Information Efficiency of U.S. Restaurant Stocks that are Cross-Listed in Germany

Abstract

We study relationships between stock returns on U.S. and German exchanges for U.S. restaurant companies. Specifically, we examine whether information asymmetry affect how much stock returns in Germany lag stock returns of the same company on U.S. markets. German and U.S. investors differ in information access because of differing stock exchange listing requirements. Our main goals are to examine if (a) stock returns of U.S. underlying shares lead stock returns of cross-listed shares on the Open Market because of information asymmetry and (b) the lead–lag relationship is more evident among shares involuntarily cross-listed on the Open Market than securities voluntarily cross-listed on the EU Regulated Market because of differences in regulation in information disclosure. We estimated cross-autocorrelations using vector autoregressions and tested the hypotheses with the Wald test. The results, in general, support both hypotheses.

Keywords

lead–lag cross-autocorrelation involuntary cross-listing vector autoregression (VAR)Frankfurt Stock Exchange information asymmetry

Random walk theorists argue that stock prices change randomly because information by definition reaches the market randomly; therefore, prices are unpredictable ex-ante. Bachelier (1900/1964) is an early advocate for the random walk hypothesis. The Fama (1965, 1970) efficient-markets-hypothesis studies, which argue that financial markets quickly exploit available information in setting security prices, serves as a theoretical foundation for much subsequent research.

Many empirical studies, however, expose limitations of the hypothesis in the real world, especially the assumption that transactions costs—including information acquisition costs—are zero. Systematic stock price correlations among financial markets and among different characteristics of stocks in a market are evident in the literature, indicating that not all markets incorporate new information in an equally timely manner. For example, stock index futures tend to lead stock prices (e.g., Harris, 1989; Stoll & Whaley, 1990), whereas stock markets lead option markets (e.g., Stephan & Whaley, 1990). Lead–lag effects operate within a single stock market (e.g., Lo & MacKinlay, 1990a; Mech, 1993) and across stock markets (e.g., Chang, McQueen, & Pinegar, 1999; Hasbrouck, 1995).

One explanation for why some stock prices move faster than others is measurement error; stock prices are not sampled at the same time but at different times (e.g., Atchison, Butler, & Simonds, 1987; Dimson, 1979; Lo & MacKinlay, 1990b; Scholes & Williams, 1977). Some stocks trade more frequently than others. Therefore, for example, Stock A’s last trade on a day can occur at 2 p.m.; whereas, Stock B’s last trade on the same day can occur at 3:30 p.m. If new information arrives at 3 p.m., the closing price of Stock B reflects the new information, whereas the price of Stock A will not reflect the information until the next trading day.

While supporting the above argument, Chan (1993) explains that the lead–lag effect could occur if market makers adjust smaller firms’ stock prices after observing larger firms’ past stock price changes. The argument assumes that larger firms produce and disseminate better quality information than smaller firms. The assumption is plausible insofar as larger firms tend to have smaller costs to publicize information (Ho & Michaely, 1988). The amount and quality of information disseminated can differ among stock exchanges as well. For a sample of 107 firms cross-listed on U.K. and/or U.S. exchanges during 1989, Frost and Pownall (1994a) find that firms make more frequent mandatory and voluntary disclosures in the U.S. stock market regardless of their domicile. Frost and Pownall (1994b) examine 110 firms listed in both United States and the United Kingdom during 1988 to 1990, and find that on average the U.S. stock market reacts more quickly to earnings announcements consistent with it being more liquid.

Chan’s (1993) theoretical argument and Frost and Pownall’s (1994a, 1994b) empirical evidence suggest investigation of the lead–lag relationship of U.S. stocks cross-listed on the Frankfurt Stock Exchange (FSE). Unique characteristics of the FSE are that the exchange provides two different markets for trading shares. The basis for these trading markets is legal requirements to provide information: (a) European Union (EU) Regulated market, where foreign companies voluntarily apply and must provide information in accordance with strict EU regulations, and (b) regulated unofficial market (also called the Open Market), in which foreign listed shares can involuntarily be listed and traded with neither an issuer’s consent or knowledge nor obligation to provide information to German investors.

Based on Chan’s (1993) argument, this study seeks to provide new evidence on role of information asymmetry across stock markets, especially in the context of involuntary cross-listing. Specifically, we empirically investigate whether (a) stock returns of U.S. underlying shares lead stock returns of involuntarily cross-listed shares on the FSE because of high (minimal) requirement for information disclosure in the United States (FSE Open Market) and (b) the lead–lag relationship of U.S. shares involuntarily cross-listed on the FSE Open Market is significantly greater than the relationship of U.S. shares voluntarily cross-listed on the EU Regulated FSE based on differences in the level of information provided and distributed in Germany.

To ensure that the sample includes companies that are involuntarily listed on the Open Market, U.S. restaurant companies are selected. The U.S. restaurant industry fits the current study’s intent well since no U.S. restaurant company, with the exception of McDonald’s, which delisted its shares from the FSE on April 28, 2005, was listed on the EU Regulated market in FSE. Afterward, McDonald’s has an involuntary listing on the Open Market. Finding an industry that only cross-listed on the Open Market involuntarily is critical for this study since having voluntarily listed shares in the same industry on the FSE would add noise to discovering the true lead–lag relationship for involuntary cross-listing cases. Strategic decisions among companies within the same industry interact since they compete with similar products. Hou (2007) finds the lead–lag relationship exhibits within the same industry stocks, while significant relationship disappears when examining across multiple industries. Also, share prices react similarly to external factors such as market trends and changes in regulations (Hou, 2007). Therefore, if U.S. companies from the same industry cross-list on the FSE both voluntarily and involuntarily, German investors may follow German returns of voluntarily cross-listed U.S. shares from the same industry as well as the underlying shares’ returns in the United States. This study argues that the U.S. restaurant industry is unusual in that the companies have generally chosen not to cross-list voluntarily.

Empirical examination of the stock return dynamics between the shares voluntarily listed on the U.S. stock market and the shares involuntarily listed on German stock markets extends the line of research that examines the role of information asymmetry on multiple stock markets. In addition, the examination on U.S. and German stock markets is worthwhile since uniqueness of each stock market (e.g., market size, foreign ownership limitation, transaction costs, and so forth) plays a role in the dynamic and industry takes an important role in the lead–lag relationship (Hou, 2007). Findings of the current study have practical implications. For example, those U.S. restaurant companies with their shares involuntarily cross-listed in foreign markets may consider improving communications with their shareholders in the foreign exchange markets. In addition, the study findings suggest that the FSE Open Market may consider amending their policy on the involuntary cross-listing and mandate applying third parties to inform foreign issuing companies so that those foreign companies can have an option to communicate the shareholders who are investing in their involuntarily listed shares.

The Frankfurt Stock Exchange and its Market Structure

The FSE, especially the Open Market, has served as one of the main overseas trading venues for many U.S. companies. Uniquely, many of the cross-listings are not initiated by the U.S. companies involved, but by third-party financial institutions, such as German banks and brokerage firms. Such involuntary cross-listing became possible when the FSE started the Open Market (known as Freiverkehr before October 10, 2005) to attract more international shares. The Open Market is a regulated, unofficial market and does not impose high levels of regulations similar to those required of firms listed on official FSE markets (i.e., Prime Standard and General Standard stocks).

The FSE has four levels of standards between two markets: Prime Standard and General Standard in the EU Regulated Market and Entry Standard and Open Market (First and Second Quotation Boards) for the regulated unofficial market. A summary of the different requirements for each level of standards appears in Table 1.

