This paper proposes a new measure of price discovery that uses the spectral decomposition. The methodology is especially important in the context of large price systems, such as interest rate parities with spot and futures contracts or dual-class shares in multiple markets. We employ high frequency data to study price discovery in dual-class Brazilian stocks and their ADRs. We find that the foreign market is at least as informative as the home market and that shocks in the dual-class premium entail a permanent effect in normal times, but transitory in periods of financial distressFinancial markets have the important function of discovering the price of a given asset. The increasing availability of highfrequency data allows us to study how efficiently and timely each market reacts to news in a much more precise manner. There is a large number of companies being listed in more than one exchange mainly because cross-listing allows raising equity capital, at a lower cost and increasing liquidity. Besides, it may also improve minority shareholder protection (Stulz, 1999), increase firm value (Doidge, Karolyi, & Stulz, 2004), and lower private benefits of control (Doidge, 2004). There are 498 foreign companies from 46 different countries listed on NYSE as of June 30, 2016. As a result, geographical price discovery is of major interest for domestic stock exchanges and companies (see, for instance, Eun & Sabherwal, 2003). This paper extends the standard price discovery methodology to deal with high-dimension portfolios. Applications include interest rate parities using both spot and future contracts in interest rate and exchange rate markets as well as dual-class assets traded on multiple markets. We focus on the latter. The idea is to exploit every piece of information about the fundamental value of a firm by looking at the prices of both common and preferred shares across different trading platforms. As a by-product, by looking at the difference between prices of common and preferred shares, we may also shed some light on the behavior of the dual-class premium.The main technical difficulty is to contrive a unique price discovery measure that does not assume a priori which share class and/or market lead the impounding of new information. For the standard information share (IS) measure of price discovery (Hasbrouck, 1995), which gauges the fraction of the variance of the fundamental price innovation due to the variance of a given asset/market price innovation, one normally imposes a triangular structure from the most informative to the least informative market price in order to handle contemporaneous correlations. ISs will thus depend on the specific ordering in the price system.One solution is to consider the average IS across different orderings of market prices. This is a simple and effective solution if there are only a few market prices. However, as the number of assets/markets increase, one would have to average over thousands J Futures Markets. 2018;38:129-155.wileyonlinelibrary.com/journal/fut