0.101^^^ 0.005

0.109^ 0.053 0.031 0.393 0.095^^^ 0.007 0.043 0.448 0.091^^ 0.032

0.068^ 0.096 0.082^^ 0.019 0.013 0.656 0.037 0.528 0.059 0.136

0.052 0.487 0.135^^^ 0.000

0.179^^^ 0.000 0.177^^^ 0.000

0.204^^^ 0.000 0.230^^^ 0.000

0.176^^^ 0.000 0.156^^^ 0.000

0.265^^^ 0.000

0.310^^^ 0.000

0.041 0.170 0.009 0.839 0.149^^ 0.032

0.286^^^ 0.000 2.263^^^ 0.000

0.501^^^ 0.000 0.912^^^ 0.000

0.006 0.915 0.100^^^ 0.001 0.096^^^ 0.004 0.094^^ 0.047

0.038 0.536 0.121^^ 0.013 0.072^^ 0.013 0.524^^^ 0.000

0.067^^ 0.039 0.130^^^ 0.002 0.067^^ 0.027 0.012 0.760

0.051 0.645 2821 0.287

0.257 0.164 2811 0.390

0.035 0.659 2791 0.289

CMHEZ** CMH

UK&EZ

0.609^^^ 0.000 2.595^^^ 0.000

HTDt HTDt+1 OMHt1 OMHt+1 CMHt1 CMHt+1

0.020 0.769 0.358^^^ 0.000 0.009 0.891 0.158^^^ 0.008

0.021 0.534 0.267^^^ 0.001 0.126^^^ 0.000 0.147 0.496

Days of the week dummies Turn of the year/month dummies Return variables

Please, see Table 8, Panel A Please, see Table 9, Panel A Please, see Table 10, Panel A

Constant p-value No. Observations R-squared

0.086 0.722 2809 0.341

0.004 0.861 2844 0.500

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Table 6 Turnover models for mid-cap indices (17 December 2007–5 February 2019). Results for linear regression models of turnover in the stocks included in the mid cap indices of the countries in Table 2 (Germany, France, Italy, UK and US). Each segment of the Table covers estimates and p-values for a different set of variables. Open Market Holiday (OMH) dummies are in the first segment; Closed Market Holiday (CMH) dummies in the second; half trading day (HTD) dummies in the third; the dummies for the day before and after the holiday in the fourth (subscripts ‘‘t  1” and ‘‘t + 1”). For clarity, results for the remaining variables are in Table 8, 9 and 10 (dummies for the days of the week, turn of the year and of the month effects and local index daily returns). Headings refer to the country of reference, or wider geographical area. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level.

OMHGER OMHFRA OMHITA OMHUK OMH

US

CMHUS CMHUK*

Germany

France

Italy

UK

US

0.348^^^ 0.000 0.065^^ 0.031 0.070^^^ 0.008 0.092 0.172 0.047 0.199

0.141^^^ 0.000 0.204^^^ 0.000 0.025 0.349 0.113 0.241 0.053^^ 0.041

0.159^^^ 0.002 0.030 0.508 0.100^^^ 0.002 0.012 0.869 0.077 0.125

0.094^^ 0.015 0.046 0.205 0.045 0.105 0.036 0.604 0.052 0.120

0.013 0.814 0.141^^^ 0.000

0.152^^^ 0.000 0.213^^^ 0.000

0.149^^^ 0.000 0.247^^^ 0.000

0.184^^^ 0.000 0.162^^^ 0.000

0.178^^^ 0.000

0.288^^^ 0.000

0.003 0.953 0.072 0.139 0.073 0.487

0.322^^^ 0.000 2.309^^^ 0.000

0.541^^^ 0.000 0.921^^^ 0.000

0.013 0.829 0.101^^^ 0.003 0.095^^ 0.012 0.066 0.174

0.045 0.429 0.052 0.188 0.101^^^ 0.002 0.522^^^ 0.000

0.035 0.331 0.099^^ 0.018 0.097^^^ 0.000 0.085^ 0.079

0.058 0.587 2,822 0.171

0.308 0.224 2,812 0.361

0.043 0.566 2,766 0.229

EZ**

CMH

UK&EZ

CMH

0.620^^^ 0.000 1.988^^^ 0.000

HTDt HTDt+1 OMHt1 OMHt+1 CMHt1 CMHt+1

0.038 0.310 0.514^^^ 0.000 0.033 0.532 0.093^^ 0.026

0.031 0.387 0.188^^^ 0.000 0.058^ 0.062 0.113 0.513

Days of the week dummies Turn of the year/month dummies Return variables

Please, see Table 8, Panel B Please, see Table 9, Panel B Please, see Table 10, Panel B

