FX forward-implied carry is a valid basis for trading strategies because it is related to divergences in monetary and financial conditions. However, nominal carry is a cheap and rough indicator: related PnLs are highly seasonal, sensitive to global equity markets, and prone to large drawdowns. Simple alternative concepts such as real carry, interest rate differentials, and volatility-adjusted carry metrics have specific benefits but broadly fail to mitigate these shortcomings. However, the consideration of a market beta premium, adjustment for inflation expectations, and the consideration of other macro-quantamental factors make huge positive differences. Not only do these modifications greatly enhance the theoretical plausibility of value generation, but they also would have almost doubled the PnL generation over the past 20 years, removed most of its equity market dependence, and greatly reduced seasonality.

The below post is based on proprietary research of Macrosynergy Ltd.

Also, it ties in with this site’s summary on implicit macro subsidies.

### Basics of FX forward-implied carry

FX forward-implied carry is the annualized return that would accrue if the spot exchange rate remained unchanged over the forward horizon of the contract. This applies to standard and non-deliverable forward contracts. As a consequence of arbitrage, this carry is for convertible currencies mostly close to the differential of interest rates for low-risk assets or deposits over the same horizon. This is called covered interest parity, a common regularity with occasional breakdowns (view post here).

Forward-implied carry is a plausible trading signal because it is related to differences in the monetary policy stances between two currency areas and thus gears positions towards areas with tighter policy. Carry is also related to differences in natural rates of real interest rates and hence favors countries with high real rates of return on capital and greater tolerance of currency strength. All other things equal, a positive carry is indicative of an implicit subsidy paid by two central banks to the market for sustaining the desired difference in financial conditions.

In practice, the popularity of the FX carry trade is bolstered by the simplicity of its calculation and by its positive performance as trading in the past, most recently during the rise of local currency markets and disinflationary policies in emerging markets in the 2000s.

However, there are many ways of calculating and adjusting FX carry, even for simple directional FX forward positions. For trading strategies, it is important to understand the conceptual differences and to learn from the lessons of the past two decades. The below empirical analysis has been conducted using forward price data for 28 developed and emerging market currencies since 2002. When currencies were temporarily not convertible or not liquid enough for trading in size those periods were blacklisted for the purpose of the analysis. The exchange rates underlying the forward contracts are the reference currency against its “dominant benchmark”, which is the currency it is naturally trading against. For most currencies, this is the U.S. dollar but for some European currencies the euro is more appropriate and for three currencies (GBP, RUB and TRY) both the euro and the dollar have been used. All data used for this analysis have been taken from the J.P. Morgan Macrosynergy Quantamental System (JPMaQS), which allows combining price data and the information status of the market on macroeconomic conditions in a simple fashion and at a daily frequency. For further information see the annex at the end of this post.

### Nominal forward-implied carry

Correlations of nominal forward-implied carry with subsequent returns at weekly, monthly, and quarterly returns have been positive and significantly so. The accuracy and balanced accuracy (average of correctly predicted positive and negative returns) for the prediction of subsequent return direction have been 55.3% and 53.5% respectively for the panel at a monthly frequency. Without considering any further context these statistics look impressive for a macro trading factor.

The simulation of a simple trading strategy based on nominal carry, using either a trimmed z-score or the sign of the carry for setting up monthly positions and scaling to 10% annual volatility, points to a long-term Sharpe ratio of 0.4-0.5 before transaction costs. However, naïve stylized PnLs also show two undesirable features of simple carry as a trading factor:

**The PnL generation is highly seasonal.**Around 80% of all value generation took place in the 2000s prior to the great financial crisis. There has been almost no positive PnL contribution since 2010.**The simple carry strategy is prone to huge episodic market drawdowns**. In the late 2000s and mid-2010s these have been related to tightening funding conditions.

These features plausibly reflect two underlying weaknesses of such a naïve carry strategy.

- First, the link between simple carry and actual subsidies or excess premia offered by the market is tenuous, i.e. too loose for the carry signal to be reliable across different economic states. Other forces such as inflation differentials, balance sheet risks, and default probabilities can at times dominate carry, without indicating real profit opportunities. This lack of precision is well known as simple carry is a “cheap” trading signal that involves neither much theoretical work nor any consideration of complementary indicators of the underlying value-generating principle.
- Second, FX carry positions often incur large directional market exposure and endogenous market risk. The latter arises from exposure to setbacks to liquidity, and risk appetite. Market beta and endogenous risk would have to be taken into consideration to estimate a minimum threshold for a currency’s carry to be attractive.