Table 1

Transparency Level for Investors and Companies on the Frankfurt Stock Exchange

	Statutory Transparency Regulations	Additional Transparency Requirements
EU Regulated market
Prime standard	• Annual and interim reports in accordance with IFRS (International Financial Reporting Standards) • Publication of directors’ dealings • Ad hoc disclosures	• Quarterly financial statements in English • Corporate action timetable • Analyst conference
General standard	• Announcement of reporting thresholds • Compulsory offer with change of control
Regulated unofficial market
Entry standard	• Insider trading rules• Market abuse directive• Provisions governing public offering	• Annual interim report in accordance with national GAAP (generally accepted accounting principles) or IFRS• Significant company news• Company profile and company calendar
Open market (First and second quotation board)

Note: Reproduced based on the transparency standards figure on the Deutsche Bourse official website at http://deutsche-boerse.com/dbag/dispatch/en/kir/gdb_navigation/lc/100_Market_Structure/10_transparency_standards

The FSE significantly reduces the level of regulations and procedural requirements for Open Market shares to the extent that listing is possible even without the consent or knowledge of underlying foreign companies so long as those companies are listed on an overseas stock exchange. Also, no requirement exists for further information disclosure for the listed companies. Accordingly, German investors have limited access to information of the Open Market cross-listed companies. Company news or analysts’ coverage information often remains absent on the official FSE website for those companies while transaction-related information (e.g., price and/or trading volume in Germany) is available. Because of the low investor protection caused by low-information disclosure requirements, the FSE designed their website such that without clicking the “I agree” button, indicating the person has read and accepted warnings of riskiness in investing the stock, information about a listed company on the Open Market would be unavailable. Information on Prime Standard and General Standard stocks are readily available without such warnings or the clicking step. The notice that appears on the FSE website when attempting to view information of the Open Market listed shares is

The following information is exclusively addressed to qualified investors, who are able to thoroughly evaluate and accept potential risks related to an investment in shares issued by this organization. The following information provided by the issuer does neither present an offer to sell nor an invitation to buy or subscribe for shares of this organization.

The shares of the organizations are neither admitted to trading on the Regulated Market nor included in trading on the Regulated Market. They are included in trading in the Entry Standard segment on the Open Market (Unofficial Regulated Market) of FWB Frankfurter Wertpaperborse (the Frankfurt Stock Exchange). Investors must be aware of the fact that this part of the Unofficial Regulated Market on the Frankfurt Stock is not subject to the high Europe-wide transparency standards and strict provisions for investor protection on organized markets.

Copying and forwarding information from the following web pages is not permitted.

Upon clicking on the “I agree” button below, and thus confirming that you have read and accept the above-mentioned warning, you will be directed to the requested content.

Because of the differences in nature of the Open Market shares, previous researchers often excluded shares listed on the Open Market in their analyses (e.g., Gozzi, Levine, & Schmukler, 2008). The current study differentiates itself from previous studies by focusing on the Open Market shares.

Literature Review

Stock Return Lead–Lag Studies

During the past 30 years, stock return dynamics have been examined for stocks that have different characteristics and trade on different stock markets. The majority of such studies investigated lead–lag relationships between large stocks and small stocks within a single market and the most common stock market investigated is the New York Stock Exchange (NYSE). Lo and MacKinlay (1990a), for example, find that returns of large-firm portfolios lead those of small firm portfolios in the United States, consistent with transactions costs, including information acquisition costs, being lower for large firms than small firms.¹ As seen in Table 2, the phenomenon of returns of large stocks leading those of small stocks is common in the markets of many countries, during various sample periods, and over various intervals of daily, weekly, and monthly returns. In addition to size, criteria such as stocks favored by institutional investors (e.g., Badrinath, Kale, & Noe, 1995) or by foreigners (e.g., Chui & Kwok, 1998) were used to investigate the lead–lag relationship.

Table 2

Stock Return Lead–lag Relationship Studies

Author/s (Year)	Country	Period	Stock Prices Dynamics
Stock price dynamics in single market
Altay (2003)	Germany, Turkey	January 1993-November 2002	Monthly returns of large size stocks lead the returns of small size stocks in Germany, and in one of the sub-period in Turkey
Bae, Ozoguz, Tan, and Wirjanto (2011)	31 Emerging countries	December 1988-April 2003	Weekly returns of stocks with large access of foreign investment lead returns of stocks with no foreign investment
Badrinath et al. (1995)	United States	1981-1988	Monthly returns on institutionally favored stocks lead returns on stocks not favored by institutional investors.
Chan (1993)	United States	1980-1989	Daily returns of large firms lead those of small firms
Chang, McQueen, and Pinegar (1999)	Hong Kong, Japan, Singapore, South Korea, Taiwan, Thailand, United States	1976 (or 1978)-1995	Monthly returns of large size stocks lead the returns of small size stocks in all six Asian exchanges and the NYSE
Chui and Kwok (1998)	China	1993-1996	Daily returns for foreigner-owned stocks lead those Chinese-owned stocks
Kanas and Kouretas (2005)	United Kingdom	1955-2000	Monthly returns for a portfolio of large stocks lead returns for a portfolio of small stocks
Lo and MacKinlay (1990a)	United States	July 1962-December 1987	Weekly returns for a portfolio of large stocks lead returns for a portfolio of small stocks
Marshall and Walker (2002)	Chile	1991-1998	Large cap portfolios react to both good and bad news sooner than the small cap portfolios do
McQueen Pinegar, and Thorley (1996)	United States	1963-1994	Small and large cap portfolios’ reactions to bad news are fast, but the reactions of small cap portfolios to good news are slower
Mech (1993)	United States	1973-1986	Weekly returns for a portfolio of large stocks lead returns for a portfolio of small stocks
Ratner and Leal (2003)	Brazil	1986-1999	Large stock portfolio returns lead small stock portfolio returns, but the lagged response of small stock portfolio returns diminish following financial liberalization
Tang (2011)	China	March 1992-February 2001	Price differences between shares owned by domestic investors and foreign investors are higher in firms with higher information disclosure disparity.
Stock price dynamics in multiple markets
Chang et al. (1999)	Hong Kong, Japan, Singapore, South Korea, Taiwan, Thailand, United States	1976 (or 1978)-1995	Found only in one case: monthly returns of large size Japanese stocks lead those of small size Thailand stocks
Frost and Pownall (1994b)	United States and United Kingdom	1988-1990	Stock price response to earnings disclosure is significantly greater in the United States than in the United Kingdom
Garbade and Silber (1979)	United States (NYSE, Midwest Stock Exchange, and Pacific Stock Exchange)	August 1973-September 1975	Transactions prices on regional exchanges contain information relevant for NYSE traders
Hasbrouck (1995)	United States (NYSE and regional stock exchanges)	August 1993-October 1993	Daily return of stocks on NYSE lead those on other regional stock exchanges in the United States
Karolyi and Stulz (1996)	United States and Japan (NYSE-traded ADRs)	1988-1992	Large shocks to broad-based market indices positively affect the daily return correlations

Note: NYSE = New York Exchange; ADR = American depositary receipt.

One background argument behind the lead–lag relationship commonly asserts that groups of stocks with high-quality information lead other groups of stocks with poor-quality information. For instance, large firms are more likely to be followed by financial analysts and reporters who search for information about these firms and large firms also receive more media exposure (e.g., Bhushan, 1989).

Examination of the lead–lag relationship also considers multiple stock exchanges (e.g., Garbade & Silber, 1979; Hasbrouck, 1995). For example, Hasbrouck (1995) examines the lead–lag effect among multiple stock exchanges in the United States and find that stock returns of firms listed on the NYSE lead those of firms listed on non-NYSE regional exchanges. Later studies extend the investigation to an international context. For example, Chang, McQueen, and Pinegar (1999) investigate the cross-autocorrelation between small and large portfolios across six Asian stock exchanges (Hong Kong, Japan, Singapore, South Korea, Taiwan, and Thailand) and the NYSE, and find a significant relationship only in the case that monthly returns of large-size Japanese stocks lead those of small-size Thailand stocks. Karolyi and Stulz (1996), using American depositary receipts backed with Japanese stocks, investigate the factors that affect the daily cross-stock return dynamics between the U.S. stock market and the Japanese stock market. They find that large shocks to national market indices, such as Nikkei Stock Average and Standard and Poor’s 500 Stock Index give a positive impact on the return relations between American depositary receipts and its underlying Japanese stocks, whereas U.S. macroeconomic announcements, shocks to the Yen/Dollar foreign exchange rate, and Treasury bill returns do not have any significant impact on the relationship even after controlling for industry.

Hypotheses Development

Chan (1993) explains the lead–lag relations in two ways. First, he supports the argument that the relationship occurs because of nonsynchronous trading (e.g., Atchison et al., 1987; Dimson, 1979; Lo & MacKinlay, 1990b; Scholes & Williams, 1977). Prices of high liquidity stocks tend to adjust to information more quickly than prices of low liquidity stocks. Second, markets focus on the shares that provide better quality information and use prices as a reference. The current study seeks to extend the context to U.S. shares involuntarily cross-listed in Germany where better quality information of the U.S. restaurant companies are found in the United States rather than Germany. The investigation of the lead–lag relationship incorporates two aspects, which develop two hypotheses. First, U.S. firms arguably disclose more and better quality information in the United States than in Germany; therefore, stock returns in the United States are expected to lead those in Germany. The firms listed on the U.S. exchanges provide information spontaneously to U.S. investors through various routes, including filings with the Securities and Exchange Commission (SEC), conference calls, face-to-face interviews, and so on. Meanwhile, such level of accessibility to information about U.S. companies is commonly not available to German investors. Domestic investors are known to have an information advantage over foreign investors because of domestic investors’ high familiarity of language, culture, and geographical proximity (Grinblatt & Keloharju, 2001) and easier access to private information about a local firm (Coval & Moskowitz, 2001).

