In most cases we find that the covered interest rate parity condition holds. Therefore, when using forward contracts to try to derive an arbitrage profit, the evidence suggests that the difference between the spot and forward foreign exchange rates is equivalent to the interest rate differentials in the respective countries. However, there is substantial evidence which suggests that the future spot foreign exchange rate changes do not move one-for-one with interest rate differentials in most countries. This may suggest that the uncovered interest rate parity may not hold and the empirical failure of this condition has been documented in a number of studies that go back to Fama (1984).

In addition, the evidence also suggests that the forward rate may not provide an unbiased estimate of the future spot rate. In has been suggested that in many cases we observe that the spot exchange rate would usually move by an amount that is less than what would be suggested by the forward exchange rate. This condition is termed a forward bias and the apparent failure of the unbiasedness hypothesis suggests that interest rate differentials may contain information about future spot exchange rates that could be profitably exploited. Both academic analysts and foreign exchange professionals have explored models that link future exchange rate changes to interest rate differentials and other easily available information (such as past exchange rates) to predict future exchange rates.

In this section we consider the application of a particular investment strategy that seeks to exploit the forward bias. As a part of this analysis we also provide a number of possible explanations as to why this condition may exist.

# 1 The Forward Bias and Carry Trades

To exploit the forward bias, we can use the regression for the unbiasedness hypothesis to find a value for the expected return on a forward position. If the expected return is positive (negative), a relatively simple investment strategy would be to go long (short) in a particular currency. While some professional currency managers possibly follow such quantitative strategies, apparent deviations from the unbiasedness hypothesis made a much less sophisticated trade popular, namely the carry trade.

If the unbiasedness hypothesis does not hold then it would suggest that the interest rate differentials are not necessarily related to the future movements in exchange rates. This would imply that we could possibly set up trades to benefit from this phenomena. The simplest way of doing so would be to make use of a carry trade investment strategy, where we would wish to:

• Borrow in low interest rate currencies (termed funding currencies)
• Invest in high interest rate currencies (termed target currencies)

The strategy is called carry as the carry represents the interest rate differential between the high- and the low-yield currencies. If the exchange rate does not change in value, the investor simply earns the carry (i.e. the difference between the interest rates).

Since the covered interest rate parity condition suggests that the forward premium is equal to the interest rate differential between the domestic and foreign currencies $$({F_t - S_t})/{S_t} = ({i_t - i^{\star}_t})/({1 + i^{\star}_t})$$, we could earn a similar return by taking an uncovered forward position in the high interest rate currencies. Once again, the naive idea is that the investor earns the forward discount (i.e. the carry) if the future spot rate happens to equal the current spot rate as the difference between the current spot and forward rates is equivalent to the interest rate differential.

The main funding currencies would include those from the highly stable developed world that pay relatively low rates of interest (such as the USD, JPY, and CHF), while the main target currencies include those that provide higher interest rates. In most cases you would want to avoid those currencies that are highly unstable to mitigate some of the risk factors and as such potential target currencies could include the AUD and NZD.

Carry Trade Opportunity To consider a hypothetical example of where a carry trade, suppose the following conditions are given:

• Spot exchange rate for USDZAR is R14.00
• Three-month forward exchange rate for USDZAR is R14.20
• The interest rate in South Africa is higher than in the United States

Hence, the rand is trading at an annualised premium in the forward market of:

$\begin{eqnarray*} \left[ 1+\left(\frac{14.20 - 14.00}{14.00}\right) \right]^4 -1 = 5.84\% \end{eqnarray*}$

From covered interest rate parity condition, we know that this is approximately the interest rate differential between 3-month rand and dollar external currency market investments. Since the dollar is relatively more expensive in the forward market, we would buy rand forward, hoping the spot exchange rate will not change by much. Our eventual return can be decomposed as follows:

$\begin{eqnarray*} fmr_{t+1} = s_{t+1} - fp_t = s_{t+1} + (1+ 0.0584)^{\frac{1}{4}} -1 = 143 \; \text{basis points} \end{eqnarray*}$ Hence the forward discount or carry of 143 basis points is the cushion on the trade. As long as the rand does not depreciate by more than 143 basis points over the next 3 months, we will come out ahead. Of course, if the unbiasedness hypothesis holds then the rand would depreciate by exactly 143 basis points and we will break even (if there are no transaction costs).

