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Carry Trades and Currency Crashes

2008; University of Chicago Press; Volume: 23; Issue: 1 Linguagem: Inglês

10.1086/593088

1537-2642

Markus K. Brunnermeier, Stefan Nagel, Lasse Heje Pedersen,

Banking stability, regulation, efficiency

Previous articleNext article FreeCarry Trades and Currency CrashesMarkus K. Brunnermeier, Stefan Nagel, Lasse H. Pedersen, Markus K. BrunnermeierPrinceton University, NBER, and CEPR Search for more articles by this author , Stefan NagelStanford University and NBER Search for more articles by this author , Lasse H. PedersenNew York University, NBER, and CEPR Search for more articles by this author , Princeton University, NBER, and CEPRStanford University and NBERNew York University, NBER, and CEPRPDFPDF PLUSFull Text Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreI. IntroductionThis paper studies crash risk of currencies for funding‐constrained speculators in an attempt to shed new light on the major currency puzzles. Our starting point is the currency carry trade, which consists of selling low interest rate currencies—“funding currencies”—and investing in high interest rate currencies—“investment currencies.” While the uncovered interest rate parity (UIP) hypothesizes that the carry gain due to the interest rate differential is offset by a commensurate depreciation of the investment currency, empirically the reverse holds, namely, the investment currency appreciates a little on average, albeit with a low predictive $$R^{2}$$ (see, e.g., Fama 1984). This violation of the UIP—often referred to as the “forward premium puzzle”—is precisely what makes the carry trade profitable on average. Another puzzling feature of currencies is that dramatic exchange rate movements occasionally happen without fundamental news announcements, for example, the large depreciation of the U.S. dollar against the Japanese yen on October 7 and 8, 1998, depicted in figure 1.1 This reflects the broader phenomenon that many abrupt asset price movements cannot be attributed to a fundamental news events, as documented by Cutler and Summers (1989) and Fair (2002).Fig. 1. U.S. dollar/Japanese yen exchange rate from 1996 to 2000View Large ImageDownload PowerPointWe conjecture that sudden exchange rate moves unrelated to news can be due to the unwinding of carry trades when speculators near funding constraints. This idea is consistent with our findings that (i) investment currencies are subject to crash risk, that is, positive interest rate differentials are associated with negative conditional skewness of exchange rate movements; (ii) the carry, that is, interest rate differential, is associated with positive speculator net positions in investment currencies; (iii) speculators’ positions increase crash risk; (iv) carry trade losses increase the price of crash risk but lower speculator positions and the probability of a crash; (v) an increase in global risk or risk aversion as measured by the VIX equity‐option implied volatility index coincides with reductions in speculator carry positions (unwind) and carry trade losses; (vi) a higher level of VIX predicts higher returns for investment currencies and lower returns for funding currencies, and controlling for VIX reduces the predictive coefficient for interest rate differentials, thus helping resolve the UIP puzzle; (vii) currencies with similar levels of interest rate comove with each other, controlling for other effects. (viii) More generally, the crash risk we document in this paper may discourage speculators from taking on large enough positions to enforce UIP. Crash risk may thus help explain the empirically well‐documented violation of the UIP.Our findings share several features of the “liquidity spirals” that arise in the model of Brunnermeier and Pedersen (2009). They show theoretically that securities that speculators invest in have a positive average return and a negative skewness. The positive return is a premium for providing liquidity, and the negative skewness arises from an asymmetric response to fundamental shocks: shocks that lead to speculator losses are amplified when speculators hit funding constraints and unwind their positions, further depressing prices, increasing the funding problems, volatility, and margins, and so on. Conversely, shocks that lead to speculator gains are not amplified. Further, Brunnermeier and Pedersen (2009) show that securities where speculators have long positions will move together, as will securities that they short.In the currency setting, we can envision a country suddenly increasing its interest rate and thereby attracting foreign capital—possibly worsening the current account.2 In a frictionless and risk‐neutral economy, this should lead to an immediate appreciation of the currency—associated with an inflow of capital—and a future depreciation of the exchange rate such that UIP holds. In the presence of liquidity constraints, however, capital only