On the other hand, information diffusion from Germany to the United States is possible since the hours of operation of the FSE precede the hours of operation of the U.S. major stock exchanges by 6 hours with 2 hours of overlap. For that reason, when world market information arrives at the FSE prior to the U.S. markets’ opening, the returns on the FSE can precede those on U.S. exchanges. Also, some may argue that if a majority of German investors are institutional investors who have the capacity to access and analyze the information submitted to U.S. regulatory agencies (e.g., SEC) and media, stock returns in the United States may not necessarily lead those in Germany.

The extent to which world information affects stock prices of cross-listed U.S. shares and its frequency, however, can be sporadic and minimal, and German institutional investors’ capabilities and intentions to search for necessary information for those involuntarily cross-listed shares can be limited. Previous literature shows that even for institutional investors, more geographically proximity institutional investors have an information advantage in stock investments over less geographically proximity institutional investors even within a country. For example, Baik, Kang, and Kim (2010) find that U.S. local institutional investors who are located within a same state with a company’s headquarter have information advantages over nonlocal U.S. institutional investors who are located outside the state where a company’s headquarter is located. Meanwhile, U.S. companies not only have the legally mandated obligation to provide regularly high levels of information to investors in United States but also voluntarily or involuntarily provide sophisticated information to them. Accordingly, U.S. investors are likely to have information advantages of U.S. companies over foreign investors; therefore, the quality and amount of information is guaranteed in the U.S. market. For these reasons, the first hypothesis is as follows:

Hypothesis 1: Stock returns of U.S. restaurants’ underlying shares listed on the U.S. exchanges lead stock returns of their shares involuntarily cross-listed in Germany.

Since the FSE operates two kinds of markets depending on the level of requirements, the cross-listed shares can be categorized into two groups: voluntarily listed shares in the EU Regulated Market or the unofficial Open Market and involuntarily listed shares in the Open Market. Being cross-listed on the Open Market, those U.S. companies are not obliged to provide information to German investors. Even at the time of application for Open Market listing, a third-party financial institution can list a stock without consent or acknowledgement of the issuing firm. Accordingly, information formally provided to German investors through the Open Market is basic company information such as name of company, address, and name of the listing stock market. In contrast, other U.S. companies that have voluntarily cross-listed on the EU Regulated Market are required to provide information specifically suited for the German market. Accordingly, differences in quality of information between in the United States and in the EU Regulated Market is less than the differences between in the United States and in the Open Market.² Technically, it is possible to voluntarily cross-list on the FSE Open Market, and in that case the issuer may disclose higher level of information than involuntarily cross-listed firms. The current study excludes such cases.

In summary, the lead–lag relationship is expected to exist among the involuntarily cross-listed shares on the FSE Open Market, whereas the relationship is expected to exist to significantly less extant among the voluntarily cross-listed shares on EU Regulated Market. With this logic, examination of the differences in the lead–lag relationship between the involuntarily cross-listed group and the voluntarily cross-listed group leads to the second hypothesis:

Hypothesis 2: The lead–lag relationship of U.S. restaurants’ shares involuntarily cross-listed on the FSE Open Market is significantly greater than the lead–lag relationship of U.S. shares voluntarily cross-listed on the EU Regulated Market on the FSE.

Method

Data

This study focuses on U.S. restaurant companies that have cross-listings on the FSE in addition to their U.S. listings. The FSE website provides categories for stocks listed in the EU Regulated Market and those in the unofficial Open Market. Verification of domicile of the firms on the list uses Capital IQ for cross-checking. Capital IQ also allows obtaining daily stock returns and trading volumes for the stocks cross-listed in both German and U.S. markets. All returns’ denominations are originally Euros for German-listed shares and U.S. dollars for the underlying shares listed in the United States, but the share prices in Euros on the German stock market are adjusted to the equivalent U.S. dollars by daily EUR/USD foreign exchange rate. The current study examines the stock return lead–lag relationship for a portfolio of U.S. restaurant companies. The ending date is June 30, 2011, the last day with data availability at the time of analysis.

Since all U.S. restaurant firms, except McDonald’s, chose not to voluntarily cross-list on foreign stock exchanges, the industry is chosen to represent involuntary cross-listing. The involuntary nature was checked by examining Forms 10-K filed with the SEC and via direct contact with the companies. While U.S. restaurant companies largely chose not to list their shares in overseas stock exchanges, one exception was McDonald’s. However, the company’s manager in investor relations confirmed that McDonald’s delisted its shares on overseas markets during 1999-2009 and has not cross-listed in any overseas exchanges afterward. The company voluntarily listed its shares in 1982 on the FSE and delisted on April 28, 2005, from that exchange. A German market maker immediately listed McDonald’s shares on the unofficial Open Market on the following day. The FSE confirmed that since April 29, 2005, McDonald’s shares have traded on the Open Market.

Meanwhile, shares of U.S. restaurant companies began appearing on the FSE Open Market as involuntarily cross-listed in 1999 and the trend is upward; 7 of 21currently traded companies first appeared on the FSE in 2010. Except the one case of McDonald’s, all sampled U.S. restaurant shares have or had their shares involuntarily listed and traded on the Open Market.

Data collection for involuntarily cross-listed shares used Capital IQ and its screening tool, which identified 26 U.S.-headquartered full-service and fast-food restaurants that had or have listings on both one U.S. exchange and the FSE. Verification of availability of historical data specifically, stock prices and trading volumes in Germany, identified five companies (CKE Restaurants, Inc., Eat at Joes Ltd., OSI Restaurant Partners, LLC., Pacific Restaurant Holdings, Inc., and Spicy Pickle Franchising, Inc.) with unavailable data, and therefore, this study excluded those companies from the sample. We excluded one more company, Burger King Holdings, Inc., since the company is no longer traded on FSE as its underlying shares delisted its shares from NYSE in 2010. Twenty homogeneous companies remained for the data set for analyzing involuntarily cross-listed shares. The companies that voluntarily and involuntarily cross-listed on the FSE are listed in Table 3. The sample period spans from 1999 to 2011 since information of involuntarily cross-listed restaurants in the FSE Open Market is only available from 1999 although information of voluntarily cross-listed U.S. companies in the Regulated Market of the FSE is available from 1992. The current study collected another data set—cross-listed shares under the Regulated Market—to examine the second hypothesis. An initial data collection for the data set used the FSE’s official website http://www.boerse-frankfurt.de. A search tool on the website produces a list of equities with various search characteristics, including market segment, transparency level, and region/country. Setting Prime Standard for transparency level and the United States for region/country, identified only one company; General Standard and United States categories rendered eight companies. Cross-checking the companies with Capital IQ for their listings on the FSE and domicile in the United States identified three of the eight to be domiciled outside the United States; therefore, the study excluded those three from the sample. Subsequently, the study finalized six companies as members of the EU Regulated securities group.

Table 3

U.S. Restaurant Companies Cross-listed on the Frankfurt Stock Exchange (FSE)

