FX forward-implied carry is a valid basis for investment strategies because it is related to policy subsidies and risk premia. However, it also contains misdirection such as rational expectations of currency depreciation. To increase the signal-noise ratio FX carry should – at the very least – be adjusted for expected inflation differentials and external deficits. Even with such plausible adjustments FX carry is a hazardous signal for directional trades because it favours positions with correlated risks and great sensitivity to global equity markets. By contrast, relative adjusted carry has been a plausible and successful basis for setting up relative normalized carry trades across similar currencies. It has historically produced respectable Sharpe ratios and low directional risk correlation. Such strategies seem to generate alpha and exploit alternative risk premia alike.

This post is based on proprietary research of Macrosynergy LLP and SRSV Ltd.

### The very basics

For the present purpose the term “FX carry” refers to the annualized carry implied by either the 1-month FX forward or, if more liquid, the 1-month non-deliverable forward. Carry thus is the annualized difference between spot and forward price and is the theoretical return that is earned if the spot exchange rate remains unchanged over the forward period.

Our empirical analysis of FX carry is based on a panel of 9 developed market currencies and 20 eligible emerging market currencies from 1999 to 2018. To be eligible EM currencies had to be largely convertible, floating and sufficiently liquid, at least for a part of the sample period.

- The developed markets group includes the Australian dollar (AUD), Canadian dollar (CAD), Swiss franc (CHF), euro (EUR), British pound (GBP), Japanese yen (JPY), Norwegian krone (NOK), New Zealand dollar (NZD) and the Swedish krona (SEK).
- The emerging markets group includes the Brazilian real (BRL), Chilean peso (CLP), Colombian peso (COP), Czech koruna (CZK), Hungarian forint (HUF), Indonesian rupiah (IDR), Israeli shekel (ILS), Indian rupee (INR), Korean won (KRW), Mexican peso (MXN), Malaysian ringgit (MYR), Peruvian sol (PEN), Philippine peso (PHP), Polish zloty (PLN), Romanian leu (RON), Russian ruble (RUB), Thai baht (THB), Turkish lira (TRY), Taiwanese dollar (TWD) and the South African rand (ZAR).

We look at carry for all of these currencies in relation to their conventional benchmarks, which is USD for most currencies, EUR for CHF, NOK, SEK, CZK, HUF, PNL and RON and a EUR/USD basket for GBP, RUB and TRY.

Periods of greatly restricted convertibility and exchange rate have been excluded. Hence, for some emerging market currencies and the Swiss franc there have been gaps in the time series. Moreover, we base our analysis on 5-day moving averages of carry at month end for the purpose of generating a trading signal. The averaging reflects the poor quality of some recorded forward/NDF curves on Bloomberg and Reuters. Apparently quality problems relate back to the ultimate providers of price data, which for several EM countries produce very volatile and implausible implied carry measures on a simple end-of-day basis.

FX carry is in principle a valid basis for investment strategies because it captures – to some extent – policy subsidies and risk premia. As to policy subsidies, __central banks often set high local real interest rates and provide liquidity in the local currency market, by selling local currency and replenishing FX reserves__, for the purpose of macroeconomic stabilization (view post here). This constitutes an implicit subsidy to carry traders up to the point where the carry position becomes overcrowded and the ensuing setback risk becomes too excessive. As to risk premia, __institutions and households that are worried about financial turmoil are often willing to forgo expected return by holding “hard currencies” rather than carry currencies__ (view post here). Hence, they are willing to pay an implicit insurance premium. Indeed, __FX carry trades have historically been most profitable when high risk premia led to both high interest rates and undervaluation of a currency__ (view post here).

### The carry signal

For the purpose of systematic carry-based strategies we focus on normalized carry. This means that __we scale positions across FX forwards such that they are all estimated to be equal to a USD1 position in the S&P500 stock index__. This makes positions roughly equal in terms of risk across currencies and allows their variation to fluctuate alongside global/U.S. equity volatility. The purpose of this convention is to make all currencies contribute roughly equally to the performance of the aggregate strategy without suppressing the influence of overall financial market volatility.

Normalization is accomplished by multiplying a USD1 FX forward position with the past standard deviation ratio of the S&P500 index return and the FX forward return, based on two equally-weighted exponential moving averages, one with a 2-year half-time lookback window (representing medium-term volatility drivers) and one with a 21-day half-time lookback window (representing short-term volatility drivers)..