Constant p-value Observations R-squared

0.081 0.717 2,810 0.282

0.017 0.396 2,833 0.422

control variables in the fifth segment is held over to Table 8 (day of the week), Table 9 (turn of reporting cycle) and Table 10 (returns). The last segment shows the constant term, with related p-value, and the R2 of each model. To economize on space, estimates for the year dummies are available only on the journal websites. None of them is significant at the 10% level, as expected. The mid/long term shifts in turnover trends are a cause of concern for mid-to-low frequency analysis of turnover shifts, but they are much less so here, since the focus is exclusively on high frequency (daily) and short lived shifts. 4. Results All of the regressions show relevant significance, decreasing with the size of the stocks. For large caps, the R2 ranges from 0.29 in the US and Italy to 0.50 in France; for mid-caps, from 0.17 in Italy to 0.42 in France; for small caps, from 0.14 in France to 0.26 in the US. 4.1. Holiday effects and home bias If OMHs are a source of distraction for investors with attention capacity constraints, the festivities should cause the trading volume to dip. If investors prefer local stocks, the drop should mainly concern the home country on holiday. If small caps are more prone to a home equity bias than large stocks, a domestic OMH should have a stronger impact on the former, while the cross-country effects of both OMHs and CMHs should be more significant for large caps. Results shown in the first segment of Table 5–7 provide support for all of these claims.

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Table 7 Turnover models for small cap indices (17 December 2007–5 February 2019). Results for linear regression models of turnover in the stocks included in the small cap indices of the countries in Table 2 (Germany, France, Italy, UK and US). Each segment of the Table covers estimates and p-values for a different set of variables. Open Market Holiday (OMH) dummies are in the first segment; Closed Market Holiday (CMH) dummies in the second; half trading day (HTD) dummies in the third; the dummies for the day before and after the holiday in the fourth (subscripts ‘‘t  1” and ‘‘t + 1”). For clarity, results for the remaining variables are in Table 8, 9 and 10 (dummies for the days of the week, turn of the year and of the month effects and local index daily returns). Headings refer to the country of reference, or wider geographical area. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level.

OMHGER OMHFRA OMHITA OMHUK OMH

US

CMHUS CMHUK* CMH

EZ**

CMH

UK&EZ

Germany

France

Italy

UK

US

0.397^^^ 0.000 0.080^^ 0.026 0.097^^^ 0.002 0.057 0.237 0.097^^ 0.011

0.066 0.205 0.280^^^ 0.000 0.005 0.919 0.078 0.301 0.040 0.635

0.058 0.318 0.006 0.893 0.352^^^ 0.000 0.120 0.103 0.078 0.136

0.064 0.234 0.043 0.278 0.041 0.519 0.141 0.156 0.033 0.475

0.002 0.984 0.120^^^ 0.003

0.106^^^ 0.000 0.160^^ 0.026

0.115^^^ 0.001 0.005 0.935

0.010 0.670 0.042 0.256

0.092^^ 0.013

HTDt+1

OMHt+1 CMHt1 CMHt+1

0.469^^^ 0.000 1.435^^^ 0.000

0.565^^^ 0.000 1.030^^^ 0.000

0.033 0.418 0.527^^^ 0.000 0.121^^^ 0.000 0.101^^ 0.038

0.063 0.287 0.011 0.901 0.148^^^ 0.000 0.155^ 0.077

0.044 0.193 0.040 0.266 0.081^^^ 0.004 0.012 0.795

0.012 0.552 2,810 0.197

0.184 0.578 2,805 0.173

0.074 0.464 2,754 0.262

0.477^^^ 0.000 0.825^^^ 0.000

HTDt

OMHt1

0.042 0.546

0.048 0.261 0.008 0.883 0.138 0.145

0.027 0.319 0.804^^^ 0.000 0.069^^ 0.020 0.081^^ 0.022

0.015 0.708 0.211^^^ 0.000 0.069 0.130 0.002 0.980

Days of the week dummies Turn of the year/month dummies Return variables

Please, see Table 8, Panel C Please, see Table 9, Panel C Please, see Table 10, Panel C