Exploiting the forward bias with a carry trade investment strategy simply implies that you invest in currencies with high forward discounts (or high interest rates) relative to other currencies. These trades have been implemented successfully by many investors over the past decade, as a number of hedge funds and other professional investors have started to view investing in currencies as an asset class in its own right. One of the most popular strategies among such investors is the carry trade and Galati, Heath, and McGuire (2007) have noted that carry trade activity has increased significantly over the first decade of the 21st century.1

Given the size of the interest rate differentials that have existed between countries, this should not be surprising. For example, Doskov and Swinkels (2015) consider the interest rate differentials between the four highest yielding and four lowest yielding currencies over the period 1901 to 2012, which at times was greater than 12%. This result is displayed in Figure 1.

Figure 1: Source: Doskov and Swinkels (2015)

Galati, Heath, and McGuire (2007) consider the relative profitability of this trading strategy after looking at the main funding and target currencies. They note that between 2002 and 2007, official interest rates were lowest in Japan and Switzerland. For this reason, the yen and Swiss franc are among the most commonly cited funding currencies. The Australian dollar, the New Zealand dollar and sterling have appreciated steadily and have been cited as popular target currencies, although a number of other currencies are often used as well (e.g. the Brazilian real and the South African rand). From 2004 and prior to the imposition of quantitative easing, the normalisation of policy rates from historically low levels in the United States has moved the US dollar from being a funding currency to a potential target. The respective interest rates of these currencies is displayed in Figure 2.

Figure 2: Source: Galati, Heath, and McGuire (2007)

It has also been suggested that carry trade schemes may potentially affect currency values by putting upward (downward) pressure on target (funding) currencies. For example, Galati, Heath, and McGuire (2007) note that when the demand for currencies that provide high interest rates increases, this would result in an appreciation in the value of the currency. However, at some point in time investors may become nervous and they would choose to cover their positions with a forward contract. As the increase in demand for forward contracts would give rise to an expected depreciation in the value of the currency, this could affect expectations about the relative stability of the country that provides the higher interest rate. Such a change in the price of these contracts may foster conditions that give rise to a self-fulfilling prophecy, where there are concerns regarding the relative financial instability of the target country. In addition, there have also been instances when the low-interest (funding) currencies have experienced sudden and relative large appreciations in value. For example, the value of the CHF has appreciated strongly in recent times (partly due to concerns about the value of the USD). Hence, if the CHF was used as a funding currency then the investor would have realised a significant loss at the point when the carry trade unwinds.

To see how carry trades have potentially affected the value of a currency, consider the case of Australia, where Galati and Melvin (2004) note that during the period where the interest rate differential (between funding and targeting country) increased, the turnover in the foreign exchange market for these currencies increased by a particularly large amount. This is illustrated in Figure 3, for transactions that involved the US and Australian dollars. Note also that value of the Australian dollar increased over this period, as demand for the target currency increased. This would also suggest that those who invested in such a carry trade scheme would have made a significant profit.

Figure 3: Source: Galati and Melvin (2004)

Following the widespread acceptance of the carry trade, it is now viewed as one of the standard currency strategies. For example, in 2006, Deutsche Bank created a carry trade index, easily investable for all types of investors, including retail investors, at a fixed fee. Deutsche Bank’s strategy involves making a diversified investment in equally weighted long or short positions in 10 possible currencies versus the U.S. dollar. The 10 currencies are the euro and the currencies of Australia, Canada, Denmark, Great Britain, Japan, New Zealand, Norway, Sweden, and Switzerland. The strategy involves going long in the three currencies that trade at the steepest forward discounts versus the U.S. dollar (that is, currencies traded in countries where money market yields are higher than those in the United States) and going short in the three currencies that trade at the highest forward premiums versus the U.S. dollar (that is, currencies traded in countries where money market yields are lower than those in the United States). The long or short positions are determined at the beginning of each month and are closed at the end of each month.

