International Correlation Risk *

Abstract This paper provides novel evidence of priced correlation risk in foreign exchange markets. In the time-series, we find that the correlation risk premium, defined as the risk-neutral and physical correlation, is 15% per year on average. In the cross-section, global correlation risk carries a risk premium of −1%. In particular, we find that currencies with a high (low) exposure to correlation risk, i.e., that perform badly (well) during periods of high correlation, have high (low) returns on average. Correlation risk can thus explain carry trade returns. To address our empirical findings, we show in a general equilibrium model with external habit formation and home bias in preferences that time-varying correlation is driven by stochastic risk aversion. Currencies that provide a hedge against adverse shocks in global risk aversion are currencies that appreciate when conditional exchange rate correlation is high. To achieve this, we take both a time-series and cross-sectional perspective. Our first contribution is to provide evidence of a large correlation risk premium in currency markets. We find that the size of the estimated correlation risk premium, defined as the difference between the risk-neutral and the objective measure exchange rate correlation, is around 15%. On average, the implied correlation is 56%, whereas the realized correlation is 41%. The correlation risk premium is almost always positive, which implies that it provides a hedge against bad states of the world. Second, we proceed by quantifying the price of FX correlation risk in the cross-section of currencies using a portfolio sorting approach, following the recent international finance literature (see e.g. Verdelhan, 2007, Lustig, Roussanov, and To address our empirical findings, we explore the implications of time variation in conditional risk aversion for currency risk premia. We consider a multi-country, multigood general equilibrium model in which preferences are characterized by external habit formation Our paper is also part of the recent literature that addresses the failure of the expectations hypothesis for exchange rates. Brunnermeier, Nagel, and Pedersen I. Data and Risk Factor Construction We start by describing the data and how to construct the currency correlation risk factor. We use daily option prices on the most heavily traded currency pairs to construct a forward looking measure of correlation risk and high frequency data on the underlying spot exchange rates to calculate the realized counterparts. Our data runs from January 1999 to December 2010. A. Data Description High Frequency Currency Data: The high frequency spot exchange rates Euro, Japanese Yen, British Pound, and Swiss Franc, all vis-à-vis the U.S. Dollar, are from Olsen & Associates. Given that the high liquidity in foreign exchange markets prevents triangular arbitrage opportunities in the five most heavily traded currencies, calculating the remaining cross rates using the four exchange rates is common practice. The raw data contains all interbank bid and ask indicative quotes for the exchange rates for the nearest even second. After filtering the data for outliers, the log price at each 5 minute tick is obtained by linearly interpolating from the average of the log bid and log ask quotes for the two closest ticks. As options are traded continuously throughout the day, this results in a total of 288 observations over a 24 hour period. 1 Currency Option Data: We use daily over-the-counter (OTC) currency options data from JP Morgan for the four currency pairs EURUSD, JPYUSD, GBPUSD, and CHFUSD plus the six cross rates (i.e., we have have options data on a total of ten exchange rates). The use of OTC option data has several advantages over exchange traded option data. First, the trading volume in the OTC FX options market is several times larger than the corresponding volume on exchanges such as the Chicago Mercantile Exchange. As a consequence, this leads to more competitive quotes in the OTC market. Second, the conventions for writing and quoting options in the OTC markets have several features that are appealing when performing empirical studies: Every day, 1 We follow the empirical literature and take five minute intervals opposed to higher frequencies to mitigate the effect of spurious serial correlation due to microstructure noise (see 5 new option series with fixed times to maturity and fixed strike prices, defined by sticky deltas, are issued. In comparison, the time to maturity of exchange-traded option series gradually declines with the approaching expiration date, and the moneyness continually changes as the underlying exchange rate moves. Therefore, the OTC option data allows for better comparability over time, as the series' main characteristics do not change from day to day. The options used in this study are plain-vanilla European calls and puts and encompass 5 option series per exchange rate: We consider a one month maturity and a total of five different strikes: at-the-money (ATM), 10-delta call and 25-delta call, 10-delta-put and 25-delta put. Spot and Forward Rates: To form our portfolios, we use daily data for spot exchange rates and one month forward rates versus the U.S. dollar obtained from Datastream. We start from daily data in order to construct the correlation risk exposure. In line with the previous literature (see Carry Portfolios: At the end of each period t, we allocate currencies into four portfolios based on their forward discounts at the end of period t. Sorting on forward discounts is the same as sorting on interest rate differentials since covered interest parity holds closely in the data at the frequency analyzed in this paper. We re-balance portfolios at the end of each month. This is repeated month by month. Currencies are ranked from low to high interest rate differentials. Portfolio 1 contains currencies with the lowest interest rate (or smallest forward discounts) and portfolio 4 contains currencies with the