One consequence of this normalization is that the carry signals of less volatile currencies become relatively larger. Since we consider carry as a proxy for policy subsidy or risk premium, and we use volatility as a proxy for market risk, __normalization gives the premium per unit of risk, a valid indicator, particularly for comparison across currenci__es. The below two chart panels show time series for FX carry across all 29 currencies for all eligible periods and illustrate that normalization makes size and variance of carry signals across currencies more comparable.

__Even after normalization nominal carries have been quite heterogeneous in terms of mean and standard deviations across currencies__. The distance between the highest and lowest mean carry is 3.4 panel standard deviations, while the ratio of the highest to lowest currency-specific standard deviation is 8.7. This means that variation in the most volatile carry has been almost 9 times greater than variation in the least volatile carry. Hence, if one used simple normalized carry as a trading signal, __absolute and relative longs and shorts across countries would be long-term in nature and that the most variable signals would have a disproportionate effect on PnLs and trading costs__.

Plausibility and empirical evidence suggest that inflation differentials are a key factor of FX carry across currencies. The below scatter illustrates the historical relation between FX carry and (estimated) expected inflation differential for the whole panel of currencies. Importantly, __to the extent that carry is explained by the differential in expected inflation it is not plausibly indicative for relative monetary policy stance or relative risk premia__. This suggests that __to serve as trading signal FX carry should be adjusted for expected inflation__. The drawback of this adjustment will be estimation errors in respect to inflation expectations, which will add noise to the trading signal.

The inflation adjustment makes the means of normalized FX carry more equal, reducing the gap between highest and lowest average carry to 2.5 from 3.4 panel standard deviations. This implies that __inflation adjustment somewhat reduces the proclivity of carry signals to produce long-term long or short positions in individual currencies__.

Correlation of real FX carry across currencies has mostly been positive, which is not surprising since carries are viewed against two common benchmarks (USD or EUR). However, there have also been negative correlations. This suggests that __real carry signals for directional carry positions are not all fluctuating in synch, pointing to some diversification benefit in a global carry strategy__.

Theoretical arguments strongly support going beyond just inflation adjustment and to use an “economically-adjusted real carry” as basis for FX carry positions.” Compared to the real normalized FX carry this involves two additional steps.

- First, one must
__adjust real carry for inconsistency with real growth differentials__. This means that the carry on currency areas with relatively high real interest rates compared to their expected growth rate is slightly penalized to account for presumed lack of sustainability of the real interest rate differential. - Second, one must
__adjust the FX carry for the concurrent external current deficit__. Countries with persistently high real carry and relative growth tend to show external deficits. That is because, at least partly, high real rates and growth outperformances reflect strong domestic spending, which itself often is the consequence of stimulative fiscal policies or domestic credit booms. Empirically, there has been a clear negative correlation between growth-adjusted real carry and current account balances (as % of GDP) across the 29 currency areas in each and every year since 2000.

To the extent that high real carry and relative growth come at the expense of an external deficit it is not plausibly a positive sign for future currency strength. Therefore, __we adjust by regressing carry on external balance__. The intention is to estimate what part of the carry is has been caused by forces that also produce an external deficit and that, hence, are neutral with respect to future FX returns. The regression coefficient is negative of a magnitude of 0.16. Thus __a current account deficit of 1% of GDP leads us to reduce the relevant real carry measure by 0.16%__ and a current account surplus of 1% leads us to increase it by 0.16%. Note that for the case of Norway we adjust the current account for the sizeable net transfers from and to the Pension Fund Global.

The economic adjustments reduce carry measures’ heterogeneity in mean and cross-sectional heteroscedasticity (differences in variation). Put simply, __economic adjustments make carry signals not just more plausible but also more similar across currencies__.

### Directional strategies

Probability of positive correlation of normalized nominal carry with subsequent 1-month and 3-month forward returns since 2000 has been close to 100% at a monthly basis. The long-bias of a nominal carry-based signal would have been 80% across all currencies and close to 100% for many EM and carry currencies. High-inflation countries tend to produce the strongest positive signals.

Intertemporal correlation of carry with subsequent 3-month returns has been positive in 25 of 29 currencies; CLP, GBP, MYR and PLN have been the exceptions.

We __analyze naive PnLs with monthly rebalancing based on a month-end carry signal__ that has been winsorized at 10%. The winsorization reflects that very high signals are often data errors or not actually tradable due to liquidity and risk management constraints.