# 2 Measures of Investment Success

To investigate the relative profitably of various trading strategies, we could make use of a number of useful measures that are discussed below.

## 2.1 Sharpe Ratios and Leverage

The relative success or failure of a trading strategy may be measured by the economic profits or returns that it generates. However, as different investment strategies may be associated with different degrees of risk, it is customary to compare the risk-adjusted returns of the respective investment strategies. The Sharpe ratio is one such measure of risk-adjusted returns, which essentially represents the excess return per unit of volatility (as measured by the standard deviation). Hence, we could make use of the expression

$\begin{eqnarray*} \text{Sharpe ratio}=\frac{\text{Average excess return}}{\text{Standard deviation of excess return}} \end{eqnarray*}$

Correcting for the volatility of returns is especially important for currency strategies, as they often employ *leverage}, which would affect the relative risk and return of an investment. For example, as a forward contract does not require any upfront investment and is just a bilateral contract with a bank, it would imply that the amount of capital that an investor could put at risk may be greater than the amount of capital that they potentially own. Since banks want ensure that their counterparties can deliver on their contracts, the investor would typically need to assure the bank that they have sufficient capital to absorb potential losses. This amount of available capital would usually be invested in relatively riskless securities, such as high-quality Treasury bills. Note that as the potential losses are going to less than the principle investment amount (in almost every case) the bank would only require that the investor would have access to sufficient capital to cover the potential loss and not the principle investment.