Constant p-value Observations R-squared

0.075 0.325 2,809 0.215

0.022 0.346 2,831 0.137

OMHs decrease domestic turnover significantly, mostly at less than the 1% level, in all countries and for all stock sizes. The UK is the exception, being the only country for which data refute the holiday distraction hypothesis. The drop in turnover ranges from 9.5% (Italian large caps) to 39.7% (German small caps), with differences across countries and stock size. The domestic OMH effect matters more in the Eurozone than in the US, peaking in Germany (average of 34.7% across stocks of all sizes). The holiday distraction is thus a function of country specific work habits and cultural traditions. Results in the first segment of Tables 5–7 also point to a persistently strong investors’ preference for trading stocks listed on the domestic exchange, even in the Eurozone. Between France and Italy, the holiday distraction carries no cross-border effect, as their cross OMH dummies are statistically insignificant in the respective models. The holiday distraction impacts at home, but not in the neighboring market, also part of the Eurozone, implying that the domestic market remains the preferred trading habitat. The holiday distraction in France and Italy acquires international relevance with respect to Germany. Their OMHs cause German turnover in large, mid and small caps to drop significantly, but such downturns are minor compared to those caused by German OMHs. Such asymmetry might follow from Germany being a larger economy, with investors more prone to holiday distractions. However, German OMHs depress the French and Italian turnover in large and mid-caps to the same extent that these countries own OMHs do, while having no impact on small cap turnover. A combined reading of this evidence reveals that the larger economy and the greater distraction argument can only be part of the story. A home bias effect must be at work, otherwise the pattern of OMH effects in Italy and France would mirror the one seen in Germany. OMHs in the UK exert no cross-country effects, confirming that British investors are immune to holiday distractions.

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Table 8 Turnover models: day of the week effects for large, medium and small caps. Panels A, B and C complete Tables 5–7 for the turnover models of large, mid and small caps respectively. These panels show estimates and p-values of the dummy variables that refer to the day-of-the-week effects, with Wednesday being the base case. Please, refer to respective tables for the full model. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level. Germany

France

Italy

UK

US

PANEL A – LARGE COMPANIES Dmon 0.198^^^ 0.000 Dtue 0.134^^^ 0.000 Dthu 0.030^^ 0.015 Dfri 0.060^^^ 0.001

0.191^^^ 0.000 0.132^^^ 0.000 0.022^ 0.073 0.002 0.881

0.165^^^ 0.000 0.128^^^ 0.000 0.015 0.236 0.045^^^ 0.000

0.166^^^ 0.000 0.095^^^ 0.000 0.010 0.413 0.017 0.302

0.130^^^ 0.000 0.018^^ 0.030 0.008 0.340 0.124^^^ 0.000

PANEL B – MEDIUM COMPANIES Dmon 0.161^^^ 0.000 Dtue 0.114^^^ 0.000 Dthu 0.012 0.284 Dfri 0.039^^^ 0.008

0.133^^^ 0.000 0.096^^^ 0.000 0.015 0.232 0.034^^ 0.011

0.107^^^ 0.000 0.118^^^ 0.000 0.007 0.624 0.054^^^ 0.000

0.154^^^ 0.000 0.078^^^ 0.000 0.020^ 0.094 0.030^ 0.070

0.071^^^ 0.000 0.037^^^ 0.001 0.002 0.810 0.042^^ 0.030

PANEL C – SMALL COMPANIES Dmon 0.088^^^ 0.000 Dtue 0.044^^^ 0.002 Dthu 0.014 0.297 Dfri 0.024 0.135