arrives slowly such that the exchange rate only appreciates gradually, occasionally disrupted by sudden depreciations as speculative capital is withdrawn. Mitchell, Pedersen, and Pulvino (2007) document the effect of slow‐moving capital in other markets.In contrast, a crash after a “currency bubble,” which can emerge when each investor holds on to his carry trade position too long since he does not know when others unwind their position, can be price correcting (Abreu and Brunnermeier 2003). Plantin and Shin (2007) show in a dynamic global games framework that carry trades can be destabilizing when strategic complementarities arise, which is the case if (i) speculators’ trades occur sequentially in random order and (ii) as in Brunnermeier and Pedersen (2009), trading requires capital and margins requirements become more stringent when liquidity is tight. Our empirical findings suggest an initial underreaction due to slow‐moving capital subject to liquidity risk but are also consistent with a long‐run overreaction.Our empirical study uses time‐series data on the exchange rates of eight major currencies relative to the U.S. dollar. For each of these eight currencies, we calculate realized skewness from daily data within (overlapping) quarterly time periods. We show in the cross section and in the time series that high interest rate differentials predict negative skewness, that is, carry trade returns have crash risk. Our finding is consistent with the saying among traders that “exchange rates go up by the stairs and down by the elevator.” We note that this saying must be understood conditionally: currencies do not have unconditional skewness—that is, the skewness of a randomly chosen currency pair is zero—because country A’s positive skewness is country B’s negative skewness. Hence, our finding is that the trader saying holds for investment currencies, while the reverse holds for funding currencies. Further, we find that high interest rate differentials predict positive speculator positions, consistent with speculators being long the carry trade on average. The top panel in figure 2 clearly shows a negative relationship between average currency skewness and the average interest rate differential. We see that the countries line up very closely around the downward sloping line, with an $$R^{2}$$ of 81%. For example, skewness is positive and highest for Japanese yen (a “funding currency”), which also has the most negative interest rate differential. At the other end of the skewness spectrum, one finds the the two major “investment currencies” Australian and New Zealand dollar, which have the second‐highest interest rate differentials.Fig. 2. Cross‐section of empirical skewness (top panel) and of risk reversal (bottom panel), reflecting implied (risk‐neutral) skewness, for different quarterly interest rate differentials $$i^{*}-i$$.View Large ImageDownload PowerPointFig. 2. Cross‐section of empirical skewness (top panel) and of risk reversal (bottom panel), reflecting implied (risk‐neutral) skewness, for different quarterly interest rate differentials $$i^{*}-i$$.View Large ImageDownload PowerPointNext, we study the risk premium associated with crash risk, that is, the “price” of crash risk. In particular, we consider the so‐called risk reversal, which is the implied volatility of an out‐of‐the‐money call option minus the implied volatility of an equally out‐of‐the‐money put. If the exchange rate is symmetrically distributed under the risk‐neutral measure, then the risk reversal is zero since the implied volatilities are the same. This means that the cost of a call can be offset by shorting the put. On the other hand, if the risk‐neutral distribution of the exchange rate is negatively (positively) skewed, the price of the risk reversal is negative (positive). Hence, the risk reversal measures the combined effects of expected skewness and a skewness risk premium. Said differently, it measures the cost of buying protection on a currency position to limit the possible gains and losses.In the cross section, the average implied skewness from risk reversals is also negatively related to the average rate differential (bottom panel of fig. 2), suggesting a close cross‐sectional relationship between our physical skewness measure and the risk‐neutral implied skewness. The time‐series relationship between actual skewness and price of a risk reversal contract is more surprising: a higher risk reversal predicts a lower future skewness, controlling for the interest rate differential. This finding is related to our finding that carry trade losses lead to lower speculator positions, a higher risk reversal, and a lower future skewness, though we must acknowledge the possible peso problem in estimation.3 Hence, after a crash, speculators are willing to pay more for insurance, the price of insurance increases, and the future crash risk goes down, perhaps because of the smaller speculator positions. This has parallels to the market