Since most carry trades originate from the funding currency country, we can consider the case of an American investor. For example, if there is exactly $1 invested in a Treasury bill for every dollar bought or sold in the forward foreign exchange market, the excess return on the trading strategy, that is, the return over and above the return on the Treasury bill, equals the return on capital at risk. If forward contracts pertain to more dollars than there are in a riskless account, the trading strategy uses leverage. For example, if for every$1 in the riskless account, $2 of forward contracts are made, the leverage ratio is 100%: $\begin{eqnarray*} \text{Leverage} = \frac{\text{Capital at risk - Capital owned}}{\text{Capital owned}} =\frac{\2 - \1}{\1} = 100\% \end{eqnarray*}$ Using leverage in a trading strategy scales up both its returns and its risk, which implies that we should focus on the risk-return trade-off when considering whether or not these trading strategies are profitable. ## 2.2 Empirical findings Burnside, Eichenbaum, and Rebelo (2012) consider a carry-trade strategy that combines individual-currency carry trades into an equally-weighted portfolio. They use monthly data for 20 currencies, where all portfolios are constructed such that the U.S. dollar is the domestic currency. Figure 4 displays the cumulative returns to investing in the carry and momentum strategies and in the U.S. stock market. The investment period spans March 1976 to January 2012. Two features of Figure 4 are worth noting. Firstly, the cumulative returns of the strategy is almost as high as the cumulative return to investing in stocks. Secondly, the cumulative returns to the stock market are much more volatile than those of the currency portfolios. Figure 4: Source: Burnside, Eichenbaum, and Rebelo (2012) In addition, the summary statistics in Table 5 show that the carry-trade strategy has an average annualized payoff of 4.5%, with a standard deviation of 5.2%, and a Sharpe ratio of 0.86. The Sharpe ratios of this strategy is higher than that of the stock market. The average excess return to the U.S. stock market over our sample period is 6.5%, with a standard deviation of 15.8% and a Sharpe ratio only equal to 0.41. These results are in line with those of Bekaert and Hodrick (2012) who suggest that the Sharpe ratio in the U.S. stock market is often estimated to be 0.30 to 0.40, where the average annualized excess return is between 5% and 6% and the annualized standard deviation is 15%. They also note that studies find that regression-based foreign exchange strategies produce Sharpe ratios similar and even higher than those available in stock markets, offering a reason for the increase in popularity of this trading strategy. Carry Trade Stock Market Excess return 4.5% 6.5% Standard deviation 5.2% 15.8% Sharpe ratio 0.86 0.41 Table 1: Returns, Risk and Sharpe Ratios The high Sharpe ratio of the carry-trade strategy reflects the large gains from diversifying across carry-trade strategies for individual currencies, where the benefits from this diversification reduce the volatility of payoffs by more than 50%. Since the average payoff is not affected, the Sharpe ratio of the portfolio doubles relative to the average Sharpe ratio of individual carry trades.2 Another striking feature of the Burnside, Eichenbaum, and Rebelo (2012) study is that they are able to show that the payoffs to carry trade strategy are uncorrelated with stock market returns. Hence, this currency-trading strategy would provide a natural source of diversification when combined with a broad portfolio of U.S. stocks. Although these results present quite a strong argument in favour of the use of this strategy, it is important to note that past performance need not repeat itself and that currency investing is risky. In particular, as the distribution for changes in the value of currencies exhibit fat tails, extreme outcomes (both positive and negative) are certainly possible, which would make the investment relatively risky. With this in mind it is worth noting that during the recent global financial crisis the Deutsche Bank carry trade index declined by more than 20% over a short period of time. This would imply that those currency funds with a 3-to-1 leverage ratio (which is not uncommon) would have generated a negative return of -80%. This feature is particularly evident in the study that is presented Rosenberg (2013), which looks at a shorter sample. Figure 5: Source: Rosenberg (2013) However, if one is able to stay in the market, then one could have made a significant return on investment, as is evident from the long-term return has been shown in Figure 7. Figure 6: Source: Doskov and Swinkels (2015) # 3 Risk Premiums and the Unbiased Hypothesis Earlier we noted that an investment strategy which is based on the covered interest rate parity condition has very little or no risk, while a carry trade investment strategy is associated with substantial risk. Therefore, one may suggest that positive returns that have been provided by the carry trade investment strategy (on average) may constitute payment for the difference in the risk premium of these