Many traders joining existing trends that further reinforce the

Many …nancial market analysts have recently commented on the unprecedented growthof the carry trade in the foreign exchange (F X) market. Such trades involve the bor-rowing or selling of currencies with low interest rates to fund the purchase of currencieswith high interest rates. Clearly, this is a speculation against uncovered interest rateparity (U IP ), which is a central theory of international …nance. Carry trades also ap-pear to involve excessive risk over long horizons since they ignore the fundamentals ofa currency and are also vulnerable to any sudden unanticipated changes in exchangerates.The related strategy of momentum trading appears to be a form of bandwagontrading, with traders joining existing trends that further reinforce the appreciation ofcurrencies with high interest rates. Galati and Melvin (2004, p. 67) note that thesubstantial increase in turnover in the F X market between 2001 and 2004 “seems tohave been driven by momentum trading and carry trades in a global search for yield.”Furthermore, despite its widespread use, The Economist (2007) recently noted that”the reasons for the success of the carry trade remain a bit of a mystery.”However, as changes in interest rates make a funding currency increasingly attractiveand the volume of carry trades grows, then from recent theory on the limits to specu-lation and empirical evidence to be presented in this paper, there will be an increase inthe speed of reversion to U IP and a vanishing of the forward premium anomaly. In-deed, the carry trade has been likened to “picking up nickels in front of steamrollers,”as reversions can occur suddenly, thus wiping out carry pro…ts (The Economist, 2007).From an academic perspective, the widespread use of carry and momentum tradingstrategies is especially interesting since it implies that a signi…cant percentage of F Xmarket participants are actively exploiting the forward premium anomaly. This papershows that such strategies appear to have some explanatory power in terms of the extent2and duration of the breakdown of U IP . It appears that carry and momentum tradingmay be pro…table in the short run; then as the deviations from U IP grow larger, themore likely it is to observe subsequent reversion to U IP .The econometric analysis in this paper is conducted through the use of a logisticsmooth transition regression (LST R) model with transition variables related to thecurrency trading strategies. This model has the advantage of identifying whether theforward F X market is in a regime where the anomaly is present, or whether it is ina regime where U IP tends to hold. A novel aspect of this paper is that it providesan explanation of the forward premium anomaly that is focused on trading behavior,rather than the traditional explanations based on the presence of time-dependent riskpremia or peso problems.The rest of this paper is organized as follows. The next section brie‡y reviewsthe UIP condition and the forward premium anomaly, while Section 3 describes thecurrency trading strategies and discusses their implications for nonlinear reversion toUIP. Section 4 then describes the econometric methodology, and Section 5 discussesand interprets the empirical …ndings. Section 6 provides a brief conclusion.2The forward premium anomalyThe theory of UIP is a key condition in international …nance and requires the expectedrate of return on a currency to equal the interest rate di¤erential, or:E t s t+1 = i ti t ;(1)where E t is the conditional expectations operator on a sigma …eld of all relevant infor-mation up to and including time t, s t is the logarithm of the spot exchange rate quotedas the foreign price of domestic currency, and i t and i t are the one-period risk-free3domestic and foreign interest rates, respectively. Hence the country with the higherinterest rate is expected to have a depreciating currency. Since covered interest parity(CIP ) is known to hold as a virtual identity, equation (1) can be expressed as:i t = f tE t s t+1 = i ts t ;where f t is the logarithm of the forward rate for a one period ahead transaction. Astandard test of UIP has been to estimate the regression:s t+1 =+ (f tUnder U IP , the null hypothesis is that= 0,s t ) + u t+1 :(2)= 1, and that the error term, u t+1 , isserially uncorrelated. The forward premium anomaly refers to the widespread …nding ofa negative slope coe¢ cient that is signi…cantly di¤erent from unity. Table 1 shows theresults from estimating (2) by ordinary least squares (OLS) for a variety of exchangerates when the numeraire currency is (a) the dollar, (b) the yen, and (c) the Swiss franc.The slope estimates are generally negative. The forward premium anomaly has beenconsistently found for most freely ‡oating currencies and appears robust to the choiceof numeraire currency. Froot and Thaler (1990) …nd the average estimated coe¢ cientacross 75 published studies to be -0.88.Explanations of the anomaly range from the presence of time-dependent risk premia,e.g., Hodrick (1989) and Mark and Wu (1997); to possible peso problems, segmentedmarkets, and heterogenous trading behavior. Excellent surveys of the forward premiumanomaly and suggested resolutions have been provided by Hodrick (1987) and Engel(1996). Maynard and Phillips (2001) and Baillie and Bollerslev (2000) have consideredsome econometric issues arising from the relatively uncorrelated spot returns beingregressed on the lagged forward premium, which has very persistent autocorrelation.43Carry and momentum tradingOur analysis of the carry trade is motivated by the limits to speculation hypothesisof Lyons (2001), where the existence of higher than usual pro…t opportunities fromconducting carry trades attracts speculative capital and induces agents to trade thesepro…t opportunities away. Conversely, when carry pro…ts appear low or negative, theforward bias is left unexploited and thereby persists.The most basic carry trade involves borrowing in low interest rate currencies, i.e.funding currencies, to invest in higher yielding target currencies. 