0.034^ 0.078 0.076^^^ 0.000 0.002 0.901 0.005 0.786

0.008 0.611 0.072^^^ 0.000 0.015 0.275 0.030^^ 0.023

0.126^^^ 0.000 0.105^^^ 0.000 0.027 0.111 0.007 0.717

0.093^^^ 0.000 0.037^^^ 0.000 0.009 0.356 0.102^^^ 0.000

Table 9 Turnover models: effects of the turn of the month and of the year for large, mid and small cap. Panels A, B and C complete Tables 5–7 for the turnover models of large, mid and small caps respectively. These panels show estimates and p-values of the dummy variables that refer to the first and last trading day of the year and the remaining months, DSY, DEY, DSM and DEM respectively. Please, refer to respective tables for the full model. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level. Germany PANEL A – LARGE COMPANIES DSM 0.057^^ 0.011 DEM 0.100^^^ 0.000 DSY 1.161^^^ 0.000 DEY 0.313^^^ 0.000 PANEL B – MEDIUM COMPANIES DSM 0.051^ 0.050 DEM 0.229^^^ 0.000 DSY 0.809^^^ 0.000 DEY 0.234^^^ 0.000 PANEL C – SMALL COMPANIES DSM 0.055^^ 0.009 DEM 0.108^^^ 0.000 DSY 0.566^^^ 0.000 DEY 0.202^^^ 0.000

France

Italy

UK

US

0.073^^^ 0.001 0.170^^^ 0.000

0.040^ 0.064 0.122^^^ 0.000 0.522^^^ 0.000 0.029 0.665

0.151^^^ 0.000 0.220^^^ 0.000

0.179^^^ 0.000 0.261^^^ 0.000 0.281^^^ 0.008 0.322^^^ 0.000

0.109^^^ 0.000 0.206^^^ 0.000

0.060^^ 0.016 0.160^^^ 0.000 0.577^^^ 0.001 0.018 0.758

0.126^^^ 0.000 0.196^^^ 0.000

0.147^^^ 0.000 0.309^^^ 0.000 0.176^^ 0.043 0.451^^^ 0.000

0.052^^ 0.037 0.045 0.101

0.034^ 0.084 0.046^^ 0.041 0.049 0.489 0.034 0.593

0.078^^^ 0.008 0.102^^^ 0.001

0.120^^^ 0.000 0.263^^^ 0.000 0.082 0.336 0.396^^^ 0.000

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Table 10 Turnover models: return effects for large, medium and small caps. Panels A, B and C complete Tables 5–7 for the turnover models of large, mid and small caps respectively. These panels show the estimates and p-values of the local index daily return variables R+t and R-t. Please, refer to respective tables for the full model. R+t and R-t are the series of the absolute value of the daily returns when positive and negative; R+t1 and R-t1 are the same series lagged one period. The symbols ^^^, ^^, ^ denote significance at the 1%, 5% and 10% level. The table below also shows the p-values for the t-test of the difference between the parameters for R+t and R-t, equality being the null hypothesis. Germany