investments. For example, let us consider the case where a bank believes that the rand is undervalued. If the forward discount on the rand relative to the dollar be 2% (which would be equivalent to the interest rate differential) and the bank believes that the rand is expected to appreciate by 3%, the risk premium would be given as $\begin{eqnarray*} rp_t = \mathbb{E}_t \big[ fmr_{t+1} \big] = \mathbb{E}_t \big[ s_{t+1} - fp_t \big] = 3\% - (- 2\%) = 5\% \end{eqnarray*}$ Note that the risk premium is the aggregate of the expected rate of appreciation and the forward discount. For this forecast to be consistent with a risk explanation, we must believe that the volatility of the rand would imply that it is so risky that it not only offers a 2% interest rate premium but also is expected to appreciate by 3%. Hence, it offers a 5% expected excess return to investors. Is this plausible (or sustainable) and could it be used to explain the potential forward bias? ## 3.1 The Variability of the Risk Premium The volatilities of forward premiums on the major currencies are about 3% (on an annualized basis). It turns out that the regression evidence implies that both the volatilities of expected exchange rate changes and risk premiums are often (much) larger than the volatilities of forward premiums. The reason for this may be derived from the regression $\begin{eqnarray*} \mathbb{E}_t \big[ s_{t+1} \big] = \phi_1 +\phi_2 fp_t \end{eqnarray*}$ where the variance of expected exchange rate changes is $\begin{eqnarray*} \mathsf{var} \Big[ \mathbb{E}_t \big[ s_{t+1} \big] \Big] = \mathsf{var} \Big[ \phi_1 +\phi_2 fp_t \Big] = \phi_2^2 \mathsf{var} \Big[ fp_t \Big] \end{eqnarray*}$ Hence, if $$\phi^2 > 1$$, which is the case for all pairs involving the yen and dollar, the expected exchange rate changes are more variable than forward premiums. To find the variance of the risk premium, recall that the risk premium is simply the expected forward market return. Therefore, $\begin{eqnarray*} rp_t = \mathbb{E}_t \big[ fmr_{t+1} \big] = \mathbb{E}_t \big[ s_{t+1} - fp_t \big] = \phi_1 +( \phi_2 - 1) fp_t \end{eqnarray*}$ Hence, $\begin{eqnarray*} \mathsf{var} \big[ rp_{t} \big] = ( \phi_2 -1)^2 \mathsf{var} \big[ fp_t \big] \end{eqnarray*}$ Consequently, as long as $$\phi_2$$ is negative, which is the case for all currencies, the implied variance of the risk premium is not only larger than the variance of the forward premium, but it is also larger than the implied variance of the expected exchange rate changes. If risk premiums are more variable than expected currency appreciation, it may be that a particular movement in the interest rate is driven by a change in the risk premium than by a change in the expected rate of appreciation of the currency. This is counter-intuitive to most economists, who think that most of the forward premium variation reflects expected currency depreciation. A number of economists have argued that survey data on forecasts of rates of appreciation from market professionals are closely related to forward premiums.3 Therefore, the survey data forecasts of rates of appreciation may be biased as well. However, there are multiple problems with survey data as they may not have the proper incentive to tell the truth. In addition, faced with a disparity of forecasts, the method that is used to represent the *market’s} forecast may be called into question. Typically, the median forecast is chosen, however, as we are interested in the marginal investor’s expectation this may not be an accurate representation. Nevertheless, basic formal models of risk, such as the CAPM, have a hard time generating risk premiums as variable as implied by the regressions.4 The recent global crisis has rekindled interest in the dynamics and economic sources of carry trade returns. In general we find that the carry trade appears to have attractive long-run returns that trickle in slowly as the carry more than compensates for the depreciation of the high-yielding currencies. However, there are periods where we experience sudden and steep movements in exchange rates, where the low-yield currencies appreciate sharply. This would expose those who are looking to benefit from a carry trade when it unwinds. When considering the distribution of the strategy’s returns we note that they are not normal, but exhibit fat tails and negative skewness. Most investors obviously dislike such return properties, and recent studies have focused on these properties of carry trade returns to provide new risk-based explanations. Unwinds of the carry trade tend to happen as a result of economic crises, and it is conceivable that people become dramatically more risk averse when they might lose their job or face large investment losses. Investors would usually refer to a *flight to quality} that occurs during such periods. Since the returns to carry trades are correlated with such macroeconomic risks, they command a positive risk premium.5 Other research focuses on the behaviour of traders. Brunnermeier, Nagel, and Pedersen (2009) stress that when a carry trade unwinds, investment managers face margin calls and may have difficulty funding their levered positions. Their