Company	Ticker in the U.S. (Exchange)	Ticker on FSE	First Trade Day on FSE (mm/dd/yyyy)
Voluntarily cross-listed companies (prime standard)
Rofin-Sinar Technologies, Inc.	RSTI (NASDAQ)	RSI	06/13/1997
Voluntarily cross-listed companies (general standard)
El DuPont Nemours & Co.	DD (NYSE)	DUP	01/02/1992
Caterpillar, Inc.	CAT (NYSE)	CAT1	02/16/1999
Dow Chemical Corp.	DOW (NYSE)	DCH1	05/24/1999
Archer Daniels Midland Company	ADM (NYSE)	ADM	07/21/1999
The Central European Russia Fund, Inc.	CEE (NYSE)	EEE	01/24/2007
Involuntarily cross-listed restaurant companies (open market)
Papa John’s International, Inc.	PZZA (NASDAQ)	PP1	08/11/1999
Brinker International, Inc.	EAT (NYSE)	BKJ	11/09/1999
Jack in the Box, Inc.	JACK (NASDAQ)	JBX	05/12/2000
P. F. Chang’s China Bistro, Inc.	PFCB (NASDAQ)	PF2	05/21/2004
Domino’s Pizza, Inc.	DPZ (NYSE)	EZV	07/14/2004
McDonald’s Corp.	MCD (NYSE)	MDO	04/29/2005
Kona Grill, Inc.	KONA (NASDAQ)	K5G	08/17/2005
Chipotle Mexican Grill, Inc.	CMG (NYSE)	C9F	01/26/2006
Morton’s Restaurant Group, Inc.	MRT (NYSE)	M8G	02/09/2006
Nathan’s Famous, Inc.	NATH (NASDAQ)	NFA	10/30/2006
Cracker Barrel Old Country Store, Inc.	CBRL (NASDAQ)	OLD	12/12/2006
Yum! Brands, Inc.	YUM (NYSE)	TGR	01/08/2007
The Wendy’s Company	WEN (NYSE)	TQK	03/03/2010
Ruby Tuesday, Inc.	RT (NYSE)	RYW	06/01/2010
Darden Restaurants, Inc.	DRI (NYSE)	DDN	08/11/2010
Denny’s Corporation	DENN (NASDAQ)	DE8	08/11/2010
The Cheesecake Factory, Inc.	CAKE (NASDAQ)	CF2	08/11/2010
Buffalo Wild Wings, Inc.	BWLD (NASDAQ)	BWW	09/28/2010
Bravo Brio Restaurant Group, Inc.	BBRG (NASDAQ)	IZA	11/02/2010
Texas Roadhouse, Inc.	TXRH (NASDAQ)	ROW	12/14/2010

We conducted the second round of data collection for delisted U.S. companies cross-listed on the FSE using the same official website of the FSE. We checked each delisted company with their country of domicile, market segment, and transparency level. However, cross-checking with Capital IQ exhibited that only one U.S. company, Burger King Holdings, Inc., has stock price information available. Capital IQ confirmed that the reason for missing information for delisted company is that the stock market, the FSE, only provides financial information, such as stock prices and trading volume of the companies that currently trade in that market. Burger King Holdings, Inc. is an exceptional case that Capital IQ provides since the company delisted from the exchange relatively recently in 2010. Therefore, the current study does not include delisted U.S. companies from the FSE.

Models

To examine the lead–lag relationship for U.S. restaurant companies involuntarily cross-listed on the FSE Open Market, the current study applies a vector autoregression (VAR) model. Sims (1980) developed the model by extending univariate autoregression, a single time series model that captures current value of a variable based on its own lagged values. In contrast, a VAR consists of multiple time series, which explain multiple variables’ own lagged values and the lagged values of all other variables included in the model (Stock & Watson, 2007). Accordingly, a VAR model allows researchers to examine cross-autocorrelations after controlling for autocorrelations (Chordia & Swaminathan, 2000), which have been found to affect stock returns (e.g., Chordia & Swaminathan, 2000; Fargher & Weigand, 1998; Hameed, 1997; Roll, 1984). The current study applies a modified version of Granger (1969) causality regressions developed by Brennan, Jegadeesh, and Swaminathan (1993) to examine Hypothesis 1, since that test allows the comparison whether or not U.S. returns predict German returns better than the reverse. Time series of underlying U.S. stock returns is said to Granger-cause another time series of cross-listed stock returns in Germany when the degree that lagged values of U.S. stock returns forecast future values of contemporaneous stock returns in Germany is significantly greater than the degree that lagged values of cross-listed German stock returns forecast future values of contemporaneous U.S. stock returns.

The model developed for testing Hypothesis 1 is as follows:

r_{G, t} = a_{0} + \sum_{k = 1}^{K} a_{k} r_{G, t - k} + \sum_{k = 1}^{K} b_{k} r_{U S, t - k} + u_{t,}

r_{U S, t} = c_{0} + \sum_{k = 1}^{K} c_{k} r_{G, t - k} + \sum_{k = 1}^{K} d_{k} r_{U S, t - k} + v_{t}

where $r_{G, t}$ and $r_{G, t - k}$ are the contemporaneous and lagged stock returns for U.S. restaurant stocks cross-listed in Germany; $r_{U S, t}$ and $r_{U S, t - k}$ are the contemporaneous and lagged stock returns of underlying stocks in the United States, and $u_{t,}$ and $v_{t}$ are error terms at time t. Calculation of the sum of coefficients for the lagged returns provides more stringent results than estimating each corresponding coefficients for each lag since the summation version not only tests predictability but also the sign of predictability (Chordia & Swaminathan, 2000; Hou, 2007).

The current study examines the lead–lag relationship using daily and weekly returns of underlying U.S. shares and their cross-listed shares in Germany. Multiple lags allow researchers to find time series dependency in returns beyond one lag. Although multiple lags might add noise to estimations, this methodology produces more reliable results because trading frequency and trading volume in Germany vary considerably among U.S. restaurant shares cross-listed in Germany. Following Chordia and Swaminathan (2000), estimates use daily returns with five lags. Following Chiao, Hung, and Lee (2004), weekly returns’ estimates use three lags. The current study tests Hypothesis 1 by investigating if the sum, $\sum_{k = 1}^{k} b_{k}$ in Equation (1) is greater than the sum, $\sum_{k = 1}^{k} c_{k}$ in Equation (2). The comparison is between a portfolio of returns in Germany and a portfolio of the underlying shares in the United States. The current study uses equally weighted returns since lagged returns of large firms tend to be noisier; therefore, lagged returns of small firms may exhibit stronger lead–lag relationships (Hou, 2007). Accordingly, using size-weighted returns may underestimate the true lead–lag relationship between German returns and the underlying U.S. returns.

The model developed for testing Hypothesis 2 is as follows:

r_{G, t}^{O} = a_{0} + \sum_{k = 1}^{K} a_{k} r_{G, t - k}^{O} + \sum_{k = 1}^{K} b_{k} r_{U S, t - k}^{O} + \sum_{k = 1}^{K} c_{k} r_{G, t - k}^{E} + \sum_{k = 1}^{K} d_{k} r_{U S, t - k}^{E} + u_{t,}

r_{U S, t}^{O} = e_{0} + \sum_{k = 1}^{K} e_{k} r_{G, t - k}^{O} + \sum_{k = 1}^{K} f_{k} r_{U S, t - k}^{O} + \sum_{k = 1}^{K} g_{k} r_{G, t - k}^{E} + \sum_{k = 1}^{K} h_{k} r_{U S, t - k}^{E} + v_{t,}

r_{G, t}^{E} = j_{0} + \sum_{k = 1}^{K} j_{k} r_{G, t - k}^{O} + \sum_{k = 1}^{K} k_{k} r_{U S, t - k}^{O} + \sum_{k = 1}^{K} l_{k} r_{G, t - k}^{E} + \sum_{k = 1}^{K} m_{k} r_{U S, t - k}^{E} + w_{t,}

r_{U S, t}^{E} = n_{0} + \sum_{k = 1}^{K} n_{k} r_{G, t - k}^{O} + \sum_{k = 1}^{K} o_{k} r_{U S, t - k}^{O} + \sum_{k = 1}^{K} p_{k} r_{G, t - k}^{E} + \sum_{k = 1}^{K} q_{k} r_{U S, t - k}^{E} + z_{t}

where $r_{G, t}^{O}$ and $r_{G, t - k}^{O}$ are the contemporaneous and lagged stock returns for U.S. restaurant stocks cross-listed on the Open Market in Germany; $r_{U S, t}^{O}$ and $r_{U S, t - k}^{O}$ are the contemporaneous and lagged stock returns of underlying stocks in the United States of those U.S. restaurants cross-listed on the Open Market in Germany; $r_{G, t}^{E}$ and $r_{G, t - k}^{E}$ are the contemporaneous and lagged stock returns for U.S. stocks cross-listed on the EU Regulated Market in Germany; $r_{U S, t}^{E}$ and $r_{U S, t - k}^{E}$ are the contemporaneous and lagged stock returns of underlying stocks in the United States of those cross-listed on the EU regulated market in Germany; and $u_{t}$ , $v_{t}$ , $w_{t}$ and $z_{t}$ are error terms at time t.

The current study compares the lead–lag relationship between the Open Market listed group and the EU Regulated Market listed group. This study does not assume a cross-group lead–lag relationship. The expectation is that the U.S. lagged stock returns of the Open Market listed group affect the contemporaneous German stock returns of the same group while not assuming an effect on contemporaneous German stock returns of the EU Regulated market. Therefore, the coefficients of lagged stock returns of the other group have a 0 constraint (i.e., $c_{k}, d_{k}, g_{k}, h_{k}, j_{k}, k_{k}, n_{k}$ , and $o_{k}$ ). The current study tests Hypothesis 2 by examining if the sum of the coefficients, $\sum_{k = 1}^{k} b_{k}$ in Equation (3) is greater than the sum of the coefficients, $\sum_{k = 1}^{k} m_{k}$ in Equation (5). The examination of the lead–lag relationship is daily and weekly with lags of 5 and 3, respectively, as specified for Hypothesis 1, and the comparison occurs for each case.

