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Do Peso Problems Explainthe Returns to the Carry Trade? Craig Burnsidey, Martin Eichenbaumz,Isaac Kleshchelskix, and Sergio Reb elo{September 2008AbstractWe study the properties of the carry trade, a currency speculation strategy in whichan investor borrows low-interest-rate cu rrencies and lends high-interest-rate currencies.This strategy generates payo¤s which are on average large and uncorrelated with tra-ditional risk factors. We investigate whether these payo¤s re‡ect a peso problem. Weargue that, with one proviso, they do. The proviso is that the de…ning characteristicof a peso event is a high value of the stochastic discount factor, not high carry-tradelosses. We reach this conclusion by analyzing the payo¤s to the hedged carry trade,in which an investor uses currency options to protect himself from the downside riskfrom large, adverse movements in exchange rates. We …nd that the same value of thestochastic discount factor that rationalizes the average payo¤s to the carry trade alsorationalizes the equity premium.J.E.L. Classi…cation: F31Keywords: Uncovered interest parity, exchange rates, carry trade. This paper is a substantially revised version of NBER Working Paper 12489 titled “The Returns toCurrency Speculation.” We thank Ravi Jagannathan for numerous discussions and suggestions and theChicago Mercantile Exchange for providing us with the currency-options data used in this paper. Burnsideis grateful to the National Science Foundation for …nancial support (SES-0516697).yDuke University and NBER.zNorthwestern University, NBER, and Federal Reserve B ank of Chicago.xWashington University in Saint Louis.{Northwestern University, NBER, and CEPR.1 IntroductionCurrencies that are at a forward premium tend to depreciate. This ‘forward-premium puzzle’represents an egregious deviation from uncovered interest parity (UIP). This paper studiesthe properties of a widely-used currency speculation strategy that exploits this anomaly.The strategy, known as the carry trade, involves selling currencies forward that are at aforward premium and buying currencies forward that are at a forward discount. Transactioncosts aside, this strategy is equivalent to borrowing low-interest-rate currencies in order tolend high-interest-rate currencies, without hedging the associated currency risk. Consistentwith results in the literature, we …nd that the carry-trade strategy applied to portfolios ofcurrencies yields high average payo¤s, as well as Sharpe ratios that are substantially higherthan those associated with the U.S. stock market.The most natural interpretation for the high average payo¤s to the carry trade is thatthey compensate agents for bearing risk. However, we show that linear stochastic discountfactors built from conventional measures of risk, such as consumption growth, the returns tothe stock market, and the Fama-French (1993) factors, fail to explain the payo¤s to the carrytrade. This failure re‡ects the absence of a statistically signi…cant correlation b etween thepayo¤s to the carry trade and traditional risk factors. Our results are consistent with previouswork documenting that one can reject consumption-based asset-pricing models using dataon forward exchange rates.1More generally, it has been di¢ cult to use asset-pricing modelssuch as the CAPM to rationalize the risk-premium movements required to account for thetime-series properties of the forward premium.2The most natural alternative explanation for the high average payo¤s to the carry trade isthat they re‡ect the presence of a peso problem. We use the term “peso problem”as de…nedby Cochrane (2001), i.e. “a generic term for the e¤ects of small probabilities of large eventson empirical work.” This de…nition of a peso problem is consistent with agents being riskaverse and is equivalent to the “rare event”problem that has received substantial attentionin the literature. In what follows we use the term “peso event” to refer to a rare event inwhich there are either large negative payo¤s to the carry trade or unusually high values ofthe stochastic discount factor (SDF).A number of authors have recently argued that the peso problem lies at the root of1See, for example, Bekaert and Hodrick (1992) and Backus, Foresi, and Telmer (2001).2See, for example, Bekaert (1996) and De Santis and Gérard (1999).1the failure of UIP.3Not surprisingly, peso problems can in principle also explain the positiveaverage payo¤s to the carry trade. To understand the basic argument, suppose that a foreigncurrency is at a forward premium, so that a carry-trade investor sells this currency forward.Assume that a substantial appreciation of the foreign currency occurs with small probability.The investor must be compensated for the negative payo¤ to the carry trade in this state ofthe world. The degree of compensation depends on the value of the SDF in the peso stateand the magnitude of the negative payo¤. Conceptually it is useful to distinguish betweentwo extreme possibilities. The …rst possibility is that the salient feature of a peso state islarge carry trade losses. The second possibility is that the salient feature of a peso state is alarge value of the SDF. A key contribution of this paper is to assess the relative importanceof these two possibilities. We do so by estimating the size of carry-trade losses and the levelof the SDF in the peso state.Our basic approach relies on analyzing the payo¤s to a version of the carry-trade strategythat does not yield high negative payo¤s in a peso state. This strategy works as follows.When an investor sells the foreign currency forward he simultaneously buys a call optionon that currency. If the foreign currency appreciates beyond the strike price, the investorcan buy the foreign currency at the strike price and deliver the currency in ful…lment ofthe forward contract. Similarly, when an investor buys the foreign currency forward, he canhedge the downside risk by buying a put option on the foreign currency. By construction,this “hedged carry trade” does not generate large negative payo¤s in the peso state. Toestimate the average payo¤ to the hedged carry trade we use data on currency options witha one-month maturity. At this stage of the analysis we wish to be eclectic about the size ofthe negative payo¤ in the peso state. So, our hedging strategy uses at-the-money optionswhich pay o¤ in all peso states, as well as in some non-peso


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