1 All else equal, pro…t-maximizing investors would prefer to fund carry trades with the lowest cost currency.Moreover, the lower the interest rate on this preferred funding currency relative toalternative funding currencies, then the more attractive it is to fund carry trades withthis particular currency. As more speculative capital is directed towards conductingcarry trades with the preferred funding currency, the limits to speculation hypothesispredicts that excess returns from the strategy will be eliminated and reversion to U IPwill occur.This study focuses on three alternative funding currencies that have had the lowestinterest rates among all developed country currencies over the past 30 years: the USdollar (U SD), the Japanese yen (JP Y ), and the Swiss franc (SF ). In particular, theU SD is de…ned to be the preferred funding currency if:Y SFminfi JP; i t gti U t SD > 0;(3a)so that, ceteris paribus, when evaluating the attractiveness of the dollar as a fundingcurrency, the most important comparison is between the U SD and the next-lowest-cost1Under CIP the carry trade is equivalently implemented by selling forward currencies that are ata forward premium and buying currencies that are at a forward discount.5currency. Similarly, the yen is the preferred funding currency if:minfi U t SD ; i SFt gYi JP> 0;t(3b)and the Swiss franc is the preferred funding currency if:Yminfi U t SD ; i JPgti SF> 0:t(3c)Given the discussion above, when either (3a), (3b), or (3c) hold and the size of thedi¤erentials is large, then there should be an increased probability that U IP will be validfor exchange rates expressed with the either the U SD, JP Y , or SF as the numerairecurrency, respectively. Conversely, the breakdown of (3a), (3b), or (3c) should lead toan increased probability of observing the forward premium anomaly. 2Momentum traders operate on a positive feedback investment rule, responding topast price movements rather than expectations about future fundamentals.Indeed,carry and momentum trading strategies are intimately related. For example, Cavallo(2006, p. 2) notes that when carry trades are pro…table, “the appreciation of high-interest-rate target currencies can encourage an increasing number of investors to enterthis strategy and, ultimately, amplify the appreciation of target currencies, as well as thepersistence of exchange rate movements of the currencies involved in these strategies.”In other words, while the carry trade seeks to exploit deviations from U IP , momentumtrading (in the form of additional carry trades) can cause deviations from U IP to grow2We are grateful to an anonymous referee for pointing out a symmetric relationship for the highestyielding currencies. While one would expect to …nd evidence of symmetry if the empirical analysisincluded a complete set of traded currencies, this is beyond the scope of the present study. Our analysisfocuses on the dollar, yen, and Swiss franc numeraires since these are some of the most heavily tradedand economically important currencies. Moreover, these three currencies are readily identi…ed as beingthe lowest yielding currencies over the past 30 years and there is substantial evidence that they haveconsistently been the most popular funding currencies for carry trades (see Galati and Melvin, 2004).6larger and last longer.Several studies have explored the link between momentum trading and higher mar-ket volatility, e.g., DeLong, Shleifer, Summers, and Waldmann (1990) and Hong andStein (1999). In the latter paper, the authors show that slow di¤usion of private infor-mation across the population of ‘news watching’traders causes an initial under reactionto news, allowing momentum traders to pro…t from trend chasing as the news gets in-corporated gradually into prices. However, due to positive feedback, trend chasingultimately leads to over reaction in the long run. When subsequent groups of momen-tum traders enter the market in later stages of the ‘momentum cycle,’prices will havealready overshot their equilibrium values so that further momentum trading becomesunpro…table, since by this time, agents are fully informed and prices necessarily revertto equilibrium. As a result, momentum trading ampli…es the cycle of overshooting andreversion and causes deviations from fundamentals to persist for longer durations. 3;4In the context of currency markets, this combination of carry and momentum tradingbehavior suggests that the spot-forward relationship might be characterized by twodi¤erent regimes. In one regime, we expect to observe exchange-rate movements thatexhibit persistent deviations from U IP .In contrast, in the other regime we mightobserve subsequent reversions to U IP that are associated with changes in fundamentalsi.e., the relationships and magnitudes in (3a)-(3c) and possibly increased F X marketvolatility.An alternative motivation of the predictions above comes from a recent paper byBrunnermeier, Nagel, and Pedersen (2008), who focus on the relationship between3It is also worth noting that this pattern of continuation and reversal is consistent with the ‘spec-ulative dynamics’of Cutler, Poterba, and Summers (1990, 1991). In particular, they document thatmonthly excess returns for exchange rates exhibit positive autocorrelation (continuation) up to twoyears, but negative autocorrelations (reversal) at longer lags. The interpretation is that in the shortrun, prices may deviate