Results

Descriptive Statistics

Table 4 provides a descriptive summary of the data. The Open Market portfolios are to examine Hypothesis 1. The German portfolio (GMO) from the Open Market portfolio is of equally weighted stock returns of U.S. restaurant companies cross-listed on the Open Market, and the U.S. portfolio (USO) from the Open Market portfolio is of equally weighted stock returns of the underlying shares in the United States. Each of the pairs has two subsets of portfolios for daily and weekly stock returns.

Table 4

Summary of Descriptive Statistics

Interval	Portfolios	No. of Observations	Mean Return	SD of Return	Minimum	Maximum
Hypothesis 1: Portfolios on the open market (German portfolio = GMO; U.S. portfolio = USO)
Daily	GMO	2,867	0.0001	0.0248	−1.0000	0.1224
	USO	2,866	−0.0001	0.0365	−1.0000	0.1207
Weekly	GMO	604	0.0021	0.0371	−0.1984	0.2258
	USO	604	0.0026	0.0366	−0.1704	0.1903
Hypothesis 1 and Hypothesis 2: Portfolios on the EU regulated market (German portfolio = GME; U.S. portfolio = USE)
Daily	GME	2,881	0.0005	0.0168	−0.1057	0.1176
	USE	2,881	0.0006	0.0174	−0.1116	0.1601
Weekly	GME	601	0.0025	0.0362	−0.1597	0.1534
	USE	601	0.0028	0.0345	−0.1848	0.1298
Hypothesis 3: Portfolios on the open market categorized by trading volume (German portfolio with high trading volume = GMH; GMH corresponding U.S. portfolios = USH; German portfolio with low trading volume = GML; GML corresponding U.S. portfolios)
Daily	GMH	1,488	0.0000	0.0310	−1.0000	0.1228
	GML	2,867	0.0001	0.0253	−1.0000	0.1224
	USH	1,486	−0.0012	0.0475	−1.0000	0.1043
	USL	2,866	−0.0004	0.0368	−1.0000	0.1207
Weekly	GMH	314	0.0027	0.0334	−0.3016	0.1378
	GML	604	0.0021	0.0388	−0.1984	0.2258
	USH	314	0.0036	0.0288	−0.1559	0.0867
	USL	604	0.0024	0.0386	−0.1917	0.1903

To examine Hypothesis 2, the current study generated E U Regulated Market portfolios with equally weighed returns. This study compares the lead–lag relationship of the Open Market portfolios with the EU Regulated Market portfolios for each subset of daily and weekly stock returns.

CKE Restaurant, Inc. is the first U.S. restaurant company to appear involuntarily on the Open Market. However, data were not available for the company; therefore, the current study excluded the company from the sample. Papa John’s International is the second U.S. restaurant company to appear involuntarily on the Open Market, and data were available; therefore, calculation of stock returns begins after Papa John’s International’s first trading day, August 11, 1999. The number of observations for daily stock returns across the sample is approximately 2,900 for the years 1999 to 2011. Although U.S. companies began cross-listing in 1992 (El DuPont Nemours & Co.), calculation of stock returns from the EU Regulated Market began on August 11, 1999, as well, to control for any year’s confounding effect. The number of observations of the German portfolio with high trading volume on the Open Market is 1,488, since McDonald’s shares began trading involuntarily on the Open Market on April 29, 2005, after the company delisted its stock from the FSE on April 28, 2005, and Yum! Brands appeared on the FSE on January 8, 2007.

Main Findings

Panel A in Table 5 presents the VAR estimation results for daily returns for Hypothesis 1. As hypothesized, U.S. underlying returns significantly predict the Open Market returns in Germany for Lag 1 (coefficient = 0.6622; p < .001) while the explanatory power of the Open Market returns to predict the underlying U.S. returns is significantly lower for Lag 1 (coefficient = 0.0133; p > .1). To confirm the relationship, the current study conducted the Wald test with Lag 1 coefficients. Asymmetric cross-autocorrelations are evident (χ² = 342.02; p < .001). With the summation of coefficients, however, the significant explanatory power of the U.S. underlying returns predict the Open Market returns in Germany disappeared due to negative cross-autocorrelations occurred from Lag 2 to Lag 5.

Table 5

Summary of Autocorrelations for Hypothesis 1: Daily Returns

Panel A: Daily Returns (No. of Observations = 2,350)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{5} a_{k}$ or c_k	$\sum_{k = 1}^{5} b_{k}$ or d_k
$r_{G, t}$	−0.0328	0.6622***	0.9219***	−0.1371***
$r_{U S, t}$	−0.0133	0.0297	0.0089	−0.0976^†
Wald test	b₁ = c₁ = 342.02***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} c_{k}$ = 6.70**
Panel Aa: Daily Returns of High Trading Volume Portfolio (No. of Observations = 1,223)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{5} a_{k}$ or c_k	$\sum_{k = 1}^{5} b_{k}$ or d_k
$r_{G, t}$	−0.3802***	0.6265***	−0.6247***	1.0286***
$r_{U S, t}$	0.0196	−0.1116***	0.1224	−0.3583**
Wald test	b₁ = c₁ = 142.87***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} c_{k}$ = 25.31***
Panel Ab: Daily Returns of Low Trading Volume Portfolio (No. of Observations = 2,350)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{5} a_{k}$ or c_k	$\sum_{k = 1}^{5} b_{k}$ or d_k
$r_{G, t}$	−0.0182	0.6757***	0.9372***	−0.1469***
$r_{U S, t}$	0.0162	0.0425	0.0057	−0.0701
Wald test	b₁ = c₁ = 358.33***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} c_{k}$ = 9.76**
Panel Ac: Daily Returns of Large Size Portfolio (No. of Observations = 1,223)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{5} a_{k}$ or c_k	$\sum_{k = 1}^{5} b_{k}$ or d_k
$r_{G, t}$	−0.4820***	0.8335***	−0.9669***	1.5892***
$r_{U S, t}$	−0.0148	−0.0280	0.112	−0.2464*
Wald test	b₁ = c₁ = 246.18***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} c_{k}$ = 48.36***
Panel Ad: Daily Returns of Small Size Portfolio (No. of Observations = 1,159)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{5} a_{k}$ or c_k	$\sum_{k = 1}^{5} b_{k}$ or d_k
$r_{G, t}$	0.4297***	0.6677***	1.0018***	−0.2477***
$r_{U S, t}$	0.0265	0.0485	0.0075	0.0447
Wald test	b₁ = c₁ = 219.58***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} c_{k}$ = 12.12***

†

p < .10. *p < .05. **p < .01. ***p < .001.

Since the literature found some company characteristics, such as trading volume and size to be an important determinant for lead-lag relationship (Chordia & Swaminathan, 2000; Lo & MacKinlay, 1990a, 1990b), the current study tests the lead–lag relationship as associated with dependence on the level of German trading volume and size, respectively, for the U.S. restaurant shares cross-listed on the Open Market.

Examination of trading volume of cross-listed U.S. restaurant companies clearly dichotomizes two extremes: a high trading volume group with annual German trading volumes greater than 50,000 shares, on average, and low trading volume group with annual German trading volumes of less than 50,000 shares, on average. German trading frequency for each group shows clear differences between the groups as well. The high trading volume group appeared to trade on more than 200 business days in Germany, on average; whereas, low trading volume group exhibited a frequency of less than 100 business days of trading, on average. The high trading volume group includes two companies, McDonald’s and Yum! Brands, and low trading volume group includes the remaining 18 companies.

Examination of size of U.S. restaurant companies used quartile breakdown because of two reasons: (a) U.S. restaurant companies do not dichotomize two extremes as it was for German trading volume and (b) previous studies frequently adopted the methodology (e.g., Chordia & Swaminathan, 2000; Hou, 2007). Four size quartiles are formed as of June 30, 2011, by market capitalization on the U.S. stock exchanges. Out of total 20 companies, the large size group includes McDonald’s, Yum! Brands, Chipotle Mexican Grill, Darden Restaurants, and Wendy’s. The small size group includes Denny’s, Bravo Brio Restaurant, Morton’s Restaurants, Nathan’s Famous, and Kona Grill.