for catastrophe insurance as documented by Froot and O’Connell (1999) and Froot (2001).Funding constraints are likely to be particularly important during financial dislocations when global risk or risk aversion increases, leading to possible redemptions of capital by speculators, losses, increased volatility, and increased margins. To measure this, we consider the implied volatility of the S&P 500, called the VIX. Note that the VIX, which is traded at the Chicago Board Options Exchange (CBOE), is not mechanically linked to exchange rates since it is derived from equity options. We show that during weeks in which the VIX increases, the carry trade tends to incur losses. We also find that risk‐reversal prices and carry trade activity (both contemporaneous and predicted future activity) decline during these times. The decrease in the price of risk reversals could be due to an increase in the price of insurance against a crash risk, or it could simply reflect an objective increase in the probability of a crash. As another proxy for funding liquidity, we also examine the effect of the TED spread, the difference between the London Interbank Offered Rate (LIBOR) interbank market interest rate and the risk‐free T‐Bill rate. An increase in the TED spread has effects similar to an increase in the VIX although with less statistical power.Further, we find that high levels of the TED and the VIX predict higher future returns to the carry trade, that is, relatively higher returns for high interest currencies and low returns to low interest currencies. Importantly, controlling for this effect reduces the predictability of interest rates, that is, this helps to explain the UIP violation. Overall, these findings are consistent with a model in which higher implied volatility or TED spread leads to tighter funding liquidity, forcing a reduction in carry trade positions, thus making the underreaction stronger and returns higher going forward.Finally, we document that currencies with similar interest rate comove, controlling for certain fundamentals and country‐pair fixed effects. This could be due to common changes in the size of the carry trade that lead to common movements in investment currencies, and common opposite movements in funding currencies.The structure of the paper is the following. Section II provides a brief summary of related papers. Section III describes the data sources and provides summary statistics. Our main results are presented in Section IV. Section V concludes.1While the Long Term Capital Management (LTCM) debacle, which occurred between the end of August and early September 1998, is not completely unrelated, it is quite distinct from the U.S. dollar/Japanese yen crash on October 7 and 8, 1998. Note also that the Fed’s surprise interest rate cut of 0.5% happened only on October 15.2If the interest rate increase is due an increase in total factor productivity the additional inflow of capital is efficient. However, if the country’s central bank increases the interest rate to slow domestic demand in order to curb inflationary pressures, additional capital inflow is counterproductive. In this case the central bank faces a dilemma—known in International Monetary Fund circles as the “Tosovský Dilemma,” named for Joseph Tosovský, former Central Bank governor of the Czech Republic, whose attempts to dampen domestic demand with higher interest rates were largely undone by larger capital inflows.3It should also be noted that the option‐implied skewness derived from risk reversals is immune to peso problems, while the realized skewness measure is not.II. Related LiteratureThere is an extensive literature in macroeconomics and finance on the forward premium puzzle, which focuses implicitly on the mean return of the carry trade. Froot and Thaler (1990), Lewis (1995), and Engel (1996) are nice survey articles. The forward premium puzzle is also related to Meese and Rogoff’s (1983) finding that exchange rates follow a “near random walk” allowing investors to take advantage of the interest differential without suffering an exchange rate depreciation. It is only a near random walk since high‐interest‐bearing currencies even tend to appreciate (albeit with a low forecast $$R^{2}$$) and in the long run exchange rates tend to converge to their purchasing power parity levels.More recently, Bacchetta and van Wincoop (2007) attribute the failure of UIP to infrequent revisions of investor portfolio decisions. Lustig and Verdelhan (2007) focus on the cross‐sectional variation between the returns of high and low interest rate currencies and make the case that the returns on currencies with high interest rates have higher loading on consumption growth risk. Burnside (2007) argues, however, that their model leaves unexplained a highly significant excess zero‐beta rate (i.e., intercept term), and Burnside et al. (2006) find that the return of the carry trade portfolio is uncorrelated to standard risk factors, attributing instead