Lukas Menkhoff, Lucio Sarno, Maik Schmeling, and Andreas Schrimpf
Carry trades and global foreign exchange volatility
Journal of Finance | Volume 67, Issue 2 (Apr 2012), 681–718

A miraculous free lunch for international investors seems to have been on offer over three decades: carry trades. In a carry trade an investor borrows money in currencies with low interest rates and invests this money in currencies with high interest rates. Following this most simple investment rule, excess returns of up to 10% p.a. could be gained over the last 30 years, without the input of any capital.

However, there is rarely a free lunch in financial markets. This is even less likely if markets are liquid, without barriers to trade (and any restrictions on short positions) and populated by sophisticated professionals. All this applies to the world's largest financial market, i.e. foreign exchange (FX). Accordingly, it does not seem very plausible that any limits to arbitrage should have hindered the elimination of the carry-trade's profitability. Therefore, if these profits are real and permanent, their rationale may be based on their inherent riskiness.

In Menkhoff-Sarno-Schmeling-Schrimpf (JF 2012), we indeed suggest that the returns to the carry trade can be understood as a compensation for risk. This means that the high carry-trade returns occur in “good times” for the investor, but that in “bad times” the carry trade performs poorly. As this idea has been investigated in various studies, we first present our specific argument, procedure and result before relating our research to other studies and showing some of its advantageous features.

Defining five carry-trade portfolios and market conditions

The examination of the carry trade follows a standard procedure: sort available currencies, in our case a maximum of 48, into portfolios of equal size, in our case five portfolios. Thus, investing in the Portfolio 5, i.e. currencies with relatively highest interest rates, and shorting the opposite Portfolio 1 results in the carry-trade portfolio. This allocation is updated at the end of each month. Repeating this exercise over 26 years—from November 1983 to August 2009—yields an excess return of more than 5% p.a. even after accounting for significant transaction costs (Figure 1). The outcome is only slightly worse when we reduce the sample to 15 developed countries, where FX markets display higher liquidity. Interestingly, these excess returns are neither related to risk factors of the CAPM and its variants nor to simple business cycle risk (as indicated by the shaded periods of NBER recessions in Figure 1 below).

1: Cumulative Carry-Trade Returns


Carry-trade returns are related to FX volatility

We introduce another measure of risk. Risk-averse investors may want to hedge themselves against unexpected changes (innovations) in market volatility. Investors demand currencies that hedge against this risk. We test whether the sensitivity of carry-trade returns to a measure of FX volatility can rationalize these returns in a standard asset pricing framework. For global FX volatility, we use the average of volatility innovations across all considered exchange rates, a measure which remains robust to some changes in its exact calculation.

2: Excess returns of carry trades depending on global FX volatility


The usefulness of this risk measure is illustrated by Figure 2. Here all monthly results on global FX volatility are ordered into four groups, ranging from lowest volatility to highest volatility. The average excess return of the carry-trade portfolios is positive except for the high volatility regime where returns become highly negative. This shows graphically the sensitivity of carry-trade returns to volatility risk.

In order to formally examine the pricing power of this risk factor we apply a standard linear asset pricing model. The graphical result of this analysis shows in Figure 3 that the realized mean returns of the five portfolios under consideration (where Portfolio 5 minus Portfolio 1 is the carry trade) nicely fit these portfolios' returns as expected from the model. In fact, the standard model relying on global FX volatility innovations as a risk factor explains about 95% of the portfolios' returns.

3: Portfolio excess returns: expected vs. realized


Liquidity risk is less important

We test the explanatory power of the global FX volatility risk factor in relation to other potential risk-based explanations. These other explanations refer to a lack of liquidity as risk, a specific carry-trade risk (HMLFX), skewness of carry-trade returns and Peso problems of carry trade strategies, i.e. the possibility of extremely rare and heavy losses.

A conventional measure of illiquidity in FX markets is the size of the bid-ask spread (BAS) and we calculate the BAS average across currencies, analogous to the procedure for global FX volatility. Second, in order to capture the crucial funding of carry-trade strategies Brunnermeier-Nagel-Pedersen (NBER 2009) suggest the TED spread as an illiquidity measure. The TED spread calculates the interest rate difference between 3 month interbank deposits and 3 month Treasury bills. Third, we take the liquidity measure introduced by Pastor and Stambaugh (P/S) for the US stock market as a proxy for FX market liquidity. We note that these three measures of (il)liquidity are clearly positive correlated to each other and to the global FX volatility, but the absolute values of correlation coefficients are always below 30% and hence imperfect.