The VAR analyses have been performed for the four subsamples of high trading volume portfolio, low trading volume portfolio, large size portfolio, and small size portfolio to check the robustness of the results following previous research (e.g., Hou, 2007). This study examined the VAR analyses for the four portfolios, separately. Results reveal that for the all portfolios, U.S. underlying returns significantly predict the Open Market returns in Germany for Lag 1 (coefficient = 0.6265 for high trading volume portfolio; coefficient = 0.6757 for low trading volume portfolio; coefficient = 0.8335 for large size portfolio; coefficient = 0.6677 for small size portfolio; all p values less than .001) whereas the Open Market returns in Germany are found not to predict the U.S. returns for Lag 1 (coefficient = 0.0196 for high trading volume portfolio; coefficient = 0.162 for low trading volume portfolio; coefficient = −0.0148 for large size portfolio; coefficient = 0.0265 for small size portfolio; all p values greater than .1). The Wald test results confirm the asymmetric cross-autocorrelation relationship with Lag 1 coefficients for all portfolios (χ² = 142.87 for high trading volume portfolio; χ² = 358.33 for low trading volume portfolio; χ² = 246.18 for large size portfolio; χ² = 219.58 for small size portfolio; all p values less than .001). Panel B in Table 6 shows the VAR estimation results for weekly returns for Hypothesis 1. The results support Hypothesis 1 both for Lag 1 and summation of coefficients from Lag 1 through Lag 3. The underlying U.S. market returns predict the Open Market returns for the first lag (coefficient = 0.8165; p < .001) and summation of the three lags (sum of coefficients = 1.5921; p < .001) with weekly examination of the return. On the other hand, the Open Market weekly returns do not predict the underlying U.S. returns for any of the lags. The Wald test results for cross-autocorrelation confirms the Granger causality in Lag 1 (χ² = 47.78; p < .001) and in the form of a summated coefficient in this study (χ² = 24.77; p < .001).

Table 6

Summary of Autocorrelations for Hypothesis 1: Weekly Returns

Panel B: Weekly Returns (No. of Observations = 585)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{3} a_{k}$ or c_k	$\sum_{k = 1}^{3} b_{k}$ or d_k
$r_{G, t}$	−0.7497***	0.8165***	−1.2736***	1.5921***
$r_{U S, t}$	−0.0977	0.0675	−0.1116	0.1931
Wald test	b₁ = c₁ = 47.78***		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} c_{k}$ = 24.77***
Panel Ba: Weekly Returns of High Trading Volume Portfolio (No. of Observations = 302)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{3} a_{k}$ or c_k	$\sum_{k = 1}^{3} b_{k}$ or d_k
$r_{G, t}$	−0.1609	0.2175*	−0.3952*	0.4522*
$r_{U S, t}$	0.0659	−0.1124	−0.0972	−0.0176
Wald test	b₁ = c₁ = 0.96		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} c_{k}$ = 2.95^†
Panel Bb: Weekly Returns of Low Trading Volume Portfolio (No. of Observations = 585)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{3} a_{k}$ or c_k	$\sum_{k = 1}^{3} b_{k}$ or d_k
$r_{G, t}$	−0.7861***	0.8467***	−1.3111***	1.6591***
$r_{U S, t}$	−0.1138	0.0863	−0.0880	0.2046
Wald test	b₁ = c₁ = 52.25***		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} c_{k}$ = 25.54***
Panel Bc: Weekly Returns of Large Size Portfolio (No. of Observations = 302)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{3} a_{k}$ or c_k	$\sum_{k = 1}^{3} b_{k}$ or d_k
$r_{G, t}$	−0.2959**	0.3424***	−0.7186**	0.6961**
$r_{U S, t}$	0.0900	−0.1494	−0.0944	−0.1407
Wald test	b₁ = c₁ = 1.78		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} c_{k}$ = 3.43^†
Panel Bd: Weekly Returns of Small Size Portfolio (No. of Observations = 287)
LHS	$r_{G, t - 1}$	$r_{U S, t - 1}$	$\sum_{k = 1}^{3} a_{k}$ or c_k	$\sum_{k = 1}^{3} b_{k}$ or d_k
$r_{G, t}$	−0.6807***	0.8175***	−0.7159**	1.0747***
$r_{U S, t}$	0.0393	0.0331	0.6005*	−0.3754
Wald test	b₁ = c₁ = 16.53***		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} c_{k}$ = 0.86

†

p < .10. *p < .05. **p < .01. ***p < .001.

The current study examined the lead–lag relationship after controlling for trading volume and size as it did for monthly returns. The results generally support Hypothesis 1. For all portfolios of high trading volume, small trading volume, large size and small size, the underlying U.S. market returns significantly predict the Open Market returns both for Lag 1 and summation of coefficients from Lag 1 through Lag 3. Meanwhile, the Open Market weekly returns do not significantly predict the underlying U.S. returns for all portfolios except small size portfolio’s summation of coefficients case. The Wald test results for cross-autocorrelation confirms the Granger causality for most of the cases.

The second hypothesis extends the asymmetric cross-autocorrelations between the cross-listed stock returns on the Open Market in Germany and the underlying shares in the United States to the shares cross-listed on the EU Regulated Market in Germany. The argument for this is that German investors have better information on the U.S. firms when the firms list their stocks on the EU Regulated Market since those companies must provide information in the form that German investors understand (e.g., some financial information is mandatorily provided in German). Meanwhile, Open Market investors are unlikely to obtain as much information as that for the shares cross-listed on the EU Regulated Market since neither the issuing company nor German financial institutions applying for cross-listing has the responsibility to provide information for investors, although German financial institutions might try to do so to increase trading volumes and attendant brokerage commissions. Therefore, German investors would closely follow the returns of the underlying shares in the United States.

As for the Hypothesis 1, the current study examined Hypothesis 2, first without controlling for any possible confounding factors, then after controlling for trading volume and size, respectively. Panel C in Table 7 shows that German returns for the shares cross-listed on the Open Market gain significant prediction from the underlying U.S. shares for the first lag (coefficient = 0.6463; p < .001) whereas underlying U.S. returns for the shares cross-listed on the Open Market do not gain significant prediction from the German returns both for first lag (coefficient = 0.0119; p > .1) and summation of the five lags (sum of coefficients = 0.0027; p > .1). For the shares cross-listed on EU Regulated Markets, the current study found a cross-autocorrelation as well. U.S. returns predict the return for cross-listed German shares for the first lag (coefficient = 0.7875; p < .001) and summation of the five lags (sum of coefficients = 1.5825; p < .001) whereas German returns do not predict the return for underlying U.S. returns for the first lag (coefficient = 0.0260; p > .1) and summation of the five lags (sum of coefficients = 0.1142; p > .1). The Wald test results do not support the second hypothesis that the lead–lag relationship for the Open Market listed shares is significantly stronger than for the EU Regulated Market listed shares. The four portfolios after controlling for either trading volume or size show similar pattern with significant cross-autocorrelation within the Open Market–listed shares and the EU Regulated Market listed shares whereas large size portfolio reveals significant Wald test results, supporting Hypothesis 2.