from equilibrium due to positive feedback trading, but at longer horizons thereis a reversion to fundamentals.4Of course, this is not to say that increased market volatility is necessarily due to momentumtrading, or that volatility is necessarily an indicator of heightened momentum trading.7investors’ risk tolerance and funding liquidity and returns to the carry trade.Inparticular, they show that carry traders are exposed to high “crash risk”: when thereis a large, positive carry (i.e., a large and positive interest di¤erential between thetarget currency and the funding currency), carry trade returns exhibit severe conditionalnegative skewness.Thus, the downside risk to the carry trade is greatest preciselywhen the carry trade appears most attractive. In our paper, since all potential targetcurrencies necessarily exhibit positive carry against the preferred funding currency,this corresponds to our prediction that U IP is more likely to hold in a regime whereconditions (3a)-(3c) are satis…ed and the respective interest di¤erentials are large inmagnitude.In addition, Brunnermeier, Nagel, and Pedersen (2008) …nd that the carry trade losesmoney on average with increases in the V IX (the S 500 option-implied volatilityindex), which is a negative proxy for global risk tolerance. Speci…cally, an increase inthe V IX appears to be associated with a decrease in investors’appetite for risk andhence an unwinding of carry trade positions.This causes losses to the carry trade,which causes investors’funding and liquidity constraints to become more binding, whichin turn leads to further unwinding of carry trades and losses.In the context of ourpaper, this reasoning gives rise to the prediction that U IP is more likely to hold in aregime where F X market volatility is high, since exchange rate volatility might alsoplausibly be related to global risk. 55Similarly, Menkho¤, Sarno, Schmeling, and Schrimf (2009, p. 2) …nd that high spread carryportfolios have lower returns in periods of relatively high volatility in the FX market; they concludethat “carry trades perform especially poorly during times of market turmoil.”84LSTR forward premium regressionsThe forward premium anomaly generally refers to the widespread phenomenon of anegative slope coe¢ cient being obtained by OLS estimation of equation (1). However,the size of the slope coe¢ cient estimate tends to be time-varying and regime-speci…c.For example, Baillie and Bollerslev (2000) …nd slope coe¢ cient estimates as low as -17during the mid 1980s, but positive coe¢ cients during parts of the 1990s, while Baillieand Kilic (2006) …nd regime-switching behavior, with the slope coe¢ cient dependingon the sign and magnitude of the forward premium.Having postulated that the slope coe¢ cient is related non-linearly to the degreeof carry and momentum trading over time, a natural approach is to specify the U IPrelationship in terms of the logistic smooth transition regression (LST R) model:s t+1 = 1+1 (f ts t )(1G(z t ; ; c)) + 2+2 (f ts t )G(z t ; ; c) + u t+1 ;(4)where u t+1 is a zero mean, stationary I (0) disturbance term, and G( ) is a transitionfunction. In this study, G( ) is chosen to be the logistic function,G(z t ; ; c) = (1 + exp(where z t is the transition variable,z t(z tc)=z t ))1;> 0;is the standard deviation of z t ,meter, and c is a location parameter. The parameter restriction(5)is a slope para-> 0 is an identifyingrestriction. The logistic function (5), is bounded between 0 and 1, and depends onthe transition variable z t . Namely, G(z t ; ; c) ! 0 as z t !z t = c, and G(z t ; ; c) ! 1 as z t ! +1. When1 , G(z t ; ; c) = 0:5 for! 1, G(z t ; ; c) becomes a stepfunction, so that the smooth transition model becomes e¤ectively a discrete switchingmodel.For= 0, G(z t ; ; c) = 0:5 for all z t , in which case the model reduces to a9linear regression model with parameters= 0:5exponent in (5) is normalized by dividing by1 + 0:5 2 ,z t ,and= 0:51 + 0:5 2 .which allows the parameterTheto beapproximately scale free and facilitates the convergence of the nonlinear least squaresestimation algorithm.The above LST R model is related to the LST AR and other non-linear time seriesmodels introduced by Granger and Teräsvirta (1993), Teräsvirta (1998), and van Dijk,Teräsvirta, and Franses (2002). The LST R modeling approach is well suited for ourpurposes because it allows for smooth and continuous adjustment between regimes, therate of which in turn depends on the state of speci…ed transition variables.Baillieand Kilic (2006) use LST R models to explain the magnitude of the forward premiumanomaly with the levels and volatility of various macro fundamentals as transitionvariables. In this study, various transition variables related to carry and momentumtrading are considered. Speci…cally, we use the interest di¤erentials de…ned in (3a)-(3c)and the conditional volatility of exchange rates as measured by GARCH(1; 1) modelsof spot exchange rate returns.In the LST R context, these considerations give rise to two regimes of interest.When the interest di¤erentials in either (3a), (3b), or (3c) are positive and large, orwhen volatility is very high, z t will be large and positive and so G( ) will approachunity. From (4), this corresponds to an upper regime consistent with U IP given by:s t+1 =with2= 0 and22+2 (f ts t ) + u t+1 ;(7)= 1: Conversely, when (3a), (3b), or (3c) do not hold, or whenspot returns volatility is low, then G( ) will approach zero and the model will be in thelower regime, corresponding to:s t+1 =1+1 (f t10s t ) + u t+1;(7)where1is consistent with the forward premium anomaly.Note, for intermediatevalues of G( ) in between zero and unity, the regression equation is given by a weightedaverage of equations (6) and (7), as in equation (4).