Carry trade: earning interest with currencies and bonds

In depth13 min read · 15 sources

A carry trade borrows money where interest rates are low and invests it where they are high. If prices stay the same, the interest rate differential remains as profit, with currencies just as with bonds, which earn coupon and roll-down when the yield curve is steep. Theory says this should not pay off on average; the data show something different, but also how violently the strategy loses in crises. Here you will learn how carry works, what the research knows about it and where its limits lie.

The idea: earning the interest rate differential

Carry is the return on an investment if its price does not change. Koijen et al. (2018) break down the expected return in exactly this way: into the carry, which is known in advance, and the expected price change. In the classic currency carry trade, an investor borrows in a funding currency with a low interest rate (for a long time, the yen or the Swiss franc, for example) and invests the money in a target currency with a high interest rate, such as the Australian dollar or emerging market currencies.

In practice, nobody takes out a yen loan for this. Professionals enter into a currency forward and buy the high-yielding currency forward. Because the forward rate already contains the interest rate differential, the buyer earns exactly this differential if the spot rate stays the same until maturity. The result is the same as above, only without a loan agreement and with little capital of your own, i.e. with leverage.

Covered and uncovered interest parity

Two equations link interest rates and exchange rates. Covered interest parity determines what the forward rate must look like so that there are no risk-free profits. If you exchange yen into dollars, invest them there and hedge the conversion back with a forward, you must not earn more than with an investment in yen (see also currency risk):

Covered interest parity is an arbitrage relationship and holds by and large, but not exactly: Du et al. (2018) find persistent, systematic deviations in major currencies that can be explained neither by credit risk nor by transaction costs. They are particularly large for forwards that sit on bank balance sheets over a quarter-end. That points to the effect of banking regulation.

Uncovered interest parity goes a step further. It claims that the high-yielding currency depreciates on average by exactly the interest rate differential. In the example, the yen would be expected to appreciate by 3.98%, so the rate would fall to the forward rate of 144.26 yen per dollar. That is exactly the break-even point of the carry trade. If it holds, the expected profit is zero, and the carry trade would be a coin toss with costs.

The forward premium puzzle

In the data, uncovered interest parity holds poorly over short periods. Hansen and Hodrick (1980) rejected, for the 1970s and the 1920s, the hypothesis that the forward rate is the market's expectation of the future spot rate. Fama (1984) showed that, besides the expected change in the exchange rate, the forward rate contains a premium that varies over time. Froot and Thaler (1990) summarised the research: the test for a bias in the forward discount rejects the null hypothesis so clearly that the power of the test is not an issue.

This finding is called the forward premium puzzle. In words: high-yielding currencies do not, on average, depreciate by the full interest rate differential. Lustig and Verdelhan (2007) show that low-yielding currencies appreciate less and high-yielding currencies depreciate less than the interest rate differential would suggest; portfolios of high-yielding currencies earned positive excess returns, portfolios of low-yielding currencies negative ones. This is exactly what the carry trade lives on.

Carry as a factor: portfolios instead of single bets

Research treats carry not as a bet on a single currency pair, but as a factor: you sort many currencies by their interest rate, buy those at the top and sell those at the bottom. Lustig et al. (2011) find a slope factor (high-yielding minus low-yielding currencies, HML-FX for short) that explains most of the differences in average excess returns. High-yielding currencies load more heavily on this factor; if you buy them and borrow low-yielding currencies, you take on global risk that is linked to the fluctuations of world stock markets. Alongside it there is the dollar factor, the average return of all foreign currencies against the dollar.

Menkhoff et al. (2012) link carry returns to global currency volatility: high-yielding currencies deliver low returns when volatility rises unexpectedly, while low-yielding currencies then deliver positive returns and thus provide a hedge. This volatility risk explains the returns better than liquidity risk does.

Koijen et al. (2018) apply the principle to equity indices, government bonds, commodities, corporate bonds and options. High carry predicts higher returns in all these asset classes, both across assets and over time. The carry strategies of different asset classes are mostly only weakly correlated. But there are phases in which they all lose at the same time, and these coincide with global recessions. Ilmanen (2011) gives a broad overview of carry alongside value, momentum and other style premia.

Crash risk: up the stairs, down the elevator

Currency traders say that high-yielding currencies take the stairs up and the elevator down. Brunnermeier et al. (2008) studied this asymmetry:

Negatively skewed means many small gains and a few large losses (see skewness and kurtosis). The authors attribute the crashes to the sudden unwinding of carry positions, which happens above all when risk appetite and funding liquidity decline. Losses then reduce future crash risk but raise its price, and currencies with similar interest rates move excessively in lockstep. Well-known examples are autumn 1998, when the yen appreciated sharply against the dollar within days, and the 2008 financial crisis.

Peso problem or risk premium?

Why does the return not disappear, even though it has been known for decades? Two explanations compete. According to the risk view, the return is a premium for losses in bad times: Lustig and Verdelhan (2007) show that high-yielding currencies depreciate on average when domestic consumption growth is weak, while low-yielding currencies then appreciate. Low-yielding currencies are therefore a hedge, and you pay for a hedge.

According to the second view, a peso problem lies behind it: a rare, very bad event occurs too seldom in the data for the averages to reflect it correctly. The name goes back to the Mexican peso, whose interest rates were long above those of the dollar, even though the exchange rate was fixed. Then came the devaluation. Burnside et al. (2011) find that carry returns are large on average and hardly linked to classic risk factors, and explain them with a peso problem of a special kind: the rare event is marked less by huge losses than by times in which money is particularly valuable.