These shortcomings of simple naïve carry motivate the consideration of alternative carry concepts. Some of these alternatives are presented below. Even though not all of them would have clearly and uniformly increased the return from carry-based trading rules, they all have applications and their value depends on context.

### Real forward-implied carry

A strong case can be made for the adjustment of nominal carry by the expected inflation differential between the two currency areas. That is because the difference in monetary policy stance and real returns is better captured by real interest rates than nominal interest rates. For example, a 2% interest rate for a country in deflation is a tight policy stance, while a 4% interest rate for a currency area with 10% inflation expectations is a highly accommodative stance.

Daily estimates of inflation expectations are not readily available in a form that is comparable over a large range of currency areas. Often researchers simply approximate inflation expectations with concurrent inflation, but this can be very misleading.

For the present analysis real carry is calculated based on daily one-year ahead inflation expectations from JPMaQS, which uses real-time macro information and an expectations formula. The estimate assumes that market participants form their inflation expectations based on the recent inflation rate (adjusted for jumps and outliers) and the effective inflation target. For recent inflation, the estimate uses an average of headline and core inflation. For the 1-year forward horizon, the weight of recent inflation to the effective target is 3/4 to 1/4. The effective inflation target is the mean of the target range announced or implied by the authorities plus an adjusted for past “target misses”, which is the last 3 years’ average gap between actual inflation and the target means. The formula implies that central banks gradually lose credibility if they miss their targets on either the high or low side over a longer period of time. However, the formula would not capture a sudden loss in credibility, which may arise from a regime change.

Inflation adjustment significantly reduces carry in high-inflation countries and removes the average negative carry in deflation countries, such as Japan and Switzerland. Overall cross-country differences in real carry (FXCRR_NSA in the graph below) have been less pronounced than differences in nominal carry (FXCRY_NSA). However, both real and nominal carry show ample volatility, a large part of which is probably not related to monetary policy differences.

The correlation of real forward-implied carry with subsequent returns has been very similar to the correlation of nominal carry. Accuracy and balanced accuracy have actually been less at 53.4% and 51.8% respectively. This may partly be an artifact of the data, however. As carry and returns are based on the same data set there is typically some “artificial” correlation added by the joint effect of distortions, such as invalidly high or low forward points. Inflation differentials are a fully independent data set.

Value generation based on the simplest naïve trading rule has been similar, if slightly better, for real carry (naïve Sharpe of 0.48) when compared to nominal carry (Sharpe 0.44) over the whole sample period, but a bit more evenly spread over the whole sample period of the past 20 years.

Overall, over the past 20 years, inflation adjustment of simple carry would not have been a game-changer. However, this may partly be an artifact of the era, which was mostly characterized by disinflationary and converging monetary policies. In disinflation, inflation of carry currencies is declining and converging toward inflation of stable funding currencies. Thus, the expectations adjustment is of limited value and only exerts a subtle influence. It is likely that in times of divergence inflation expectations would make a greater difference. Moreover, the subtle impact of inflation expectations becomes more notable if one uses more advanced carry concepts, as shown below.

### Interest rate differentials

A case could be made that short-term interest rate differentials provide slightly different and sometimes more meaningful information on policy rate differentials that FX forward data. Differences between on-shore and FX-implied interest rate differentials (“cross-currency basis”) can arise from frictions in financial intermediation, obstructions to arbitrage, and sudden large imbalances in demand and supply. The cross-currency basis may itself contribute to a valid trading strategy but clouds the information value of forward-implied carry as an indicator of monetary policy differences.

Indeed, on-shore rate differentials, represented by 1-month Libor for most countries (OIS from 2021 in developed markets and some other rates in EM over the whole sample period), have been a lot more stable than forward-implied carry, both in nominal and real terms. Also, some notorious carry distortions arising from convertibility restrictions (such as in Malaysia in the early 2000s) have not affected on-shore rates differences. On the downside, on-shore rate differentials have often not been accessible for international investors due to restrictions and taxation.

