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We analyze exchange rates along with equity quotes for 3 German firms from New York (NYSE) and Frankfurt (XETRA) during overlapping trading hours to see where price discovery occurs and how stock prices adjust to an exchange rate shock. Findings include: (a) the exchange rate is exogenous with respect to the stock prices; (b) exchange rate innovations are more important in understanding the evolution of NYSE prices than XETRA prices; and (c) most (but not all) of the fundamental or random walk component of firm value is determined in Frankfurt.

Stocks of many non-US firms are traded in the United States. The issue of where price discovery occurs for such firms is surprisingly understudied. For instance, we lack evidence that yields a firm answer to the question of whether US trading follows the home market or the home market follows the US. Furthermore, how do the prices in both markets adjust to an exchange rate shock? Does arbitrage avoidance require both markets to simultaneously adjust to a new exchange rate or does the adjustment tend to occur all in one market? While there is no paper that attempts to address both of these issues as will be done here, there is a literature that addresses the relationship between prices of foreign equities and their US listings. This literature is overwhelmingly focused on low-frequency daily returns so that issues of non-synchronous prices are potentially important. Exceptions include Ding et al. (1999), who examine the links between Singapore and Malaysia trading for one Malaysian firm, and Eun and Sabherwal (2003), who examine the links between US and Canadian trading for a sample of Canadian firms. These studies show significant price discovery in both the home and foreign market. While these papers are innovative and instructive, they differ from the analysis developed below in that they do not model the exchange rate process, but use exchange rates to convert equity prices into common units across countries. In addition, their samples have more time aggregation between observations than the sample employed below. Harris et al. (2001) examine high-frequency spread and transaction price dynamics for Daimler-Chrysler (DCX) after the creation of the global ordinary DCX shares and show how US interest in DCX trading decreased in the first six months following the merger of Daimler-Benz and Chrysler. While analysis in an intra-day setting is required to provide hard evidence, lower-frequency studies have found an independent effect of the US market. For instance, Kim et al. (2000) use daily data on 21 Japanese, 21 British, 5 Dutch, 5 Swedish, and 4 Australian firms to estimate VAR models of the impact of the underlying shares, the New York afternoon exchange rate, and the US market index on ADR prices. They find that the underlying shares appear to be most important, but there is a significant independent role for the exchange rate and the US market index in pricing ADRs. While their paper does not specifically address the issue of price discovery, their findings of a role for the US factor suggest that the issue of price discovery requires a more detailed analysis. Other studies using daily data on individual stocks have focused on other markets. Kato et al. (1990) examine seven UK, eight Japanese, and eight Australian stocks also traded in New York and find evidence that the price in the home country leads the price in New York. They convert home country prices into dollars using a daily exchange rate taken from the Wall Street Journal. Lau and Diltz (1994) study seven Japanese stocks also traded in New York and find bi-directional causality but a stronger impact of NYSE returns on Tokyo returns than the reverse. They convert the Tokyo prices into dollars using daily exchange rates from the Chicago Mercantile Exchange. Lieberman et al. (1999) examine six Israeli stocks that are listed in New York and find that price discovery appears to occur in Israel for five of the firms with Teva having a dominant role for the US. They suggest that the result for Teva is due to Teva being a multinational firm. Their study converts the Israeli prices into dollars using a daily exchange rate from the Bank of Israel. Wang et al. (2002) examine a group of Hong Kong stocks that are also traded in London and find bi-directional causality for local market returns between the two markets but with Hong Kong being the dominant market. The exchange rate is not incorporated into their analysis. The evidence from low-frequency daily data indicates that the issue of price discovery for cross-listed shares is rather unsettled. Generally, the papers are not actually conducting tests for price discovery in the recent sense of the word but are examining pricing links across markets. One may draw inference, however, that while the majority of low-frequency evidence points toward the home market as being the dominant source of pricing, results are mixed and some studies find the US prices to be dominant. Aside from Kim, Szakmary, and Mathur, the low-frequency studies do not allow for an independent role of the exchange rate but, instead, translate home market prices into dollars. One goal of this paper is to provide evidence on the information shares of US and home-market trading using contemporaneously sampled, high-frequency data. A second goal is to provide evidence on the equity price response at home and in the US to an exchange rate shock. There is a large literature on the effect of exchange rate changes on equity prices, but this literature has focused on the foreign exchange exposure effect of exchange rate changes for a single firm in its home country. Such studies have (quite properly) conducted analyses at a low time series frequency as they were concerned with issues related to the management of foreign exchange risk exposure. There is a limited literature that examines higher-frequency evidence of exchange rate changes and stock prices. Karolyi and Stulz (1996) examined the determinants of correlations between open to close daily returns on eight Japanese stocks traded in the United States with a matched sample of US stocks. Their data included daily returns on yen/dollar futures contracts. They found that shocks to the currency futures returns had no measurable influence on the Japanese and US stock price correlations. Bailey et al. (2000) studied the impact of the Mexican peso/US dollar exchange rate on prices of Mexican firms traded on the NYSE. They sampled stock prices and exchange rates at 30-min intervals and found that peso depreciation was associated with decreases in the stock prices. Ours is the first study to examine the high-frequency response of pairs of internationally cross-listed equity prices to exchange rates at the time resolution relevant for arbitrageurs. One might think of price discovery for a US-listed European stock, e.g., the German Deutsche Telekom (DT) to be determined in the following way. News in Germany is most important for this stock, so during home-market business hours, the price fluctuates with public and private information revelation. Once US trading begins in the ADR,1 the price of the stock may include relevant information coming from the North American market as inventory and information-based trading occurs during the overlap between European and American trading hours. In addition, dollar/euro exchange rate fluctuations will have implications for the stock prices in both Europe and America. After an exchange rate shock, arbitrage will restrict the ADR price so that it does not deviate too far from the home-market price when both are measured in a common currency. For instance, dollar depreciation would tend to increase the dollar price of the ADR and/or lower the euro price of the underlying home-market shares. Since there has been no intra-daily analysis of how international stock prices adjust to exchange rate shocks, we do not know if adjustment is symmetric in both the home country and the US markets or if most or all of the adjustment to an exchange rate shock occurs in one market location. Our analysis will provide a first look at this issue. The use of high-frequency, intra-day data allows a view of the market dynamics that cannot be achieved in daily data or lower-frequency intra-day data. Besides the issue of non-synchronous quotes that arises in using closing prices from different international markets, one cannot make meaningful inferences regarding price discovery except at the high-frequency relevant for actual trading. Furthermore, the pattern of adjustment of stock prices to exchange rate shocks would be lost due to time aggregation. Traders respond quickly to new information, so to infer the stock price response to an exchange rate shock one must examine the data immediately after the change in the exchange rate. At a low frequency, there will be many reasons why stock prices change so that one cannot clearly identify the link between a change in the exchange rate and a subsequent change in the price of a stock. The gain from using high-frequency data is essentially that there may be one-way causality existing among variables at a high sampling frequency that dissolves into contemporaneous correlation at a lower sampling frequency. We investigate the issue of price discovery for three large German blue-chip firms that are traded on the XETRA system in Germany and the New York Stock Exchange (NYSE) in the United States: Daimler-Chrysler, Deutsche Telekom, and SAP. The paper is organized as follows: Section 2 presents a brief overview of relevant institutional detail regarding the trading venues, trading mechanisms, and firms studied. Section 3 introduces the basic equilibrium relationships in the context of a simple microstructure model of the market. Section 4 provides the framework for analysis and discusses issues of methodology. Section 5 presents and discusses the data and estimation results. Finally, a summary and conclusion is provided in Section 6.