Funding and target currencies

Which currency is the funding currency and which the target currency follows solely from interest rates and changes with monetary policy. Typical patterns:

• Funding currencies have low interest rates: for a long time the yen and the Swiss franc, and at times also the euro during the period of negative policy rates. They tend to be strong in crises: according to Campbell et al. (2010), the franc, the euro and the dollar acted as protection for equity investors. That is bad for carry traders, because they are in debt in these currencies.
• Target currencies (carry currencies) have high interest rates: commodity currencies such as the Australian and New Zealand dollars and many emerging market currencies. Their interest rates are often high because inflation, debt or political risks are higher. The interest premium is also a risk premium.
• Emerging markets offer more carry, but also capital controls, wider bid-ask spreads and sudden devaluations. The peso problem is particularly tangible here.

Bond carry: coupon and roll-down

Carry also exists without currencies. With an unchanged yield curve, a bond earns two returns: the coupon and the roll-down. With an upward-sloping curve, it slides each month into a shorter maturity with a lower yield, and its price rises. If you finance long-term bonds with short-term money, you profit from the steepness of the curve in this way. Koijen et al. (2018) count government bonds among the asset classes in which high carry predicts higher returns.

This fits the research on the yield curve. According to the pure expectations hypothesis, a steep curve should herald rising interest rates that exactly eat up the advantage of long-term bonds. Campbell and Shiller (1991), by contrast, found that when the gap between long and short rates is large, long-term yields tend to fall in the short run. This is a counterpart to the forward premium puzzle in currencies. One variant is the duration-neutral position: buying short-term bonds and selling long-term ones or vice versa, with both sides having the same duration. Then only the shape of the curve and the carry of the two maturities matter.

For advanced readers: decomposition and regression

Using logarithms, the return on a forward purchase can be broken down cleanly. If s is the log spot rate of the foreign currency in the base currency and f the log forward rate, then with covered interest parity f − s ≈ i_b − i, and:

If β is less than 1, the high-yielding currency depreciates on average by less than the interest rate differential, and part of the carry is left over. It is exactly this hypothesis, β = 1, that the tests summarised by Froot and Thaler (1990) reject. What matters in practice: the carry component is known in advance, the exchange rate component is not, and the exchange rate component determines the risk. An interest rate differential of 4 percentage points corresponds to only 0.33% a month, while exchange rates can easily move by several percent in a month. Carry is therefore mainly exchange rate risk with a small, known drift.

Many implementations therefore manage the risk and scale down positions when measured volatility rises (target volatility). Moreira and Muir (2017) show for many factors that volatility-managed portfolios achieve better Sharpe ratios, and Harvey et al. (2018) that such management reduces extreme losses. Because carry losses often go hand in hand with rising volatility (Menkhoff et al. 2012), this makes sense; but the benefit is not certain, because a crash can come out of calm markets.

Costs, hedging and implementation

• Transaction costs: in G10 currencies, bid-ask spreads are small; in emerging markets, they are considerably wider. Monthly rebalancing adds up; if you switch rarely, you save.
• Rolling: forwards usually run for one to three months and are then renewed. This also costs some spread.
• Leverage and margin calls: forwards, futures and contracts for difference require little capital, but they do require collateral. A crash can trigger margin calls and forced sales, i.e. exactly the unwinding that Brunnermeier et al. (2008) describe.
• Hedging: options against a sudden appreciation of the funding currency cost a premium and reduce the carry. A filter that exits when market volatility is high is cheaper, but it often only reacts after the first loss.
• Taxes: taxes on interest and on gains from forwards reduce the return in practice; backtests usually leave them out.

For euro investors, incidentally, carry is part of every currency hedge. A currency-hedged fund share class on dollar investments sells dollars forward; if the dollar interest rate is above the euro rate, it costs this differential. That is a carry trade in reverse. More on this in the article currency risk.

Limits and common mistakes

• “The interest rate differential is a guaranteed profit.” No. Only the interest component is certain; the exchange rate component can wipe it out several times over in a single month.
• “The backtest shows that it works.” Long calm phases are deceptive. A peso problem means precisely that the worst event may be missing from the sample (see backtest overfitting).
• “The Sharpe ratio says it all.” With negatively skewed returns, it underestimates the risk. Drawdown and the worst months belong in the picture too (see maximum drawdown).
• “A high interest rate means a strong currency.” Often the opposite is true: high interest rates compensate for higher inflation and risks.
• “Many currencies diversify away the crash risk.” In crises, high-yielding currencies move together; diversification then helps little (see correlation and diversification).

What this means for private investors

A direct carry trade with forwards or leveraged products is risky and often expensive for private investors; this article is not investment advice. Still, the knowledge is useful. It explains why a currency hedge costs or earns money, why emerging market bonds in local currency have high interest rates and high currency risks, and why long-term bonds pay more than a savings account when the curve is steep, as long as interest rates do not rise. If you want to recalculate carry rules, the Carry page also shows you the months in which things went badly wrong.

How Portfolio Lab calculates it

The Carry page tests both variants on monthly data. Currencies: at each month-end, it ranks the G10 currencies, and on request eleven emerging market currencies as well, by their interest rate differential to the base currency (US dollar or euro). By default, it buys the three highest-yielding currencies forward and sells the three lowest-yielding ones, equally weighted; alternatively, it only buys high-yielding currencies against the base. The forward rates follow from covered interest parity, and costs are 3 basis points per traded notional; on top of this there are leverage, a volatility target without look-ahead to later data and a crash filter based on the VIX or currency volatility. Bonds: for US Treasuries or German Bunds, it calculates the coupon and roll-down of a par bond for each maturity with an unchanged curve and holds the maturity with the highest expected return or a duration-neutral long/short position. The comparison series are an equally weighted currency basket, fixed maturities and the money market. The details are in the methodology.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.