Table 7

Summary of Autocorrelations for Hypothesis 2: Daily Returns

Panel C: Daily Returns (No. of Observations = 2,350)
LHS	$r_{G, t - 1}^{O}$	$r_{U S, t - 1}^{O}$	$\sum_{k = 1}^{5} a_{k}$ or e_k	$\sum_{k = 1}^{5} b_{k}$ or f_k
$r_{G, t}^{O}$	−0.0310	0.6463***	0.9223***	−0.1517***
$r_{U S, t}^{O}$	0.0119	0.0093	0.0027	−0.1355*
	$r_{G, t - 1}^{E}$	$r_{U S, t - 1}^{E}$	$\sum_{k = 1}^{5} l_{k}$ or p_k	$\sum_{k = 1}^{5} m_{k}$ or q_k
$r_{G, t}^{E}$	−0.5439***	0.7875***	−1.1285***	1.5825***
$r_{U S, t}^{E}$	0.0260	−0.0472	0.1142	−0.1863
Wald test	b₁ = m₁ = 33.53***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} m_{k}$ = 273.86***
Panel Ca: Daily Returns of High Trading Volume Portfolio (No. of Observations = 1,223)
$r_{G, t}^{O}$	−0.3700***	0.6012***	−0.6395***	1.0003***
$r_{U S, t}^{O}$	0.0277	−0.1210***	0.0577	−0.2694**
$r_{G, t}^{E}$	−0.7692***	0.8742***	−1.7761***	2.1174***
$r_{U S, t}^{E}$	−0.0075	−0.0339	0.0678	−0.1415
Wald test	b₁ = m₁ = 43.32***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} m_{k}$ = 31.97***
Panel Cb: Daily Returns of Low Trading Volume Portfolio (No. of Observations = 887)
$r_{G, t}^{O}$	−0.5917***	0.8746***	−1.5025***	2.0923***
$r_{U S, t}^{O}$	0.0793	0.0171	0.4654*	−0.4824*
$r_{G, t}^{E}$	−0.4672***	0.9412***	−1.1051***	2.0248***
$r_{U S, t}^{E}$	0.1325^†	−0.0060	0.3402	−0.3637^†
Wald test	b₁ = m₁ = 9.25**		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} m_{k}$ = 0.6536
Panel Cc: Daily Returns of Large Size Portfolio (No. of Observations = 1,223)
$r_{G, t}^{O}$	−0.4672***	0.8091***	−0.9186***	1.4934***
$r_{U S, t}^{O}$	−0.0265	−0.0391	0.0063	−0.2534*
$r_{G, t}^{E}$	−0.5518***	0.7006***	−0.9081***	1.1405***
$r_{U S, t}^{E}$	−0.0212	−0.0293	0.0835	−0.1500
Wald test	b₁ = m₁ =10.77***		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} m_{k}$ = 0.0238*
Panel Cd: Daily Returns of Small Size Portfolio (No. of Observations = 1,159)
$r_{G, t}^{O}$	0.4292***	0.6691***	1.0015***	−0.2481***
$r_{U S, t}^{O}$	0.0222	0.0241	0.0075	−0.0057
$r_{G, t}^{E}$	−0.5593***	0.7874***	−1.3283***	1.8158***
$r_{U S, t}^{E}$	−0.0352	−0.0397	−0.0016	−0.1107
Wald test	b₁ = m₁ = 8.31**		$\sum_{k = 1}^{5} b_{k}$ = $\sum_{k = 1}^{5} m_{k}$ = 216.98***

†

p < .10. *p < .05. **p < .01. ***p < .001.

The current study examined the second hypothesis with weekly returns as well. Panel D of Table 8 exhibits the VAR estimation results. The weekly results support Hypothesis 2. Underlying U.S. returns for the shares cross-listed on the Open Market significantly predict the German returns on the Open Market for the first lag (coefficient = 0.8251; p < .001) and the summation of the three lags (sum of coefficients = 1.5939; p < .001) whereas the opposite relationship does not occur significantly for both the first lag (coefficient = −0.1156; p > .1) and summation of the three lags (sum of coefficients = −0.2387; p > .1). Underlying U.S. returns for the shares cross-listed on the EU Regulated Market significantly predict the German returns, as well, for the first lag (coefficient = 0.6099; p < .001) and summation of the three lags (sum of coefficients = 0.9005; p < .05) whereas the opposite relationship does not occur significantly for both the first lag (coefficient = −0.0449; p > .1) and summation of the three lags (sum of coefficients = −0.0326; p > .1). The Wald test results reveal that the lead–lag relationship is significantly stronger for the Open Market listed shares than the EU Regulated Market listed shares, supporting the second hypothesis both for Lag 1 (χ² = 4.89; p < .05) and summation of the three lags (χ² = 8.92; p < .01). The VAR analyses results after controlling for either trading volume or size reveal that similar pattern exist within each stock market whereas small size portfolio results provide significantly stronger relationship among the Open Market listed shares than the EU Regulated Market listed shares, supporting Hypothesis 2.

Table 8

Summary of Autocorrelations for Hypothesis 2: Weekly Returns

Panel D: Weekly Returns (No. of Observations = 565)
LHS	$r_{G, t - 1}^{O}$	$r_{U S, t - 1}^{O}$	$\sum_{k = 1}^{3} b_{k}$ or e_k	$\sum_{k = 1}^{3} m_{k}$ or f_k
$r_{G, t}^{O}$	−0.7439***	0.8251***	−1.3261***	1.5939***
$r_{U S, t}^{O}$	−0.1156	0.0915	−0.2387	0.2765^†
	$r_{G, t - 1}^{E}$	$r_{U S, t - 1}^{E}$	$\sum_{k = 1}^{3} l_{k}$ or p_k	$\sum_{k = 1}^{3} m_{k}$ or q_k
$r_{G, t}^{E}$	−0.4968***	0.6099***	−0.7336***	0.9005***
$r_{U S, t}^{E}$	−0.0449	0.0904	−0.0326	0.1694
Wald test	b₁ = m₁ = 4.89*		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} m_{k}$ = 8.92**
Panel Da: Weekly Returns of High Trading Volume Portfolio (No. of Observations = 302)
$r_{G, t}^{O}$	−0.2238**	0.2660**	−0.4238**	0.5161**
$r_{U S, t}^{O}$	0.0296	−0.0895	−0.4444	0.0023
$r_{G, t}^{E}$	−0.7736***	0.8124***	−1.2680***	1.4036***
$r_{U S, t}^{E}$	−0.2188^†	0.2509^†	−0.2784	0.4212
Wald test	b₁ = m₁ = 13.06***		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} m_{k}$ = 6.20*
Panel Db: Weekly Returns of Low Trading Volume Portfolio (No. of Observations = 212)
$r_{G, t}^{O}$	−0.6996***	0.7360***	−1.3409***	2.3506***
$r_{U S, t}^{O}$	−0.0885	0.0263	−0.1802	0.2307
$r_{G, t}^{E}$	−0.8775***	0.8699***	−1.8115***	2.1676***
$r_{U S, t}^{E}$	−0.1358	0.0220	−0.3663	0.5391^†
Wald test	b₁ = m₁ = 0.97		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} m_{k}$ = 2.48
Panel Dc: Weekly Returns of Large Size Portfolio (No. of Observations = 302)
$r_{G, t}^{O}$	−0.3064***	0.3482***	−0.6974***	0.7283***
$r_{U S, t}^{O}$	0.0714	−0.1400^†	−0.1083	−0.0791
$r_{G, t}^{E}$	−0.5792***	0.6950***	−0.9417***	1.1533***
$r_{U S, t}^{E}$	−0.0819	0.1718*	−0.1105	0.2988
Wald test	b₁ = m₁ = 6.91**		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} m_{k}$ = 1.81
Panel Dd: Weekly Returns of Small Size Portfolio (No. of Observations = 287)
$r_{G, t}^{O}$	−0.6548***	0.7551***	−0.8224***	1.1089***
$r_{U S, t}^{O}$	0.0760	−0.0568	0.4413^†	−0.3219
$r_{G, t}^{E}$	−0.0859	−0.0368	−0.1973	0.2219
$r_{U S, t}^{E}$	0.0201	−0.1544	−0.1080	0.1281
Wald test	b₁ = m₁ = 27.17***		$\sum_{k = 1}^{3} b_{k}$ = $\sum_{k = 1}^{3} m_{k}$ = 7.06^†

†

p < .10. *p < .05. **p < .01. ***p < .001.

In examining the hypotheses, the Phillips–Perron test was conducted to investigate stationary property of all the portfolios examined, respectively, and all the portfolios were found stationary.³

Discussion

The main purposes of the current study are twofold: (a) to examine if stock returns of U.S. underlying shares lead stock returns of involuntarily cross-listed shares on the Open Market because of information asymmetry and (b) to investigate if the lead–lag relationship is more evident among securities involuntarily cross-listed on the Open Market than securities voluntarily cross-listed on the EU Regulated Market because of differences in regulation in information disclosure. To achieve the aims, the current study estimated cross-autocorrelations using VARs and confirmed the hypotheses with the Wald test. The logic behind the first hypothesis is that the U.S. stock market has higher quality information for U.S. restaurant companies than the German stock market, especially the Open Market; therefore, German investors closely follow stock returns in the United States. The sampled restaurant companies voluntarily listed their shares on U.S. exchanges, which require high levels of information disclosure. Therefore, U.S. restaurant companies have legal obligations to provide information to the U.S. market. Plus, local investors are known to have higher quality and amount of information of firms compared with nonlocal investors. On the other hand, German investors have limited information for involuntarily listed U.S. restaurant firms because neither the issuing firm nor German financial institutions have a legal responsibility to provide information about the involuntarily cross-listed firms. For this reason, German stock returns follow U.S. stock returns for the underlying shares to a significantly greater degree than the opposite case of U.S. stock returns following German stock returns. This phenomenon is known as Granger causality, which suggests that it is more likely that the information in U.S. stock returns causes German investors to trade than vice versa. The current study examined the Granger causality with coefficient of the first lag for daily and weekly returns because the first lag tends to show most significant impact. In addition, the study examined summation of coefficients over multiple lags.

