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Crash-Neutral Currency Carry Trades Crash-Neutral Currency Carry Trades Jakub W. Jurek∗ Abstract Currency carry trades exploiting violations of uncovered interest rate parity in G10 currencies have historically delivered significant excess returns with annualized Sharpe ratios nearly twice that of the U.S. equity market (1990-2008). Using data on foreign exchange options, this paper investigates whether these returns represent compensation for exposure to currency crashes. After eliminating net dollar exposure and hedging crash risk, excess returns to crash-neutral currency carry trades are statistically indistinguishable from zero; returns to non-dollar-neutral portfolios remain positive, but are only weakly significant. The choice of option maturity has a significant impact on the realized excess returns, with quarterly hedging producing annualized returns that are 1-2% higher than those obtained from monthly hedging. First draft: October 2007 This draft: April 2009 ∗Jurek: Princeton University, Bendheim Center for Finance, e-mail: [email protected]. I thank John Campbell, Itamar Drechsler, Steve Edelstein, John Galanek, John Heaton, Mark Mueller, Monika Piazzesi, Erik Stafford, Adrien Verdelhan, and seminar participants at Duke University, Yale University, the Fall 2008 NBER Asset Pricing Meeting, the 2008 Princeton-Cambridge Conference, the 2008 Princeton Implied Volatility Conference, the 2008 Conference on Financial Markets, International Capital Flows and Exchange Rates (European University Institute), the 2009 Oxford- Princeton Workshop on Financial Mathematics and Stochastic Analysis, the Society for Quantitative Analysts and the Harvard Finance Lunch (Fall 2007) for providing valuable comments. I am especially grateful to J.P. Morgan for providing the FX option data. Electronic copy available at: http://ssrn.com/abstract=1262934 Uncovered interest parity predicts that high interest rate currencies should depreciate relative to low interest rate currencies, such that investors would be indifferent between holding the two. Empirically, not only do high interest rate currencies not depreciate relative to their low interest rate counterparts, they tend to appreciate. This finding, often referred to as the forward premium anomaly, is one of the most prominent features of exchange rate data. Historically, the currency carry trade { a strategy designed to exploit this anomaly { has delivered significant excess returns with annualized Sharpe ratios nearly twice that of the U.S. equity market (Figure 1). Using data on foreign exchange options, this paper investigates whether these excess returns reflect compensation for exposure to the risk of large devaluations (crashes) in currencies with high interest rates. I show that after hedging crash risk, returns on portfolios of currency carry trades that are constructed to be dollar-neutral, are statistically indistinguishable from zero (1999-2008). Returns on portfolios that are not constrained to be dollar-neutral are only weakly significant and depend on the choice of portfolio weights (equal- vs. spread-weighted). Finally, I examine the performance of the crash hedge during the credit crisis of 2008, and find significant improvements from using quarterly, rather than monthly, hedging. The currency carry trade exploits the forward premium anomaly by borrowing funds in currencies with low interest rates and lending them in currencies with high interest rates. This strategy captures the interest rate differential (carry) between the two currencies, but leaves the investor exposed to fluctuations in the exchange rate between the high interest rate currency and the low interest rate currency. Historically, since high interest rate currencies have tended to appreciate relative to their low interest rate counterparts, the currency exposure has actually turned out to be an additional source of return. As a result, currency carry trades have been characterized by an extremely attractive risk-return tradeoff. For example, a simple strategy which equal-weighted nine individual carry trades implemented in currency pairs involving the U.S. dollar and one of the remaining G10 currencies earned an annualized excess return of 4:42% with an annualized volatility of 5:05% (Sharpe ratio = 0.88) over the period from January 1990 to December 2007.1 In the latter part of the sample (1999- 2007), simple equal- and spread-weighted portfolios of carry trades delivered even higher Sharpe ratios of 1.06 and 1.35, respectively. To illustrate this, Figure 1 plots the total return indices for the carry strategy vis a vis the total return indices for the three Fama-French risk factors and the momentum portfolio. As can be readily seen from the plot, the returns to the carry strategy dominate the returns to each of the