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Previous article FreeCommentRobert E. CumbyRobert E. CumbyGeorgetown University and NBER Search for more articles by this author Full TextPDF Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinked InRedditEmailQR Code SectionsMoreIn this paper, Berge, Jordà, and Taylor significantly enhance our understanding of an important problem that has long occupied (plagued?) those studying international finance. About 30 years ago researchers began publishing evidence of systematic deviations from uncovered interest parity or, equivalently, of forward exchange rate bias. This raised an immediate set of questions. The first questions involved whether those results were a quirk of the sample period or the statistical tests employed. Over time it became apparent that the results were, in fact, robust. The more thorny questions involved what to make of the results. To what extent were the apparent deviations from uncovered interest parity or the corresponding apparent profits from the carry trade (which attempts to exploit deviations from uncovered interest parity by borrowing in low interest rate currencies and lending in high interest rate currencies) due to the absence or underrepresentation in the sample of large adverse events—the so-called peso problem—and to what extent were they real? And to the extent that they were real, did they reflect compensation for bearing risk or mispricing (inefficiency), or both? Those questions have proven to be perennial as well as thorny. Two surveys of this literature, Hodrick (1987) and Engel (1996), stand up extremely well to rereading today and contain excellent analytical descriptions of the accumulating evidence in the 10 or 15 years after the first evidence of a systematic forward bias emerged from the literature. Engel’s concluding paragraph (1996, 183) provides a summary of the state of knowledge at the time: “Progress in any scientific field is usually made in small increments. While Hodrick’s (1987) conclusion—‘We do not yet have a model of expected returns that fits the data’—is equally applicable today, progress has been made. What we have learned since 1987 is that many simple explanations for the forward exchange rate bias do not work. We have ruled many things out, but have not yet settled on the ‘true’ story.” Perhaps unfortunately, his conclusion could easily have been written a dozen years later.Although it remains true that we “have not yet settled on the ‘true’ story,” this paper, along with its companion, Jordà and Taylor (2009), has given us a few considerable “increments”—both methodological and substantive. The authors develop and implement utility-based methods to evaluate forecasts that I expect will be of considerable value to others. In addition, these papers advance our understanding of both the role of peso problems in the dynamics of the returns to the carry trade and the role of risk factors in accounting for average carry trade returns.One conclusion that I believe emerges from this paper and from Jordà and Taylor (2009) is that the peso problem is an important component of the dynamics of returns to the carry trade. That is not to say that the peso problem can fully account for those returns—these papers suggest that it decidedly does not.1 Indeed, the focus of both papers is on examining trading strategies that incorporate carry trade features but do not exhibit peso-problem dynamics.Brunnermeier, Nagel, and Pedersen (2008) show that relatively infrequent and sudden depreciations of high interest rate currencies are a fundamental feature of exchange rate dynamics—that is, exchange rates exhibit conditional skewness.2 Indeed, they argue that these crashes of high interest rate currencies reflect an endogenous response as traders in a market in which the carry trade is prevalent encounter funding (liquidity) constraints and need to unwind carry positions.Conditional skewness is apparent in the returns to a naive carry strategy in both this paper and in its companion, Jordà and Taylor (2009). Quite sensibly, the authors consider more sophisticated trading strategies that do not suffer from negative skewness (crash dynamics). A problem with naive carry strategies is that as the likelihood of a crash increases, interest differential rises, and carry trades appear to be more profitable. The main goal of a more sophisticated strategy is to identify signals strong enough to override the widening interest differential and lead the trader to close out the trade before a crash occurs.In both papers, the more sophisticated strategy is based on directional signals derived from exchange rate forecasts based on lagged interest differentials, lagged exchange rate changes, and lagged inflation differentials in a vector error correction model with the cointegrating vector arising due to stationary real exchange rate dynamics. In both papers, the VECM-based trading strategy eliminates the negative skewness from the strategy’s profits. In Jordà and Taylor (2009), the VECM is augmented by dividing the sample according to the distance between the real exchange rate and its long run value and the size of the interest differential, and in this paper it is augmented with yield curve factors. In both papers, the performance of the trading profits generated by the directional signals of the augmented VECMs is considerably better than those generated by the VECMs.The obvious question is, why—what is it about the VECM-based forecasts and, especially, the augmented VECM-based forecasts that leads them to overcome the influence of the interest differential and greatly reduce the likelihood of being caught in a crash? Presumably, the basic VECM results in a greater likelihood of a timely exit because crashes are more likely when real exchange rates are farther from their long run or average values. If the stationary dynamics imposed by the VECM then outweigh the influence of the interest differential on the exchange rate forecasts when real exchange rate deviations are large, the resulting directional forecasts will leave the trader more likely to close out a trade before a crash occurs. Although this is a plausible explanation, it would be nice to have it nailed down more explicitly. A seemingly more important source of the greater ability of these trades to avoid crashes is the presence of the lagged exchange rate in the regressions—referred to by the authors as a momentum factor. This is somewhat of a puzzle—including only a single lag of the exchange rate generates forecasts that notably improve trade performance.What is it about the augmented VECMs that causes them to generate even more timely directional forecasts? When Jordà and Taylor (2009) divide the sample by the size of the deviation of the real exchange rate from its long run value and the size of the interest differential, they find that when both are large, the coefficient on the interest differential changes sign, so that the interest differential reinforces (rather than offsets) the real exchange rate in generating forecasts and will lead to greater likelihood of a timely exit.3 I suspect that this result may relate to the results in Clarida, Davis, and Pedersen (2009), who find that the coefficient on the interest differential