Although the results generally support Hypothesis 1, the daily returns results of the summation of coefficients over five lags for low trading volume portfolio and small size portfolio do not support Hypothesis 1 because of negative cross-autocorrelations occurred from the second lag through the fifth lag. Interestingly, however, the study finds that the weekly returns results both for the low trading volume portfolio and small-size portfolio support Hypothesis 1. Such discrepancy can be explained with matches between data set and appropriate lags. Hou (2007) argues that examination of only weekly returns is valid in his lead–lag analyses because, although daily or even intra-daily returns can improve precision, they may introduce confounding microstructure influences such as bid-ask bound and nonsynchronous trading. In the case of low trading volume portfolio in the current study, it would be more appropriate to refer to the weekly returns results since nonsynchronous trading is evident. Characteristics of the low trading volume portfolio reveal significantly low yearly trading volume in the Open Market in Germany, less than 50,000 shares, on average, as well as sporadic trading with a frequency of less than 100 business days of trading, on average. We argue that the weekly results are more suited for the small size portfolio as well. One of the reasons why the current study controlled for size was because prior research has found that market makers adjust small firms’ stock prices after observing larger firms’ past stock price changes. Argument made by prior studies for this phenomenon is that amount and quality of information that larger firms produce and disseminate is greater than small firms (Ho & Michaely, 1988). Therefore, the small size portfolio can be more appropriate to refer to the weekly returns since small firms’ stock prices will take more time to adjust their prices compared with large firms’ cases.

The significant difference in the lead–lag relationship reveals that German investors are unlikely to have information for U.S. restaurant companies as quickly and as much as U.S. investors do. Rather, they closely follow the U.S. returns assuming that U.S. stock returns contain more timely and detailed information about U.S. companies.

The argument supporting the second hypothesis is that the Granger causality is stronger among Open Market shares’ lead–lag relationship than among EU Regulated Market shares’ lead–lag relationship. Contrary to the Open Market, the EU Regulated Market mandates the listed firms disclose company information to meet the stringent level of EU regulations, in a form familiar to German investors (e.g., information written in German, statements reflecting German or European accounting rules, order of information disclosure, etc.). Having information on shares considered for investment, German investors are less likely to rely on stock returns of underlying U.S. shares as much as the investors of Open Market shares do. Furthermore, U.S. firms are more likely to disseminate firm information voluntarily in the German market to serve their German investors when they voluntarily cross-list.

In fact, the findings show that Granger causality exists for the EU Regulated shares as well. That means German investors who invest in cross-listed shares on the EU Regulated Market still closely follow the stock returns of their underlying U.S. stock returns. However, the extent to which they rely on the U.S. stock returns is significantly lower than in the case of the shares cross-listed on the Open Market for the weekly return results. As it was in the first hypothesis, the second hypothesis was supported for large-size portfolio in the daily returns whereas it was supported for small-size portfolio in the weekly returns. Same argument can be applied for these discrepancies that small-size stock returns take more time to adjust stock prices than large-size stock returns. The high trading volume portfolio and low trading volume portfolio results generally do not support the second hypothesis, both for daily returns and weekly returns. Interpretation of the results, however, should be made with caution since the portfolio of the high trading volume for the Open Market listed shares and the portfolio of the low trading volume for the EU Regulated Market listed shares is very thin; the high trading volume portfolio for the Open Market listed shares is composed of only two firms—McDonald’s and Yum! Brands, and the low trading volume portfolio for the EU Regulated Market listed shares is composed of only one firm—The Central European Russia Fund, Inc.

The current study is the first attempt to examine the lead–lag relationship in the involuntary cross-listing context based on the information asymmetry arguments. U.S. restaurant industry is the choice of sample since an absolute majority of involuntarily cross-listed U.S. restaurants are cross-listed on the Open Market in Germany, which provides homogeneity, and the authors could confirm the involuntariness by contacting each company. This study confirms Chan’s (1993) argument on information asymmetry that information differences significantly determine the lead–lag relationship of the U.S. restaurant shares involuntarily cross-listed on the Open Market in Germany. Previous studies often examined the role of information diffusion in the lead–lag relationship of stock returns by comparing size, analyst coverage, and market share (e.g., Badrinath et al., 1995; Brennan et al., 1993; Hou, 2007). The current study examines differences in information diffusion in the context of involuntary cross-listing. Information discrepancy is evident between German investors and U.S. investors for the U.S. restaurant companies because of regulation requirements’ differences as well as likely voluntary disclosure differences. The finding suggests that significantly reducing the information disclosure regulations prohibits investors from obtaining necessary information of a firm with potential for investment and inhibits better decisions. As competition among the world stock markets increases, many stock exchanges have reduced their regulations. An example is the SEC’s amendment of Rule 12g3-2(b).⁴ But stock markets should understand that deregulation of involuntary cross-listing may be counterproductive for the protection of its investors. Furthermore, competition between stock exchanges could lead to a “race to the bottom” in disclosure to investors (e.g., Dye & Sunder, 2001).

From the U.S. restaurant industry’s point of view, involuntary cross-listing means that these companies may have shareholders of which the companies are unaware. Also, those investors are outside the firm’s obligation to disseminate information. Therefore, information of the company is not likely to be efficiently transmitted to shareholders. If a U.S. restaurant company finds a need to communicate with those foreign investors more effectively, they may have to consider providing some information to a foreign stock exchange or the foreign media where their shares are involuntarily cross-listed. Voluntary information disclosure on the foreign exchange can be critical considering more and more class action lawsuits are occurring between local shareholders and foreign companies (Lamont & Etzold, 2009).

By understanding both the benefits and disadvantages that deregulation of information disclosure brings for involuntary cross-listing, the FSE Open Market may mandate the applying third party financial institutions to inform the involuntary cross-listing to issuing companies so that those involuntarily cross-listed companies would be able to choose to provide information to their German shareholders. The regulation amendment would help German investors be better informed of the shares they invest in the FSE Open Market and issuing companies better communicate with their shareholders while easiness of application of German financial institutions is not hugely hampered.

For those German equity investors who are interested in publicly traded U.S. restaurants, the findings may provide some practical guidelines for their portfolio development. Understanding the U.S. stock returns leads the FSE Open Market returns in terms of U.S. restaurant stocks; any significant changes of those stocks in the United States may become an important predictor of their price changes in the FSE Open Market, which can assist the investors to modify their investment portfolio in the FSE Open Market, accordingly.

Limitation and Suggestions for Future Studies

This study examined the role of information asymmetry caused by differences of information disclosure regulation on lead–lag relationships between U.S. shares cross-listed in Germany and the underlying shares listed in the United States. The differences of the listing nature between involuntariness and voluntariness may also be reflected in the press releases to media. Voluntarily listed firms may issue press releases to media in the foreign market similar to practices in their domestic market and thus gain foreign media coverage. In contrast, involuntarily cross-listed firms would be less likely to seek media coverage in the foreign media. Future studies may compare the foreign media coverage to support the argument on information discrepancy in domestic stock market and foreign stock market.

The current study has a small sample size by focusing on specific group of U.S. restaurant companies cross-listed on the FSE. Therefore, portfolios tend to be thin. This is a trade-off for analyzing with homogenous group of sample while producing less noisy results. This study may have a survival bias since the sample companies only contains those who are currently listed on the FSE. It is because the FSE only provides financial information such as stock prices and trading volume of the companies that currently trade in that market.

The FSE prices for involuntarily cross-listed shares can be bid or ask prices where no actual transaction occurred. A better analysis might be of bid prices and ask prices, separately, since that context differentiates buyer-initiated prices from seller-initiated ones (Hasbrouck, 1995). However, the FSE does not provide information for the price’s being a bid price or an ask price for the prices associated with no actual transaction.

Footnotes

Notes

Yoon Koh, PhD (e-mail: ykoh@uh.edu), is an assistant professor in the Conrad N. Hilton College of Hotel and Restaurant Management at the University of Houston, Houston, Texas. Seoki Lee, PhD (e-mail: leeseoki@psu.edu), is an associate professor in the School of Hospitality Management at The Pennsylvania State University, University Park, Pennsylvania. Sudipta Basu, PhD (e-mail: sudipta.basu@temple.edu) is a professor in the Fox School of Business and Management at Temple University, Philadelphia, Pennsylvania.

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