alternatives when the strategies are scaled to have the same ex post volatility. However, the currency carry trade is also exposed to the risk of significant declines, as evidenced by the 20% loss sustained in 2008, driving down the full sample Sharpe ratio to 0.57. The returns to currency carry trades are characterized by two main features. First, the volatility of the strategy is low and stands at roughly one half the volatility of any given X=USD exchange rate, suggesting that exchange rate innovations are largely uncorrelated in the cross-section. Second, 1The set of G10 currencies consists of: Australian dollar (AUD), Canadian dollar (CAD), Swiss franc (CHF), Euro (EUR), British pound (GBP), Japanese yen (JPY), Norwegian krone (NOK), New Zealand dollar (NZD), Swedish krona (SEK), and the U.S. dollar (USD). 1 Electronic copy available at: http://ssrn.com/abstract=1262934 although the low volatility allows the total return index to have an extremely smooth upwards progression, the strategy is punctuated with infrequent, but severe, losses. The skewness of the monthly returns to the equal-weighted carry strategy over the period from January 1990 to December 2008 is negative (-1.62) and its magnitude is nearly twice as large as the skewness of excess returns on the U.S. equity market or the momentum portfolio.2 The very high realized Sharpe ratio of the carry trade and the prominence of negative skewness suggests that the excess returns earned by currency carry trade strategies may represent compensation for exposure to rare, but severe, crashes in currencies with relatively higher interest rates.3 This hypothesis parallels the claims of Barro (2006), Martin (2008) and Weitzman (2007), who argue that crash risk premia play an important role in reconciling estimates of the equity risk premium, and the findings of high volatility and crash risk premia in equity option markets documented by Coval and Shumway (2001), Pan (2002), Bakshi and Kapadia (2003), and Driessen and Maenhout (2006) among others. Of course, the estimated historical mean returns to the currency carry trade may suffer from an upward bias relative to their population counterparts, if the frequency and/or magnitude of crashes in the sample was unusually low (Rietz (1988)). This paper contributes to the literature by investigating whether crash risk premia can account for the empirically observed violations of uncovered interest parity. Under the crash risk hypothesis, excess returns to currencies with relatively higher interest rates represent compensation for exposure to the risk of rapid, large devaluations. In the ensuing analysis, I define crashes as exchange rate shocks that exceed some pre-specified threshold or a multiple of the option-implied volatility. Once exposure to crash risk is hedged, excess returns to currency carry trades are predicted to decline, or be eliminated altogether, if the exposure to currency crashes is the sole risk factor for which investors demand compensation. To investigate the crash risk hypothesis, I adopt two lenses. First, I investigate the time-series properties of the risk-neutral moments (variance, skewness and kurtosis) extracted from foreign exchange options. Since the distributions of currency returns embedded in option prices are forward-looking, they provide a convenient approach for assessing the market's ex ante perceptions regarding the likelihood of crashes, as well as, the cost of insuring against such events. Contrary to the predication of the crash risk hypothesis, I find that risk-neutral skewness does not forecast excess currency returns.4 Nonetheless, the dynamics of risk-neutral skewness exhibit very interesting behavior. In particular, I show that option-implied and realized skewness respond in opposite directions to lagged currency returns, such that the option-implied skewness forecasts 2Brunnermeier, Nagel and Pedersen (2008) argue that realized skewness is related to rapid unwinds of carry trade positions, precipitated by shocks to funding liquidity. Plantin and Shin (2008) provide a game-theoretic motivation of how strategic complementarities, which lead to crowding in carry trades, can generate currency crashes. 3Currency carry trade returns generally appear to be unrelated to risk factors proposed by traditional asset pricing models (Burnside, et. al (2006)), although Lustig and Verdelhan (2007a, 2007b) dispute these findings and argue in favor of a consumption risk factor. Brunnermeier, Gollier, and Parker (2007) argue that high returns of negatively skewed assets may be a general phenomenon. 4Bates (1996) arrives at a similar conclusion for dollar/yen and dollar/mark exchange rates during in the 1984- 1992 sample. Unlike his paper, which relies on a calibrated jump-diffusion model, I use model-free estimates
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