When we replace in the asset pricing exercises volatility innovations by innovations of the three (il)liquidity measures we get reasonable results: the values of R2 are (for the case of all countries) between 0.70 and 0.74, the factor prices have the expected sign, and are significantly different from zero for the BAS. However, these results are not quite as good as for the global FX volatility as risk factor. This impression is supported by asset pricing tests where we consider two risk factors, i.e. global FX volatility risk and (il)liquidity risk. We orthogonalize (il)liquidity risk with respect to volatility innovations, i.e. we consider only that part which is not explained volatility already. Table 1 shows the results based on risk price estimates (with standard errors in parentheses): the volatility risk factor carries a consistently negative risk price of about –0.06 to –0.08 and is highly significant, whereas the (il)liquidity risk factors are not significant when jointly included with volatility and a DOL factor (this dollar factor serves as a control variable).

1: Explaining the cross-section of five carry trades
Bid-Ask 0.21 0.01 –0.08** 0.98
(0.31) (0.02) (0.04)
TED Spread 0.21 –0.08 –0.06** 0.98
(0.25) (0.24) (0.03)
Pastor-Stambaugh (P/S) 0.18 –0.01 –0.08** 0.97
(0.29) (0.04) (0.04)
Standard errors are in parentheses. One, two, and three stars mark statistical significance at the 10%, 5%, and 1% level, respectively.
These are the averaged stage-2 coefficients from enhanced Fama-Macbeth-style regressions, explaining five carry-trade excess returns with stage-1 exposures from 1983 to 2009. The independent variables are (currency exposures to) our FX volatility measure, plus a number of control measures: DOL, a dollar factor (a control); BAS, the prevailing average bid-ask spread across all currencies; and P/S, the Pastor-Stambaugh measure. For more detail, see Table VI in our original JF paper.

Volatility captures all relevant pricing information

Next we turn to a specific carry-trade risk factor (HMLFX) introduced by Lustig-Roussanov-Verdelhan (RFS 2011). This risk factor is the return to the carry-trade portfolio itself and is able to explain the pricing of the five portfolios introduced above. When comparing this risk factor with global FX volatility, we find that our volatility factor basically captures all of the information in HMLFX relevant for pricing the cross-section of carry portfolios. Transforming our non-tradable volatility factor into a factor-mimicking portfolio for volatility innovations, we find that the resulting excess return is highly negatively correlated with HMLFX and even yields slightly lower pricing errors on the cross-section of carry portfolios. Moreover, the average return to the factor-mimicking portfolio of –1.3% p.a. is well in line with the average return to another volatility hedge portfolio: A zero-beta portfolio of long currency straddles (long position in both call and put options with the same strike price) that hedges against shocks to global volatility.

Skewness is unimportant

Skewness of returns is another risk factor suggested in the literature on carry trade (e.g., Brunnermeier-Nagel-Pedersen, NBER 2009). Even though there is some evidence in favor of skewness in our data, when assessing skewness as a systemic risk factor, results are not statistically significant. Similarly, we do not find clear evidence in favor of Peso problems as a source of carry-trade risk (Burnside-Eichenbaum-Kleshchelski-Rebelo (RFS 2011)). We also tested whether extreme volatility spikes drive our results. This was not the case, either.


In summary, our paper has proposed that a measure of innovations in global FX volatility as a systemic risk factor explaining carry-trade returns. This factor is a robust risk factor explaining the risk in carry-trade strategies well in comparisons to alternatives. Volatility risk works better than various forms of illiquidity risk or risk from skewness, and its power does not seem to be driven by neglected Peso problems. All of these explanations show that the high carry-trade returns are no free lunch, and among these explanations the risk of being exposed to innovations in global FX volatility is eminent.

Masaccio (1401–1428): Tribute Money. Italy, 1427. Did we not already have this subject covered above? Were all the renaissance artists obsessed with the theme of Tribute Money? Again, here St. Peter takes direction from Jesus, produces the tax money from the mouth of a fish, and pays it to the tax collector to whom it rightfully belongs. In modern times, taxation is still full of miracles—just different types of miracles.