clients may withdraw money as well. These forces would subsequently cause the managers to unwind their positions, selling the high-yield currencies and buying the low-yield currencies. In doing so, they exacerbate the losses on the carry trade. If the unwinding process is bad enough, the investment managers may go out of business. Knowing that this might happen causes an insufficient allocation of risky capital to the carry trade, keeping the returns higher than they should be. This explanation combines the presence of risk premiums with the idea of limits to arbitrage we encountered before. The new explanations also rely on the fact that there are infrequent disastrous returns to the carry trade. These events by themselves can provide a potential explanation of the forward bias, as we discuss in what follows. ## 3.2 Further empirical evidence and theoretical explanations ### 3.2.1 Unstable Coefficients Figure 8 presents rolling estimates of the slope coefficients from the regression model to characterize its dynamic features over time. $\begin{eqnarray*} s_{t+1} = \phi_1 + \phi_2 fp_t + \varepsilon_{t+1} \tag{3.1} \end{eqnarray*}$ The first estimate uses the first $$5$$ years of monthly data. The next estimate results from rolling the data forward by 1 month and re-estimating the regression, again with 5 years of data. Figure 7: Source: Bekaert and Hodrick (2012) In the regression analysis of the unbiasedness hypothesis, the estimates of the slope coefficient, $$\phi_2$$, are very far from 1, but Figure 8 indicates that there is dramatic instability in these coefficients across 5-year intervals. During the major appreciation of the dollar relative to the other major currencies in the early 1980s, the estimated slope coefficient decreased from -5 to -10. Clearly, this was probably because of the unexpectedly strong appreciation of the dollar and not a response to an increase in the variability of risk premiums. The large carry trade unwinds in the 2007 to 2008 period increased the coefficients towards 1. This evidence indicates a potential problem with the assumption of rational expectations underlying the statistical analysis. In the following section we explain how this might happen. ### 3.2.2 Peso Problems A phenomenon called the peso problem arises when rational investors anticipate events, typically dramatic, that do not occur during the sample or at least do not occur with the frequency that investors expect. Peso problems invalidate statistical inference conducted under the rational expectations assumption based on data drawn from the period. The peso problem got its name from considering problems that would have arisen in analysing Mexico’s experience with fixed exchange rates. During 1955 to 1975, the Mexican authorities successfully pegged the USDMXP exchange rate at MXP 12 per USD. Now suppose we assume that the market sets the forward rate in such a way that it is an unbiased predictor of the future spot rate, where we assume that the unbiasedness hypothesis holds. To determine whether a statistician would conclude that the forward rate is an unbiased or a biased predictor in this case we could perform the following calculation. Let $$S_{\text{peg}}$$ be the USDMXP exchange rate at which the Mexican authorities are currently pegging, and $$S_{\text{dev}} >S_{\text{peg}}$$ is the rate that the Mexican authorities will choose if they devalue the peso. Suppose that the market knows $$S_{\text{dev}}$$ and let $$p_t$$ be the probability that the market assigns to the event that the peso will be devalued during the next month. Then, the 1-month forward rate is an unbiased predictor of the future spot rate when it is the probability-weighted average of the two possible events: $\begin{eqnarray*} F_t = \mathbb{E}_t \big[ S_{t+1} \big] = (1 - p_t ) S_{\text{peg}} + (p_t ) S_{\text{dev}} \end{eqnarray*}$ The forward rate is the probability of no devaluation multiplied by the current exchange rate plus the probability of a devaluation multiplied by the new exchange rate. As the market’s assessment of the strength of the government’s commitment to the peg changes over time, $$p_t$$ will change, and so will the forward rate. As long as the devaluation does not materialize, the dollar will trade at a forward premium relative to the peso (in pesos per dollar, $$F_t > S_{\text{peg}}$$), and peso money market investments will carry higher interest rates than dollar investments. Suppose the Mexican authorities successfully peg the peso to the dollar between time $$T_0$$ and time $$T_2$$, when they eventually devalue the peso. Suppose also that the market knew during the time period between $$T_0$$ and $$T_2$$ that the Mexican authorities might devalue the peso at any time. If the statistician takes data from an interval of time during which no devaluation occurs, say, between $$T_0$$ and $$T_1$$, where $$T_1 < T_2$$, and compares forward rates with realized future spot rates, she will conclude that the forward rate is a biased predictor of the future spot rate. During the statistician’s sample, the realized future spot rate is always below the forward rate. Hence, the statistician rejects the null