the forward premium to market frictions (bid‐ask spreads, price pressure, and time‐varying adverse selection in Burnside, Eichenbaum, and Rebelo [2007]). Jylhä, Lyytinen, and Suominen (2008) argue that inflation risk is higher in high interest rate currencies and show a positive relationship between carry trade returns and hedge fund indices.Our analysis is among the first to examine empirically the skewness of exchange rate movements conditional on the interest rate differential, that is, on the crash risk of carry trade strategies. Farhi and Gabaix (2008) develop a model in which the forward premium arises because certain countries are more exposed to rare global fundamental disaster events. Their model is calibrated to also match skewness patterns obtained from FX (foreign exchange) option prices. Instead of focusing on exogenous extreme productivity shocks, we provide evidence consistent with a theory that currency crashes are often the result of endogenous unwinding of carry trade activity caused by liquidity spirals. Bhansali (2007) argues that carry trades are essentially short volatility and documents that option‐based carry trades yield excess returns. Jurek (2007) finds that the return to the carry over the period 1999–2007 with downside protection from put options of various moneyness is positive. Further, he finds that the more protection one buys on the carry trade, the smaller is the average return and Sharpe ratio. Ranaldo and Söderlind's (2007) finding that safe‐haven currencies appreciate when stock market volatility increases can be related to our third set of findings that unwinding of carry trades is correlated with the volatility index, VIX.Gagnon and Chaboud (2007) focus primarily on the U.S. dollar to Japanese yen exchange rate and link the crashes to balance sheet data of the official sector, the Japanese banking sector and households. Galati, Heath, and McGuire (2007) point to additional data sources and net bank flows between countries that are useful for capturing carry trade activity. Klitgaard and Weir (2004) make use of weekly net position data on futures traded on the CME—as we do—and document a contemporaneous (but not predictive) relationship between weekly changes in speculators’ net positions and exchange rate moves. Finally, there are numerous papers that study crash risk and skewness in the stock market. Chen, Hong, and Stein (2001) seems to be closest to our study.44See also Barberis and Huang (2007) and Brunnermeier, Gollier, and Parker (2007), in which belief distortions create a preference for positive skewness, resulting in higher expected returns for assets and trading strategies with negatively skewed payoffs.III. Data and DefinitionsWe collect daily nominal exchange rates to the U.S. dollar (USD) and 3‐month interbank interest rates from Datastream from 1986 to 2006 for eight major developed markets: Australia (AUD), Canada (CAD), Japan (JPY), New Zealand (NZD), Norway (NOK), Switzerland (CHF), Great Britain (GBP), and the euro area (EUR), as well as the eurodollar LIBOR. For the period before the introduction of the euro on January 1, 1999, we splice the euro series together with the exchange rate of the German mark to the U.S. dollar, and we use German 3‐month interbank rates in place of euro interbank rates. For most tests below we use a quarterly horizon to measure exchange rate changes, and hence 3 months is the appropriate horizon for interest rates to apply uncovered interest parity in straightforward fashion.We denote the logarithm of the nominal exchange rate (units of foreign currency per dollar) by st=lognominal exchange rate. The logarithm of the domestic U.S. interest rate at time $$t$$ is denoted by $$i_{t}$$ and the log foreign interest rate by $$i^{*}_{t}$$. We denote the return of an investment in the foreign currency investment financed by borrowing in the domestic currency by zt+1≡i*−it−Δst+1, where $$\Delta s_{t+1}\equiv s_{t+1}-s_{t}$$ is the depreciation of the foreign currency. It is a measure of exchange rate return in excess of the prediction by uncovered interest parity since under UIP, $$z_{t}$$ should not be forecastable: Etzt+1=0. Hence, one can think of $$z$$ as the abnormal return to a carry trade strategy where the foreign currency is the investment currency and the dollar is the funding currency. In most of our analysis, and in line with most of the literature on UIP, we look at interest rate differentials and currency excess returns expressed relative to the USD. Carry traders, however, do not necessarily take positions relative to the USD. For example, to exploit the high interest rates in AUD and the low interest rates in JPY in recent years, carry traders may have taken a long position in AUD, financed by borrowing in JPY (or the synthetic equivalent of this position with futures or OTC currency forwards). Our analysis nevertheless sheds light on the profitability of such a strategy. The AUD in recent years offered higher