France

Italy

UK

US

Average

PANEL A – LARGE COMPANIES 7.439^^^ R+t 0.000 R-t 10.663^^^ 0.000 6.807^^^ R+t1 0.000 7.789^^^ Rt1 0.000

6.529^^^ 0.000 9.748^^^ 0.000 6.189^^^ 0.000 6.732^^^ 0.000

6.035^^^ 0.000 7.404^^^ 0.000 3.967^^^ 0.000 4.885^^^ 0.000

3.921^^^ 0.000 6.451^^^ 0.000 3.229^^^ 0.000 3.920^^^ 0.000

3.517^^^ 0.000 5.533^^^ 0.000 3.884^^^ 0.000 2.818^^^ 0.000

PANEL B – MEDIUM COMPANIES 3.253^^^ R+t 0.000 Rt 5.090^^^ 0.000 R+t1 2.658^^^ 0.000 R-t1 3.835^^^ 0.000

6.418^^^ 0.000 6.211^^^ 0.000 4.486^^^ 0.000 4.849^^^ 0.000

3.984^^^ 0.000 0.448^ 0.071 2.288^^^ 0.000 0.262 0.134

6.002^^^ 0.000 4.154^^^ 0.000 3.465^^^ 0.000 3.492^^ 0.000

3.141^^^ 0.000 2.915^^^ 0.000 2.883^^^ 0.000 1.521^^^ 0.007

PANEL C – SMALL COMPANIES 6.799^^^ R+t 0.000 R-t 7.720^^^ 0.000 + Rt1 4.753^^^ 0.000 R-t1 6.428^^^ 0.000

14.115^^^ 0.000 0.687 0.247 7.114^^^ 0.000 0.542 0.220

12.330^^ 0.000 5.281^^^ 0.000 5.589^^^ 0.000 7.507^^^ 0.000

11.486^^^ 0.000 4.291^^^ 0.001 6.203^^^ 0.000 3.143^^ 0.012

5.525^^^ 0.000 3.781^^^ 0.000 4.257^^^ 0.000 3.184^^^ 0.000

5.488 7.960 4.815 5.229

4.560 4.593 3.156 3.424

10.051 5.268 5.583 5.066

p-value of the F-test for R+t = R-t Large Caps Mid Caps Small Caps

0.000 0.005 0.380

0.000 0.827 0.000

0.036 0.000 0.000

0.007 0.069 0.000

0.009 0.748 0.009

Instead, OMHs in EZ-3 countries’ affect the UK turnover, with a pattern that also supports the persistence of an equity home bias. OMHs in Italy, the most peripheral of the EZ3 countries to the global financial system (Yeandle and Wardle, 2019), show no significant effect for UK stocks of any type. OMHs in France and Germany have a significant impact only on UK larger stocks, this despite Germany’s bigger economy and more pronounced investors’ holiday distractions. As for the passive component of the home bias, in all three Eurozone countries the national holiday distraction weighs more on the turnover of small caps than of large caps. The average of their domestic OMH estimates is 18.7% for large caps and almost twice as much for small caps (34.3%). The reluctance of investors to deal with foreign small caps forces domestic investors to take the lead in holding such stocks, exacerbating their turnover sensitivity to the domestic holiday distraction compared to large caps. The only exception to this pattern is the US, where trading drops in a similar manner for stocks of all sizes because of the holiday distraction of domestic investors (from 12.0% to 14.1%). The incidence of foreign capital on the total of the US equity markets lacks sufficient substance to produce a passive component of home bias weighing selectively on small caps. Being immune from the holiday distraction, the UK market continue to provide no useful indication. The active component of home bias appears to be weaker the larger the size of the stocks involved. The foreign investors’ distraction or inactivity due to the occurrence of one of their national holiday weighs on the domestic equity turnover asymmetrically, being more relevant for large caps than for small caps. Results are stronger for CMHs, given that they cut off access to the market completely.

