The “carry trade” is the most popular trading strategy in currency markets. Traders borrow in currencies with low interest rates (negative forward premium) and invest in currencies with high interest rates (positive forward premium), profiting from the margin. Yet according to the uncovered interest parity this strategy should not work. If investors are both rational and risk-neutral, then exchange-rate changes will eliminate any gain arising from the differential in interest rates across countries. It is well documented, however, that exchange-rate changes do not compensate for the interest-rate differential. If anything, the opposite holds true empirically – high-interest-rate currencies tend to appreciate while low-interest-rate currencies tend to depreciate. As a consequence, carry trades form a profitable investment strategy, violate the uncovered interest parity and give rise to the “forward premium puzzle” (Fama 1984).

Considering the very liquid foreign-exchange markets, the dismantling of barriers to capital flows between countries, and the existence of international currency speculation during this period, it is difficult to understand why carry trades have been profitable for such a long time. A simple and theoretically convincing solution for this puzzle is the consideration of time-varying risk premia. If investments in currencies with high interest rates deliver low returns during “bad times”, then carry trade profits are merely a compensation for higher risk-exposure by investors. However, the empirical literature has serious problems to convincingly identify risk factors that drive these premia until today.

# What is the risk in carry trades?

In a recent paper we suggest a resolution (Menkhoff et al. 2011). We start by sorting currencies into portfolios according to their forward premium (or, equivalently, their relative interest-rate differential versus US money market interest rates) at the end of each month, as first proposed in academic research by Lustig and Verdelhan (2007). We form five such portfolios. Investing in the highest relative interest-rate quintile, i.e. portfolio 5, and shorting the lowest relative interest-rate quintile, i.e. portfolio 1, therefore results in a carry-trade portfolio. This carry trade leads to large and significant average excess returns of more than 5% even after accounting for transaction costs and the recent market turmoil. These returns cannot be explained by standard measures of risk (e.g. Burnside et al. 2011) and seem to offer a free lunch to investors.

We argue that these high returns to currency carry trades can indeed be understood as a compensation for risk. Finance theory predicts that investors are concerned about variables affecting the evolution of the investment opportunities and wish to hedge against unexpected changes (innovations) in market volatility, leading risk-averse agents to demand currencies that can hedge against this risk. We test whether the sensitivity of excess returns to global foreign-exchange volatility risk can rationalise the returns to currency portfolios in a standard asset-pricing framework. We find that high-interest-rate currencies are negatively related to innovations in global foreign-exchange volatility and thus deliver low returns in times of unexpectedly high volatility, when low interest rate currencies provide a hedge by yielding positive returns.

To prove this point, we carry out the empirical analysis using data for spot exchange rates and 1-month forward exchange rates versus the dollar over the sample period from November 1983 to August 2009, obtained from BBI and Reuters (via Datastream). The total sample consists of 48 countries, but we also study a smaller sub-sample consisting of only 15 developed countries with a longer data history.

From these data, we construct carry-trade portfolios and examine their excess returns. We also construct a proxy for global foreign-exchange volatility, which is simply the cross-sectional standard deviation of volatility across all currencies in the portfolio, calculated month by month from daily data. Figure 1 shows cumulative returns for the carry-trade portfolio for all countries and for the smaller sample of developed countries. Shaded areas correspond to NBER-defined recessions. Interestingly, carry trades among developed countries were more profitable in the 80s and 90s; only in the last part of the sample did the inclusion of emerging markets' currencies improve returns to the carry trade. Also, the two recessions in the early 90s and 2000s did not have any significant influence on returns. It is only in the last recession -- that also saw a massive financial crisis -- that carry-trade returns show some sensitivity to macroeconomic conditions. By and large, most of the major spikes in carry-trade returns (e.g. in 1986, 1992, 1997/1998, 2006) seem rather unrelated to the US business cycle. The graph also shows our proxy for global foreign-exchange volatility and its innovations, which appears to pick up obvious times of turmoil, including the recent financial crisis.

**Figure 1.** Cumulative carry trade returns

Figure 2 provides a graphical analysis to illustrate our point (we carry out extensive tests to establish our results in our paper). We visualise the relationship between global foreign-exchange volatility risk and currency excess returns. To do so, we divide the sample into four sub-samples depending on the value of global foreign-exchange volatility innovations. The first sub-sample contains the 25% months with the lowest realisations of foreign-exchange volatility risk and the fourth sub-sample contains the 25% months with the highest realisations. We then calculate average excess returns for these sub-samples for the return difference between portfolio 5 and 1. Results are shown in Figure 2 for the sample of all countries and for the smaller sample of 15 developed countries.

**Figure 2.** Distribution of global foreign-exchange volatility

**All Countries**

**Developed countries**

Bars show the annualised mean returns of the carry-trade portfolio. As can be seen from the figure, high-interest-rate currencies clearly yield higher excess returns when volatility risk is low and vice versa. Average excess returns for the long-short portfolios decrease monotonically when moving from the low to the high-volatility states for the sample of developed countries, and almost monotonically for the full sample of countries. While this analysis is intentionally simple, it intuitively demonstrates a clear relationship between global foreign-exchange volatility innovations and returns to carry-trade portfolios.

# How well does this risk explain the returns to carry trades?

The answer is: surprisingly well. In fact, we can explain over 95% of the variation in the cross-section of our sorted portfolios. This point can be seen visually in Figure 3, which shows the mean excess returns from the five portfolios (the actual data) and the corresponding mean excess returns predicted by the asset pricing model based on our global volatility risk variable. Essentially, we obtain almost a 45 degree line, indicating that the volatility-risk proxy captures almost fully the variation in portfolio returns.

**Figure 3.** Realised mean excess returns

**All countries**

**Developed countries**

# Conclusion

We propose a measure of global foreign-exchange volatility innovations as a systematic risk factor that explains the returns from carry trades. There is a significantly negative co-movement of high-interest-rate currencies (carry-trade-investment currencies) with global foreign-exchange volatility innovations, whereas low-interest-rate currencies (carry-trade-funding currencies) provide a hedge against unexpected volatility changes. Further analysis shows that liquidity risk also matters for the cross-section of currency returns, albeit to a lesser degree. These results also extend to other cross-sections of asset returns such as individual currency returns, equity momentum, and corporate bonds.

# References

Burnside, C, M Eichenbaum, I Kleshchelski, and S Rebelo (2011), “Do Peso Problems Explain the Returns to the Carry Trade? [1]”, *Review of Financial Studies*, forthcoming.

Fama, EF (1984), “Forward and Spot Exchange Rates” , *Journal of Monetary Economics*, 14:319-338.

Lustig, H and A Verdelhan (2007), “The Cross Section of Foreign Currency Risk Premia and Consumption Growth Risk” , *American Economic Review*, 97:89-117.

Menhoff, L, L Sarno, M Schmeling, and A Schrimpf (2011), “Carry Trades and Global Foreign Exchange Volatility [2]”, *Journal of Finance*, forthcoming. CEPR Discussion Paper 8291.