Correlation and accuracy of interest rate differentials in respect to subsequent FX forward returns have been similar to those for forward-implied carry, in both nominal and real terms. The accuracy of nominal rates differentials for predicting subsequent monthly returns has been 55.1% at a monthly frequency. Balanced accuracy has been still 53.3%.

However, value generation has been less, with most of the difference arising in the 2000s. For the simplest type of carry-based strategy, the 20-year Sharpe ratio has been 0.33 based on on-shore rates differentials versus 0.44 for FX forward-implied carry. Moreover, interest rate differentials would not have mitigated the drawbacks of extreme seasonality and directionality of carry strategies over the past 20 years. The broad pattern of good and bad seasons for the PnL has been similar for both versions of the carry. There has been little diversification benefit from using both.

All this suggests that the cross-currency basis has been a useful component of the FX carry signal over the past 20 years. This is plausible, as a large basis often indicates supply-demand imbalances that offer short-term premia to the unconstrained investor.

### Vol-targeted carry

As volatility is a popular metric of the riskiness of an FX forward position the attractiveness of carry should be affected by the standard deviation of the related return. A plausible intuitive metric of vol-adjusted carry is the ratio of annualized carry to annualized standard deviation of return, which measures the carry of a vol-adjusted position. It can be interpreted as the expected Sharpe ratio under the assumption that today’s spot rate is an appropriate unbiased estimator of the future spot rate.

Specifically, we define vol-adjusted carry as 1-month FX forward carry against the dominant benchmark divided by the expected annualized standard deviation of the forward return. The volatility expectation is, in turn, based on an exponential moving average of daily returns with a half-time of 11 active trading days. For (target) return calculations forward positions are all scaled to a 10% (annualized) volatility target.

Vol-adjustment does not affect the direction of a carry signal but its size, reducing the signal for currencies with higher market risk and periods with broad market turmoil. The former is conducive to a more sensible allocation of risk across currencies and the latter contributes some built-in risk management.

Correlations and accuracy of vol-adjusted real carry with respect to subsequent vol-adjusted returns has on average been slightly weaker than for non-adjusted real carry and returns.

Since sign signals or unadjusted and volatility-adjusted carry are the same, we need to compare the performance of more proportionate signals, here represented by the zn-scores (z-scores around zero) of the respective volatility measure. This simple exercise suggests that volatility adjustment has not been a game-changer for directional carry strategies, and indeed delivered a slightly lower Sharpe ratio over the past 20 years. The same has been true for real carry measures.

The inferior performance of volatility-adjusted carry as a trading signal is not surprising. While volatility is a valid adjustment factor for the attractiveness of carry, it is plausibly also positively related to risk premia. Most investors dislike mark-to-market risk and many regulatory rules and risk management conventions put a charge on it. Hence, biasing a simple carry strategy against higher-volatility currencies may cost return. This thus not mean that volatility adjustment cannot be useful. For example for relative positions across carry currencies volatility adjustment is usually necessary in order to contain the unintended directionality of a trade.

### Hedged carry

One of the greatest drawbacks of standard carry metrics is they do not consider the “market beta” of currency positions, or any other source of risk premia for that purpose. Currencies with high sensitivity to movements in global risk asset markets should plausibly command higher risk premia and, hence, require a higher carry to be attractive propositions. Typically, popular high-carry currencies display a strong correlation with global equity and credit markets.

One way of taking this into consideration is to focus on FX forward positions that are hedged against directional market risk. For this purpose, we estimate the betas of individual FX forward positions with respect to a global directional risk basket. The basket is a vol-weighted composite of the three global asset class baskets. The global equity index future basket is a fixed-weighted composite of Standard and Poor’s 500 Composite (40%), EURO STOXX 50 (25%), Nikkei 225 Stock Average (10%) FTSE 100 (10%), and Hang Seng China Enterprises (15%). The global credit index is an inversely volatility-weighted basket of CDX and iTraxx investment-grade and high-yield indices for the U.S. and the euro area. The global currency basket focuses on small, emerging market and commodity currencies (excluding pegs) and is an inverse volatility-weighted composite of 1-month forward shorts in USD or EUR against AUD, INR, KRW, NOK, NZD, PLN, RUB, SEK, TRY, ZAR. Hedge ratios are calculated based on historical “beta”, i.e. OLS regression coefficients of past forward returns with respect to global directional risk basket returns.