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The UK CMH dummy causes a significant drop in the large cap turnover in all the EZ-3 countries, but is significant only for Germany in the case of small caps. CMHs in the US cause a significant dip in the turnover for stocks of any size across all European countries despite the time zone difference and the reduced overlap of the trading sessions, the Italian small caps being the sole exception to this. However, the drop is always greater for large than for small caps, averaging respectively –20.6% and 7.4% across the four EU countries. Similarly, the Eurozone CMHs strongly depress UK turnover for large caps, but retain no significant effect on the UK small caps. They also fail to exert any significant effect on US turnover, unless they happen concurrently with the UK CMHs. In this case, the drop in the US trading activity becomes significant only for large caps. In short, because of their higher visibility and liquidity, large caps are more appealing for foreign investors, which makes them exposed to a weaker active home bias compared to small caps. Results for the OMHs corroborate the asymmetrical active component of home bias across stocks of different sizes. The OMH dummy for Germany causes a significant drop in the large caps turnover in all remaining European countries, but always fails to prove significant for small caps. The OMH dummy for France has a similarly significant effect on large cap turnover in Germany and the UK, but only in Germany in the case of small caps. Italian OMHs fail to affect the equity turnover to a significant degree in any other country, the only exception being Germany. Another salient factor revealed is the visibility of the investable market. During US CMHs, trading in Europe falls the most for UK large caps (26.5%), the most visible class of stocks in the country with the most developed financial sector. Instead, there is no consequence for Italian small caps, the least visible class of stocks in the country most peripheral to the international financial system among those here considered. Moreover, the trading slowdown induced on Eurozone markets by UK CMHs is significant for small stocks only in Germany, the most ‘‘core” market in the area. The dummies for the half-day trading sessions (HTDt and HTDt+1) behave as expected. As shown in the third segment of Tables 5–7, turnover in the US and France is halved on HTDs. The effect is milder in the UK for large and medium caps, confirming the peculiarity of this country with respect to holiday distractions. Moreover, the estimate for HTDt+1 shows that when the standard trading schedule resumes, trading goes back to normal in the US, a country where the half-day effect does not interfere with the end of the year effect (turnover roughly doubles after having dropped by half for all type of stocks). Where such interference occurs, in the UK and France, HTDt+1 also captures the start of year anomaly, revealing a rebound that far exceeds the recovery of the standard turnover level. This is particularly evident for larger stocks, typically held by professional asset managers, the class of investors most engaged in rebuilding their positions after year’s end window dressing trades.

4.2. Pre- and post-holiday effects The turnover behavior on the day before and after a holiday provides further insights into discriminating between competing hypotheses on the underlying trading motives. If investors catch up with their portfolio rebalancing triggered by the random liquidity shocks that occurred on a no trading day, turnover should surge. The additional flow of price sensitive news during the trading suspension, however small, should magnify this effect. Turnover might also increase on the eve of a holiday if investors anticipate their portfolio adjustments. Alternatively, if the holiday is a distraction for bounded rational investors, its effects may spill over to the prior and the following day, slowing down the trading activity. The same competing hypotheses apply to Fridays and Mondays. As shown in the fourth segment of Tables 5–7, the evidence consistently rejects the random liquidity shocks hypothesis in favor of the distraction hypothesis. There is no turnover anomaly on the eve of OMHs in any market and for stocks of any size, with the exception of the US large caps whose turnover drops. A similar downturn occurs for all countries and stocks on the eve of a closed market festivity, with CMHt1 failing to reach significance in only three of the 15 models. Friday trading shows a pattern similar to the day before CMHs, only less marked and with a couple of reasonable exceptions (Table 8). For small and mid-caps the sign of the Friday dummy is negative and often significant in the European markets, while it is significantly positive only in the US. For large caps, the same dummy is significantly negative only for Italy, while in Germany and the US turnover sees an upswing on Fridays. These two countries host the largest exchange equity derivatives markets whose traded contracts usually expire on Friday. This causes trades in the underlying assets, mainly large caps, to spike, as investors must settle their derivative positions. As for the post-holiday, OMHt+1 shows a significant positive sign in all models, except for mid and small caps in the UK and small caps in the US. Rather than signaling a surge in turnover due to the investors catching up with the liquidity shocks that occurred while the country was on holiday, this finding reveals that trading is merely recovering from the OMH trading slump. The trading behavior after a CMH also validates the holiday distraction hypothesis. CMHt+1 is either significantly negative or insignificant. The sole exception is the UK, where stocks of all sizes see a significant surge in turnover after a CMH, confirming the immunity of this country from this type of distractions. The data on the first trading session after the weekend make an even clearer case for the lack of any turnover rebound motivated by the desire to catch up with the liquidity shocks that occurred during the trading halt. The Monday dummy is always negative, failing to reach significance only for Italian small caps (Table 8).