hypothesis that the forward rate is an unbiased predictor of the future spot rate. The statistician has rejected the null hypothesis, but the null hypothesis is true. How did the statistician go wrong? In other words, what led to the peso problem in this case? When we do statistical analysis on a financial time series using the rational expectations assumption, we assume that a reasonably long sample of returns is representative of the true distribution of returns that investors thought they faced when they made their investments. For the forward market example, we would assume that the ex post spot rates reflect all the possible events that investors thought might happen when they entered into their forward contracts. If there are important events that investors thought might happen but that did not happen, or if relatively rare events happened too frequently, the historical sample means, variances, and correlations in the data may tell us very little about the means, variances, and correlations of returns that investors thought they faced. The historical means, variances, and correlations may also be relatively uninformative about the moments that investors will face in the future. It is in this sense that the past performance of foreign investments may be poor indicators of the returns that investors can expect in the future. In the case of the Mexican peso, even though the forward rate seemed to be a biased predictor of the future spot rate over 20 years, the devaluation eventually occurred in 1976, thereby validating the prediction embedded in the forward rate. For the peso problem to explain the evidence regarding carry trade returns and the forward bias we discussed before, the peso events must be anticipated by market participants and, when they occur, they should wipe out the gains accrued before so that excess returns from currency speculation average out to zero. Burnside et al. (2008) claim that even the 2008 disastrous returns do not suffice to make this true. They argue that carry traders can hedge the downside risk using options without sacrificing all their returns, which is inconsistent with a strict interpretation of the peso problem. However, they can explain the carry trade returns if they assume agents become very risk averse when an unwind happens. It appears that time-varying risk premiums remain critical to explain speculative currency returns. ### 3.2.3 Carry Trades and Currency Crashes Another useful empirical insight is provided by Brunnermeier, Nagel, and Pedersen (2009) trace the evolution of a typical carry-trade cycle from the gradual buildup of speculative positions in long high-yield/short low-yield carry-trade strategies to the forced unwinding of those positions when the volatility regime shifts and liquidity conditions tighten. They suggest that in a typical carry-trade cycle, an initial widening in high-yield/low yield interest rate spreads tends to attract capital into the high-yield market. To gain that confidence, investors often rely on successful back-tests of risky strategies before they are ready to commit meaningful amounts of capital to the trade. As evidence accumulates that the uptrend in carry-trade returns appears sustainable, only then will more capital be committed to the trade. This wait-and-see approach gives rise to a gradual adjustment in portfolio allocations, which in turn gives rise to a gradual increase in the capital inflows into the target currency. Given the steady increase in inflows one would observe trend-persistence in positive excess returns that may be earned on foreign exchange carry trades. This gradual build-up then places carry-trade investors in a vulnerable position in which a sudden shock might force investors to unwind these speculative positions, thereby precipitating a crash in carry-trade returns. While it is often the case that capital tends to move slowly into carry trades, the exit from carry trade positions tends to be rapid. This would imply that there is a strong link between currency carry trades and currency crashes that are associated with the sudden unwinding of these positions. In many respects, this is not dissimilar to the herding and fire-sale behaviour that is evident on many financial markets. Consistent with models in which the erosion of capital increases insurance premia, we find that the price of protecting against a crash in the aftermath of one increases despite the fact that a subsequent crash is less likely. Furthermore, they note that currency crashes are positively correlated with increases in implied stock market volatility and indicators of funding illiquidity. This could be the outcome of a setting in which higher volatility leads to lower available speculator capital due to higher margins and capital requirements, inducing traders to cut back on their carry trade activities. Moreover, we find that a higher volatility could be used to predict higher carry returns going forward and that controlling for this effect reduces the foreign exchange return predictability of interest rates. Finally, their finding that currencies with similar interest rates comove with each other, after controlling for other