A hedged carry is a carry on the main FX positions minus the carry on the global directional risk basket times the estimated hedge ratio. Across asset classes carry has been defined as the value appreciation that accrues to the owner of an asset if there is no expected or unexpected price change (view post here).

Across the 28 non-dollar and non-euro currencies hedged carry has been much lower than unhedged carry, reflecting their average positive betas and that this is a signal with much less average directional exposure to these currencies. Indeed, if one uses real carry as basis for hedging average real carry across all currencies (light blue bars below) has been close to zero. Real carry in some higher beta currencies has shifted from being a predominantly positive signal to being mainly a negative signal.

Using hedged carry as opposed to unhedged carry and taking it as a signal for hedged FX forward positions is a positive game changer for PnL generation. Correlation and accuracy are smaller than for unhedged carry, but not balanced accuracy, which is actually slightly higher. However, the naïve PnL generation has been significantly better. For the simplest type of strategy (sign-based positioning) the Sharpe ratio has been 0.51 for nominal carry (versus 0.43 unhedged) and 0.67 for real carry (versus 0.48 unhedged). Moreover, directionality and intermittent drawdowns of hedged carry strategies have been much less pronounced. In the case of real carry, the 2000s and 2010s contributed evenly to the PnL generation.

The analysis of hedged carry strategies also reveals that inflation adjustment is a lot more important than suggested by the comparison of simple carry strategies. The reason is that hedged strategies have far less of a long bias in standard carry strategies. They earn mainly non-directional premia (implicit subsidies) rather than market beta premia. And this requires a more precise estimation of premia. The more general point is that __the seemingly subtle influence of inflation becomes very noticeable if the precision of the signal becomes critical__.

### Fundamentally enhanced carry

Beyond market beta there are other plausible and conceptually independent indicators of risk premia. For example, currency areas with large external deficits, highly negative international investment positions, or poor economic performance pose – all other things equal – a risk of sudden bouts of depreciation.

There is no widely accepted standard for integrating such fundamentals with carry. However, a useful simple approach is to normalize both carry and complementary fundamental indicators, i.e. forming z-scores around neutral levels, and then calculating a weighted score. For example, we calculated an enhanced carry based on [a] a real vol-targeted or hedged carry score and [b] a composite metric of external balances. Daily information on external balances for the purpose of backtesting is available from JPMaQS. We calculated a score that reflects half external ratios and recent (1-year) changes in such balances.

The below charts compare the hedged real carry and external balances strength z-score, illustrating that they are on average uncorrelated and that fluctuations of the fundamental score are a lot more gradual.

__This simple enhancement exemplifies the beneficial effect of considering quantitative-fundamental information beyond inflation adjustments__. While correlation and accuracy ratios do not increase, naïve PnL generation improves in terms of risk-adjusted return and robustness to global market fluctuation. For the simplest sign-based strategy, the enhanced hedged carry produces a 20-year Sharpe ratio of 0.78, up from 0.67 without the enhancement. Also, robustness to market downturns has been greater and value generation has been fairly even.

It is important to note that the above fundamental enhancement just used an unweighted “kitchen sink” of external balance metrics. It has not been optimized and actually uses only one category of type of quantamental information, i.e. external balances. __Optimization will likely show a much stronger positive influence of fundamental enhancement__, albeit for the purpose of realistic backtesting sequential out-of-sample procedures would need to be applied.

## Annex: J.P. Morgan Macrosynergy Quantamental System (“JPMaQS”)

Data for the above analysis come from the J.P. Morgan Macrosynergy Quantamental System (“JPMaQS”). JPMaQS is a service that makes it easy to use quantitative-fundamental (quantamental) information for algorithmic trading. Historically, quantamental information has come in formats that make it hard to trade on it: publication timestamps have been disregarded and forgotten, history has been compromised by revisions, models are applied with hindsight, and data records suffer from errors and missing information. JPMaQS strives to clean up this mess for the benefit of all market participants.

Information on JPMaQS and its contents can be viewed here, albeit access requires password and username for J.P. Morgan Markets for now.