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In short, investors are both distracted on the eve of a holiday (weekend) and slow to refocus after trading resumes. This distraction overrides the effect of the extra hours’ worth of potential news flows and random liquidity shocks occurring when the market is closed. This result generalizes the work of Jain and Joh (1988) who find that the weak Monday start in the S&P500 stocks’ turnover is concentrated in the first hour of trading. 4.3. Other calendar anomalies As for the remaining calendar anomalies, Table 9 shows a strong surge in turnover on the last trading day of the month (DEM). This upswing persists only in part on the first trading session of the next month (DSM) that marks the start of a new reporting cycle for asset managers. In all models, DEM is significantly positive, while DSM is significantly negative, but of a smaller order of magnitude. A strong turnover increase at the turn of the month is consistent with window dressing trading by institutional investors. They have an incentive to download loser stocks at the end of the month, reinvesting the proceeds at the start of the new month. Across stocks, the effects of such incentive are weaker for small caps, as they are less palatable to large investors. Across countries, said effects are stronger in the US and the UK, home of the most developed asset management industries. For the countries without shorter sessions at the year’s end (Germany, Italy and the US) separate dummies single out the last and first trading day of the year (DEY and DSY) since the yearly reporting cycle is more important than the monthly cycle. Admittedly, investors might dilute their end of year portfolio rebalancing process over a longer period by frontloading their window dressing trading in early December to avoid the distraction of the Christmas Season. However, our work aims to detect patterns of turnover on pre-specified dates. It is not suited to for slow-moving turnover changes occurring over fuzzily defined periods since they are outside the scope of our analysis. The results for the turn of the year diverge from those of the turn of the month in a way that is unique to each country, which highlights once again the role of country specific institutional and cultural traits. In the US, results for DEY and DSY magnify those seen for the turn of the month. The first trading session of the year strengthens the already significant turnover surge of the closing session of the previous year. In Germany, the turnover slows drastically at the year’s end, the distraction factor overwhelming the window dressing motive. This makes room for a massive turnover rebound in the opening session of the new year. Volumes more than double for large caps, the preferred target of asset managers, while escalating by over 50% for small caps, whose clientele consists of a greater share of retail investors. Italy shows no significant turnover change in the last trading day of the year, as if the effects of the holiday distraction and the window dressing motive cancel each other out, while experiencing a strong turnover surge on the first session of the year, like the US and Germany. 4.4. Return effects The absolute value of same day return enters the regression models separately for positive and negative price changes (R+i t and R-i t ) to ensure consistency with the extensive literature suggesting a positive correlation of the turnover with both the rate of returns and their absolute values. These variables also serve as instruments for the flow of price sensitive information, a factor that affects the daily trading volume. Results shown in Table 10 deviate significantly from the literature on trading in a setting with heterogeneous investors and short sale constraints. Theoretical models assume that these constraints make short positions costlier to hold than long positions. Hence, turnover has to be more sensitive to positive than to negative returns because investors find it easier to adjust to positive than negative price sensitive news. Furthermore, the existing empirical analyses support such hypothesis. In line with such previous literature, our results confirm a strong positive co-variation of turnover changes with both positive and negative same day returns. However, unlike it, they also reveal that turnover is significantly more sensitive to positive than to negative returns only for small caps (average across countries is 10 for R+ and 5.3 for R-), with the exception of Germany, where no meaningful difference appears. Instead, in the case of large caps, turnover is always significantly more reactive to a price decrease than to a price increase (average of 5.5 for R+ and of 8.0 for R-). Evidence on mid-caps also contrast with previous findings, providing conflicting results. The estimated turnover sensitivity to positive rather than negative returns varies from country to country. It is significantly stronger on the downside in Germany, on the upside in the UK and Italy, while no difference emerges in the US and France. Overall, the results suggest that short sales constraints continue to make short positions costlier to hold than long positions only for small caps, but have ceased to do so for large caps. Such evidence is consistent with the advances in stock lending technology and practices. It also aligns with the growth of the market for equity derivatives products, especially for stocks included in the headline blue chip indices. Both factors have noticeably lowered, if not nullified, the cost differential between taking short and long positions, at least for large caps. It is worth noting that with short sale constraints turning ineffective, the turnover of large caps does not respond to positive and negative price sensitive news symmetrically. Rather its price sensitivity tilts in the opposite direction to that traditionally suggested, being always stronger in the case of downturns. Two factors might explain this finding. First, convex portfolio strategies dictated by investors’ decreasing risk aversion are more prominent in downtrends than uptrends. Professionals form the main investors’ clientele for large caps. Compared with retail investors, they are more consistent in imple-