effects, suggests that carry trades affect exchange rate movements. In summary, they argue that the results of their investigation are consistent with the view that macroeconomic fundamentals determine which currencies have high and low interest rates and that they also influence the value of currencies in the long-run. They also suggest that illiquidity and capital immobility could lead to short-run currency underreaction to changes in economic fundamentals and occasional currency crashes due to liquidity crises. # 4 Conclusion Understanding the rationale for widely-used currency strategies is important as they affect exchange rate movements, which has normative and positive implications of capital flows. In addition, the profitability of simple currency-trading strategies presents perhaps even more of a challenge to traditional asset-pricing theory and there are still a number of unresolved questions that need to be answered. In an interesting investigation, Burnside, Eichenbaum, and Rebelo (2012) suggest that the failure of UIP is not surprising from a theoretical perspective as it would require for agents to be risk neutral. So, a natural explanation for both the failure of UIP and the profitability of the carry trade strategy is the presence of a risk premium that compensates investors for the covariance between the payoffs to the currency strategies and their stochastic discount factor. However, they note that the profitability of these strategies is not a compensation for risk, as measured in conventional portfolio management theory. The rationale for this is that the covariance between the payoffs from this strategy and those from conventional investments is not statistically significant. In addition, the authors find that the skewness of the carry-trade payoffs is statistically insignificant, and possibly less skewed than the payoffs to the U.S. stock market. Furthermore, the dangers associated with the fat tails of the currency strategies are also much less pronounced than those associated with the stock market. This area of research has important implications for our understanding of macroeconomic and financial events and it has been suggested that we need to incorporate realistic financial frictions into modern modelling frameworks, while also allowing for heterogeneity in expectations and disagreement among agents. # 5 References Bekaert, Geert. 1996. “The Time Variation of Risk and Return in Foreign Exchange Markets: A General Equilibrium.” Review of Financial Studies 9: 427–70. ———. 2011. “Valuing Currency Management: TOM Vs. U.S. Commerce Bank.” 100310. Columbia CaseWorks. Bekaert, Geert, and Robert J. Hodrick. 2012. International Financial Management. New York: Prentice Hall. Brunnermeier, Markus K., Stefan Nagel, and Lasse H. Pedersen. 2009. “Carry Trades and Currency Crashes.” In NBER Macroeconomics Annual 2008, Volume 23, 313–47. NBER Chapters. National Bureau of Economic Research, Inc. Burnside, Craig, Martin Eichenbaum, and Sergio Rebelo. 2012. “Understanding the Profitability of Currency-Trading Strategies.” Research Summary 3. NBER Reporter 2012. Vol. Number 3. National Bureau of Economic Research. Burnside, Craig, Martin Eichenbaum, Isaac Kleshchelski, and Sergio Rebelo. 2006. “The Returns to Currency Speculation.” WP 12489. NBER. ———. 2008. “Do Peso Problems Explain the Returns to the Carry Trade?” NBER Working Paper. Chinn, Menzie, and Jeffrey A. Frankel. 2002. “Monetary Policy, Capital Flows and Financial Market Developments in the Era of Financial Globalisation: Essays in Honour of Max Fry.” In, edited by Bill Allen and David Dickinson. London: Routledge. Doskov, Nikolay, and Laurens Swinkels. 2015. “Empirical Evidence on the Currency Carry Trade, 1900-2012.” Journal of International Money and Finance 51: 370–89. Fama, Eugene F. 1984. “Forward and Spot Exchange Rates.” Journal of Monetary Economics 14 (3): 319–38. Frankel, Jeffrey A., and Kenneth Froot. 1990. “International Business Reader.” In, edited by D. Das. Oxford: Oxford University Press. Galati, Gabriele, and M. Melvin. 2004. “Why Has Fx Trading Surged? Explaining the 2004 Triennial Survey.” BIS Quarterly Review. Bank of International Settlements. Galati, Gabriele, Alexandra Heath, and Patrick McGuire. 2007. “Evidence of Carry Trade Activity.” BIS Quarterly Review 3: 27–41. Giovannini, Alberto, and Philippe Jorion. 1989. “The Time-Variation of Risk and Return in the Foreign-Exchange Stock Markets.” Journal of Finance 44 (2): 307–25. Rosenberg, Michael R. 2013. The Carry Trade: Theory, Strategy, and Risk Management. Bloomberg. Verdelhan, Adrien. 2010. “A Habit-Based Explanation of the Exchange Rate Risk Premium.” Journal of Finance 65: 123–45. 1. Bekaert (2011) suggests that assets under management in currency related funds grew from under$5 billion to over \$25 billion between 2000 and the end of 2007.

2. See, Burnside et al. (2006) for the benefits of diversification gains that may be achieved with carry trade strategies.

3. See, Frankel and Froot (1990) and Chinn and Frankel (2002).

4. See, for example, Bekaert (1996) and Giovannini and Jorion (1989).

5. See, Verdelhan (2010) for a recent example of such a model.