interest rates than USD, so our regressions predict an appreciation of the AUD relative to the USD. The JPY in recent years offered lower interest rates than USD, and hence our regressions predict a depreciation of the JPY relative to the USD. Taken together, then, our regressions predict a depreciation of the JPY relative to the AUD. Thus, while we do not directly form the carry trade strategies that investors might engage in, our regressions are nevertheless informative about the conditional expected payoffs of these strategies.Much of our analysis focuses on the skewness of exchange rate movements. To that end, we measure the skewness of daily exchange rate changes ($$-\Delta s$$) within each quarter $$t$$, denoted Skewnesst.As a proxy for carry trade activity, we use the futures position data from the Commodity Futures Trading Commission (CFTC). Our variable Futurest is the net (long minus short) futures position of noncommercial traders in the foreign currency, expressed as a fraction of total open interest of all traders. Noncommercial traders are those that are classified as using futures not for hedging purposes by the CFTC. This basically means that they are investors that use futures for speculative purposes. We have data from 1986 for five countries (CAD, JPY, CHF, GBP, EUR), and, in our quarterly analysis, we use the last available CFTC positions report in each quarter. A positive futures position is economically equivalent to a currency trade in which the foreign currency is the investment currency and the dollar is the funding currency, and, indeed, few speculators implement the carry trade by actually borrowing and trading in the spot currency market. We note, however, that the position data are not perfect because of the imperfect classification of commercial and noncommercial traders and, more importantly, because much of the liquidity in the currency market is in the over‐the‐counter forward market. Nevertheless, our data are the best publicly available data, and they give a sense of the direction of trade for speculators.We use data on foreign exchange options to measure the cost of insuring against crash risk or, said differently, the risk‐neutral skewness. Specifically, we obtain data from JPMorgan Chase on quotes of 25$$\Delta $$ 1‐month risk reversals.5 A risk reversal is the difference between the implied volatility of an out‐of‐the‐money FX call option and the implied volatility of an out‐of‐the‐money FX put option. This is a measure of the cost of a long position in a call combined with a short position in a put, that is, the cost of buying insurance against foreign currency appreciation, financed by providing insurance against foreign currency depreciation.6 If the underlying distribution of exchange rate movements is symmetric, the price of the call exactly offsets the price of the put, and the value of the risk reversal is zero. Hence, if the price of the risk reversal differs from zero, investors believe that foreign exchange movements are positively or negatively skewed (in risk‐neutral terms). In other words, with constant risk premia, a more positive skewness would lead to a higher value of this risk reversal, and a more negative skewness would lead to a more negative value of the risk reversal. Of course, due to risk premia the risk‐neutral skewness is not necessarily equal to the physical skewness of exchange rate changes. Figures A1, A2, and A3 in the appendix depict the time series of exchange rates, interest rate differentials, skewness, and futures positions for the various currencies.5Taking the derivative of the option price with respect to the spot exchange rate gives the option delta. An at‐the‐money call with exercise price at the current forward exchange rate has a call delta of about a half, that is, the option price reaction is only half of the change in the underlying exchange rate. The label 25$$\Delta $$ refers to how far out of the money the options are, namely, the strike of the call is at a call delta of 0.25, and the strike of the put is at a call delta of 0.75.6Both options that form the risk reversal can be priced using the Garman and Kohlhagen (1983) formula, which is a modified Black‐Scholes formula taking into account that both currencies pay a continuous yield given by their respective interest rates. Inputting the implied volatility and other parameters into the Garman and Kohlhagen (1983) formula gives the option price in dollar terms, but the options are quoted in terms of implied volatility.IV. ResultsA. Summary Statistics and Simple Cross‐Sectional EvidenceA currency‐by‐currency perspective. We begin by highlighting some basic features of each currency separately in our summary statistics in Table 1.Table 1 Summary Statistics (Means) AUDCADJPYNZDNOKCHFGBPEUR$$\Delta s_{t}$$−.003−.002−.003−.005−.002−.004−.004−.004zt.009.004−.004.013.007−.001.009.003$$i^{*}_{t-1}-i_{t-1}$$.006.002−.007.009.005−.004.005−.001Futures