changes sign when the “Fama regression” is estimated over periods of high exchange rate volatility. If my suspicions are correct, volatility is likely to be high when both interest differentials and deviations of real exchange rates from their long run value are high.In the current paper, the Nelson and Siegel (1987) level, slope, and curvature yield curve factors—more precisely the level, slope, and curvature factors for the yield curve differentials—are added to the VECM, resulting in more timely directional forecasts. Again, insight into why including the yield curve factors leads to more timely directional forecasts might be found in Clarida et al. (2009). When they regress carry trade returns on relative yield curve level and slope factors, they find that the level factor is positively correlated with carry trade returns and the slope factor is negatively correlated with carry trade returns. By including the slope and curvature factors in the augmented VECM, the authors are able to improve the directional forecasts—when the slope (and, possibly the curvature) is unusually high, lower carry trade returns are predicted and the directional signals obtained from the augmented VECM are more likely to lead to a timely exit.That the returns from the more sophisticated trading strategies explored by the authors do not exhibit negative conditional skewness and are profitable on average suggest that peso problems do not fully account for carry trade profits. This raises the question of whether any profits arising from either the naive or sophisticated carry trade strategies reflect compensation for the risk associated with those trading strategies.The authors are to be commended for considering returns based on rolling out-of-sample directional forecasts. This choice undoubtedly affects their results, especially because it includes the recent financial crisis, a period that was extremely unfavorable for carry trades. If fact, one might suspect that their evaluation period might overweight the kind of infrequent but large “crashes” that reduce carry trade returns. Average returns from the naive carry trades are indeed negative (as well as negatively skewed) over their evaluation period when the authors consider an equally weighted basket of currencies. In contrast, the average returns to the trading strategies based on the VECM and augmented VECM estimates are positive.Are the positive returns to the equally weighted portfolios compensation for risk? At a casual level, other recent work suggests that risk premia associated with naive carry trade returns may be significant. Brunnermeier et al. (2008) and Clarida et al. (2009) find that carry trade losses tend to arise in periods of high volatility. And if Brunnermeier et al. correctly attribute these periods to ones in which trades encounter liquidity problems, carry trade losses arise just when the value of funds is greatest and when risk premia are likely to be high.The authors provide a great deal of insight by regressing returns from both naive carry trades and more sophisticated strategies on several risk factors considered in the literature. More precisely, they regress the returns to equally weighted portfolios on 11 different risk factors, one at a time. The results are a bit mixed.The risk factors appear to be important, as the intuition would suggest, in explaining the returns to naive carry trades. Eight of the 11 risk factors are significant at conventional levels when the returns from a naive carry strategy are considered. And when the naive carry strategy is augmented with the yield curve factors, five of the 11 risk factors are significant at conventional levels. The intercepts—the estimates of risk-adjusted rates of return—on the other hand, are significant at the 90% level for only one of the risk factor regressions with the naive carry trade returns (and that intercept is significantly negative). This rises to three with the carry+ returns.When the VECM-based directional forecasts are used, the authors find significant coefficients on five of the 11 risk factors. And when the returns are computed from the directional forecasts derived from the VECM with the yield curve factors included, the authors find that none of the risk factors are significant in their regressions. This leads them to be skeptical that the returns to these more sophisticated trading strategies are, in fact, compensation for risk. But in those same regressions, none of the intercepts, which are estimates of the average risk adjust return, are significant at conventional levels. When the VECM-based directional forecasts are used, the average t-ratio on the intercepts is 1.0. The average t-ratio rises to 1.5 when the VECM+-based forecasts are used. At first blush, an average t-ratio of 1.5 appears worthy of note, but these intercept estimates are far from independent—they are all essentially slightly different estimates of the sample mean of the same series.What should one make of these results? One possibility is that the relatively small sample size has led to imprecise estimates of the slopes and/or the intercepts. Another is that the authors have taken what is learned from the risk factors that help explain returns to naive carry strategies to create more sophisticated trading strategies that generate returns uncorrelated with the risk factors.How might clearer results be obtained? I have two suggestions. First, the authors might consider alternatives to equally weighting the portfolios. Perhaps a portfolio constructed in the spirit of Treynor and Black (1973), in which the portfolio’s weight for each currency depends on the alpha for that currency relative to the variance of the idiosyncratic part of the return, would be interesting. Or portfolios chosen to maximize the Sharpe ratio might be considered.4 Second, the authors might consider multiple risk factors in a regression rather than regressions with one risk factor at a time. In particular, it might be interesting to combine equity market risk (either the CAPM or Fama and French factors), a liquidity premium (the TED spread), and one or more volatility measures.Notes1. Burnside et al. (2008) use options strategies and find that the peso problem cannot explain carry trade profits in their sample, which ends in January 2008. Jurek (2009) also uses currency options data to examine carry trade returns.2. They note that these dynamics are consistent with a common expression among traders that currencies “go up the stairs and down the elevator,” at least for high interest rate currencies.3. Flood and Taylor (1996) and others have also found that the sign of the interest differential in the standard “Fama regression” changes when the sample is segmented by the size of the interest differential.4. These alternatives may not improve portfolio performance, however. DeMiguel, Garlappi, and Uppal (2009) find that estimation error can lead equity portfolios constructed with more sophisticated methods to underperform equally weighted portfolios.ReferencesBrunnermeier, Markus K., Stefan Nagel, and Lasse Pedersen. 2008. “Carry Trades and Currency Crashes.” Working Paper 14473 (November), NBER, Cambridge, MA.First citation in articleGoogle ScholarBurnside, A. 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