A Primer on FX Carry Trading

Carry Trades and the Interest Parity Condition

The uncovered interest rate parity (UIP) condition states that, under risk neutrality, the gain from borrowing a low interest rate currency and investing in a higher interest rate one will, in equilibrium, be matched by an equally large expected loss by a depreciation of the high interest rate currency. This condition, combined with the hypothesis of rational expectations, implies that the forward rate should be an unbiased estimator of the corresponding future spot rate. Expected profits on the carry trade would be zero if the forward premium were an unbiased predictor of the rate of appreciation of the foreign currency. Thus, the finding of non-zero profits on the carry trade can be related to the classic interpretation of sampling variability of the estimator with respect to its expectation. Absence of covered interest arbitrage opportunities implies that high interest rate currencies trade at forward discounts relative to low interest rate currencies, and low interest rate currencies trade at forward premiums.

where:

• i_d is the interest rate in the domestic currency or the base currency (i.e. denominator)
• i_f is the interest rate in the foreign currency or the quoted currency (i.e. numerator)

Thus, the carry trade can also be implemented in forward foreign exchange markets by going long (short) in currencies trading at forward discounts (premiums). Such forward market trades are profitable as long as the currency trading at the forward discount depreciates less than the forward discount itself. Via the covered interest rate parity condition (CIP), this implies that the forward rate F_t at time t for delivery in period t+1 is the rational forecast for the corresponding spot rate S_t+1. Following Fama (1984) the CIP condition is usually tested by regressing FX returns, S_t+1 – S_t, on the forward premium, F_t – S_t (the so-called Fama regression) and checking if α=0 and β=1 in the linear relationship:

However, in a multitude of studies Fama’s β is found to be significantly smaller than 1 and usually negative. Given that the empirical evidence suggests that the β coefficient in the Fama regression typically is significantly smaller than zero, an investment that borrows in low interest rate currencies and invests in high interest rate ones (carry trade) should on average generate positive returns. One of the reasons of this positive returns is due to the currency skewness, an important risk factor that captures that carry trade is subject to reversal risk, carry trade activity drives exchange rate dynamics until market liquidity dries up and a currency crash erupts. In other words, carry trade activity generates the risk of a currency crash that justifies the positive returns it gains on average as we could see in recent times in Argentina and Venezuela.

EM Carry Trading Strategy

In this section, we will propose a naive carry trading strategy. We collected historical data for 26 Emerging Market countries, listed in Table 1 with some basic statistics. Since carry trading profits arise when interest rate differentials are greater than the EM currency depreciation, we need to know two essential variables for each country: the spot exchange rate against the US dollar and the short-term interest rate. Since no LIBOR or equivalent money market rate exists for EM countries, we derived the 1-month foreign interest rate using points of 1-month forward contracts on exchange rate (USD to foreign currency). There could be other ways to compute the foreign short-term interest rate. For example, one could look for the EM country’s overnight interbank rate or the yield of short-term sovereign bonds. We choose our approach since forward contracts (or equivalents, such as non-deliverable forwards) are available on almost any EM currency and we regard it as the most consistent approach. On the other hand, using short-term sovereign bonds yields poses the problem that very few EM countries have 1-month bonds and their shortest bonds have a maturity ranging from 3 months to 3 years, making it difficult to compare data. We included the EM country in our carry portfolio starting from the first date in which both forward and spot exchange rates data were available.

For the purpose of our naive carry trading strategy, we will act as American investors, thus computing our P&L in US dollars. As American investors, we will invest in those EM countries whose 1-month interest rate is greater than our reference rate, i.e. the US dollar 1-month LIBOR. In other words, we will invest in all those EM countries providing us with a positive interest rate differential. For the sake of diversification, we will build an equally-weighted portfolio, assigning the weight 1/N to every EM investment. Since carry trading consists of borrowing in a low-yield currency and investing in a high-yield currency, we will borrow US dollars to fund our trade. For the sake of simplicity, we will pay the US dollar 1-month LIBOR. As one can understand, we are building a zero-investment portfolio. Each month we compute our return by translating into US dollars our holdings denominated in foreign currency and pay the US dollar 1-month LIBOR. Moreover, each month we rebalance our portfolio, determining the EM countries in which to invest depending on their interest rate differential against the US dollar 1-month LIBOR. The table below shows basic risk-return statistics of our naïve carry trading strategy implemented from January 2001 to September 2018. Data are annualized.

Conclusions

As we can see, our strategy produces a statistically significant positive mean return. This is a standard finding of a “forward discount bias”. This means that in the short run the exchange rate losses will not fully offset the interest differential gains of the naive carry strategy. Someone may argue that this evidence denies the uncovered interest parity. The UIP states that because of no-arbitrage, the expected return generated by a domestic asset will be equal to the expected return of a foreign asset after adjusting for the change in foreign currency exchange rates. As we can see from the definition of UIP, statistically significant positive mean return of a naïve carry trading strategy does not deny UIP. Indeed, UIP is an ex-ante, not an ex-post, condition: it relies on expected returns and not realized returns. The “forward discount bias” refers to the fact that, in the short-run, exchange rate expectations seem to be systematically wrong. Though this may be true for the short-run, for longer timespans it is difficult to reject ex-post UIP, suggesting that interest arbitrage holds in the end, and that the possible profit opportunities are a matter of timing.

Another fact worth mentioning is that our strategy is a zero-investment one, i.e. we fully fund our position by raising US dollar-denominated debt. From this perspective, it is difficult to explain the statistically significant positive mean return. Two possible explanations arise. The former is that we have just discovered a profitable quasi-arbitrage, though this is very hard to believe. The latter is that our positive return is actually a risk premium. The risk premium could be a compensation for the large negative skew we are taking on. The negative skewness is represented by a longer left tail showing that our naïve carry strategy is subject to a risk of pronounced periodic crashes. In other words, our strategy shows extremely negative returns when EM currencies tend to suddenly crash. This issue is commonly referred to as “peso problem”. There is plenty of evidence of peso problems: just look at the current sudden selloff of Argentinean Peso and Turkish Lira. By looking at Table 1, we get further evidence of the “peso problem” we are exposed to. The Maximum monthly drawdown column shows the steepest foreign exchange rate depreciation of the EM currency against the USD. As we can see, EM currencies experience tremendous selloffs (remember that these are monthly data!). The maximum drawdown statistics could have been even harsher for Thailand, Malaysia, South Korea and Indonesia because our data do not cover the Asian Crisis of 1997 and 1998, when a currency crisis hit hard these Asian countries forcing them to leave the peg (except for Malaysia, which, however, implemented capital restrictions). The only one exception is Saudi Arabia that has successfully maintained the peg against the USD.

The thesis according to which the positive mean return is a risk premium is strengthened by the fact that the most recent asset pricing models use multiple systemic factors, including skewness. Antti Ilmanen in his book “Expected Returns: an Investors’ Guide to Harvesting Market Rewards” classifies FX carry trading in the family of strategies that sell lottery tickets. These lottery tickets have a negatively skewed return distribution and show large negative payoffs during financial crisis. The family of strategies that sell lottery tickets includes, beyond FX carry trading, short-volatility and short-correlation strategies (FX carry trading is de facto selling volatility of the EM currency) and credit carry (short government bonds to long corporate bonds).