positions….059−.097……−.067.052.031Skewness−.322−.143.318−.297−.019.144−.094.131Risk reversals−.426−.0991.059−.467.350.409.009.329Note: Quarterly data, 1986–2006 (1998–2006 for risk reversals). $$\Delta s_{t}$$ is the quarterly change in the foreign exchange rate (units of foreign currency per U.S. dollar), zt is the return from investing in a long position in the foreign currency financed by borrowing in the domestic currency. Futures positions refers to the net long position in foreign currency futures of noncommercial traders. Risk reversals are the implied volatility difference between 1‐month foreign currency call and put options, as described in the text. View Table Image Table 1 shows that there is a positive cross‐sectional correlation between the average interest rate differential $$i^{*}_{t-1}-i_{t-1}$$ and the average excess return $$z_{t}$$, which points to the violations of UIP in the data. For example, the currency with the most negative average excess return (JPY) of −0.004 also had the most negative average interest rate differential relative to the U.S. dollar of −0.007. The currency with the highest excess return (NZD) of 0.013 also had the highest average interest rate differential of 0.009.It is also apparent from Table 1 and from figure 2 that there is a clear negative cross‐sectional correlation between skewness and the average interest rate differential. This negative correlation between interest rate differentials and skewness shows that carry trades are exposed to negative skewness. An investor taking a carry trade investing in AUD financed by borrowing in USD during our sample period would have earned both the average interest rate differential of 0.006 plus the excess FX return on AUD relative to USD of 0.003 but would have been subject to the negative skewness of −0.322, on average, of the daily return on the carry trade. An investor engaging in carry trades borrowing in JPY and investing in USD would have earned the interest rate differential of 0.007 minus the loss from the excess return of JPY relative to USD of 0.003, but would have been subject to negative skewness of −0.318.The summary statistics also show that speculators are on average carry traders since there is a clear positive correlation between the average interest rate differential and the average net futures position of speculators in the respective currency. For example, speculators have large short positions in JPY, which has the most negative average interest rate differential.Finally, the last row of table 1 shows the average value of risk reversals, for the subset of our sample from 1998 to 2006 for which we have risk‐reversal data. Recall that the risk reversals provide a measure of the risk‐neutral skewness in currency changes. The table and figure 2, bottom panel, show that countries with low interest rates tend to have positive risk‐neutral skewness, while countries with high interest rates tend to have negative risk‐neutral skewness.A portfolio perspective. We also consider the cross‐sectional relationship between carry and returns by looking at the performance of long‐short portfolios where we vary the number of currencies included in the portfolio as reported in Table 2. Specifically, our carry portfolio has long positions in the $$k$$ currencies with the highest interest rates in the beginning of each week (quarter) and short positions in the $$k$$ currencies with the lowest interest rates, where each currency is weighted equally and we consider $$k=1,2,3$$.Table 2 Summary Statistics for Carry Trade Portfolio Returns 1 Long, 1 Short2 Long, 2 Short3 Long, 3 ShortWeeklyQuarterlyWeeklyQuarterlyWeeklyQuarterlyAverage return.002.022.001.016.001.018Standard deviation.017.068.013.051.011.045Skewness−.717−.700−.537−.748−.695−.977Kurtosis2.851.6741.534.6612.5971.968Annualized Sharpe ratio.704.654.592.638.747.784Note: Quarterly data, 1986–2006, weekly data 1992–2006 for an equally weighted carry trade portfolio that is long in the $$k=1,2,3$$ currencies with the highest interest rates in the beginning of each week/quarter and short in the k currencies with the lowest interest rates. View Table Image We see that the carry trade portfolios have large Sharpe ratios, negative skewness, and positive excess kurtosis. This means that the carry trade is profitable on average but has crash risk and fat tails.We find no evidence that the negative skewness or excess kurtosis get diversified away as more currencies are added to the carry trade portfolio, at least with the simple equal‐weighted portfolio strategies that we are considering here. The fact that skewness cannot easily be diversified away suggests that currency crashes are correlated across different countries, depending on interest rate differentials. This correlation could be driven by exposure to common (crash‐) risk factors, and later we provide evidence that liquidity risk is one such driving risk factor.To get a sense of the magnitudes, we can compare the skewness of the carry trade por