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menting stop loss strategies when prices drop, while being less keen on increasing risk exposures when prices move up. Second, stock correlations increase during down-markets. Negative news is more systematic than positive news, fostering wider portfolio rebalancing waves that an indices based analysis accurately captures. Nuances in results of mid and small caps are also informative. Short sale constraints continue to dictate turnover sensitivities in countries with less developed exchange equity derivatives market, namely Italy, the UK and France. In Germany and the US, home to the most developed of such exchanges, turnover sensitivities to positive and negative returns have either turned symmetrical (US mid caps, German small caps) or inverted their relative strength (German mid caps). -i The preceding day return variables, R+i t1 and Rt1, show a strong negative covariation with the change in turnover for all stocks and in all countries, as should be the case in reasonably efficient markets where the turnover surge correlated to a large price movement must quickly fade.

4.5. Sensitivity analysis A matter of concern is the robustness of our findings with regard to some relevant factors, such as the metrics used to measure the daily shifts in the trading activity, the discretionary timing of the portfolio rebalancing decisions, and the time span covered by the analysis. For each of these factors, we perform a sensitivity analysis, the results of which provide further support to our findings.1 The first sensitivity check ascertains the robustness of our findings in relation to the metrics of the daily turnover change used. We run a parallel analysis based on the turnover continuous rate of change obtained as the log difference of turnover levels. No material difference emerges, with the exception of the strength of the negative influence on US trading exerted by the CMHs in the Eurozone. With continuous changes, said effect reaches the statistical significance that lacks with discrete changes. The consistency of our results regardless of the metrics used is as expected. The two metrics are identically suitable for our analysis since we do not have to aggregate the data through time (a case for continuous rates) or across markets (a case for discrete rates). The second sensitivity check aims to verify that our results also hold when considering the possibility that market participants might factor in the OMH effects even earlier than on the trading day (t  1). To implement this check, while preserving the high frequency approach needed in our analysis, we augment our models with two new right-hand side dummy variables, OMHt2 and CMHt2. By doing so, we are able to account for the possibility that the holiday effect on rebalancing decisions might not emerge on, or immediately around, the holiday because investors have already rationally adjusted their portfolio in anticipation of the expected liquidity shocks. Throughout the 15 augmented models, all findings previously discussed remain valid. Furthermore, of the 30 additional estimated parameters, only one is significant at the 5% level and four more at the 10% level, with no detectable pattern across either countries or stock sizes. The holiday effect at (t-2), if any, must be of a smaller magnitude compared to (t  1) in the case of both a holiday distraction and an anticipatory response to future liquidity shocks. With the former, a longer lead-time is associated with a lower distraction. The latter, instead, would both kill the option value and cause less precise forecasting, lowering the investors’ incentive to act. As for the robustness of the results in relation to the time span covered, a previous version of this work is based on a shorter sample (17 December 2007–5 March 2015), consisting of roughly 1800 observations instead of the approximately 2800 we currently employ. Despite the increase in sample size of more than 50%, the results remain the same. None of the findings hinges on the sample used, which supports their robustness with regard to the time span selected. If anything, this sensitivity check makes an even clearer case for the phenomenon our work signals: a strengthening over time of the new pattern of turnover sensitivity to stocks returns. As trading technology evolves, the traditional cost asymmetries between holding long and short positions is progressively disappearing for all type of stocks.

5. Conclusion We investigate turnover patterns across Eurozone markets before, during and after open and closed market holidays. We obtain that in most countries the trading activity responds to investors’ attention capacity constraints, albeit to a different extent, as forged by country specific institutions and culture. These patterns signal the persistence of a bias toward trading domestic stocks, even in a highly integrated economic area such as the Eurozone. This home bias predominantly affects small caps, as they are even less appealing than large caps to foreign investors. As a result, small caps end up mainly in the hands of a clientele of local investors, giving rise to a stronger passive form of home bias. 1 For the sake of conciseness, here we do not include the confirmatory results of these sensitivity analyses. All relative tables are available on the journal website.

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