Nominal normalized carry would have produced a positive PnL with a long-term Sharpe ratio of 0.4-0.5 since 2000. However, a __closer look at the details casts much doubt over carry’s value as a systematic directional trading signal__. First, on its own nominal carry failed to produce positive returns since early 2012. Second, the nominal carry strategies produced outsized drawdowns during various crises and correlation with global direction risk has been 80%.

The basic issue with the carry signal is that __FX carry has done a poor job in predicting negative returns__. For most EM and some developed countries the signal simply recommended a long all the time. And since FX longs produced positive returns in 55% of all observed months since 2000, the hit ratio of the carry signal posted a respectable 55%. However, there has been a big gap between the positive return hit ratio (sensitivity) and the negative return hit ratio (specificity), with the former printing 79% and the latter 24%. The balanced accuracy of the hit ratio has thus been only 51%.

Economic adjustment leaves correlation probability of the carry signal with subsequent returns at close to 100%. Also, the long bias has been 80%, as high as for nominal carry.

The naive PnL based on economically-adjusted real carry has produced similar Sharpe ratios as the unadjusted carry signal, around 0.5. Also, all the other features of the carry PnL have been preserved: downside skew, large crisis-related drawdown, 75% positive correlation with global directional risk and lack of predictive power for negative FX returns. __On the whole, the economic adjustment has not changed the character of the global directional carry strategy__.

This is not surprising.. __Directional carry strategies have a predominant positive correlation with global financial market risk because carry is a well-recognized risk premium__. And all adjustments that we have looked at so far have only modified and qualified the carry signal to exclude some factors that would be clearly misleading. These adjustments do not remove the basic principle of the directional carry trade, which is (most of the time) to join a “crowd” of investors in receiving a subsidy or a risk premium, irrespective of whether the premium exceeds the downside risk of the trade.

In principle, there are two ways in modifying the carry trade. The first is to estimate setback risk and change positions according to market conditions, which will not be further explored here. The second approach is to use carry for relative trades across similar currencies, which are harder to calibrate and trade for most investors, and hence are less prone to erosion of risk premia through overcrowding.

### Relative position strategies

A relative position here is a __long or short position in one dominant currency (versus its natural base currency) against a basket of opposite-sign positions in similar currencies. Position size is determined by expected volatility__. As stated above, per convention we equalize volatility of currency positions to that of the S&P500, which is the contract most people are familiar with. That means that one unit position in the dominant currency, for example, is expected to produce the same volatility as USD1 invested in the S&P500 future. The opposite basket position is a set of positions each equal to the volatility of the S&P500 divided by the number of basket constituents.

__The term “similar” here means being influenced to a large extent by communal global factors__, such as equity and credit markets, global USD trends or flows into and out of large global investment benchmarks. To form baskets of similar currencies we need to apply judgment on [1] which communal factors should be neutralized and [2] which currencies are similar in respect to these factors. In the present context we form two baskets. The first basket consists of up 15 developed and emerging market carry currencies, selected according to popularity and liquidity. These currencies should all be subject in roughly similar fashion to global financial risk shocks and G2 currency strength. The second basket consists of up to 20 EM currencies with sufficient exchange rate flexibility and convertibility since 2000, which should all be subject to EM benchmark flows and USD/EUR fluctuations.

This implies that a relative position represents a bet on normalized idiosyncratic currency outperformance. As a consequence, positions and carry signal, including its various adjustment factors, must all be scaled by relative expected volatility to S&P500. A relative position is different from a hedged position, which only seeks to strip out a specific global factor.

#### Relative carry signals and value generation for 15 carry currencies

A relative normalized position is a long/short normalized position in one of the 15 eligible liquid carry currencies (versus their natural base currencies) against an opposite-sign position in the carry currency currencies basket. This positioning aims at approximate neutrality to FX carry shocks. Compared to simple normalized carry, relative normalized nominal carry is more similar in variance.

__The economic adjustments to relative nominal carry change the medium-term characteristics of the signal significantly__. In particular, the inflation-adjusted version of relative carry reduces the differences in mean significantly, underscoring that inflation is a key factor of long-term carry differentials across currencies.

The probability of positive correlation of relative real normalized carry with subsequent relative normalized returns returns has been close to 100% on a 1-3 month horizon. A naive PnL based on relative nominal normalized carry produced very modest Sharpe ratios of 0.3-0.4 since 2002, with great seasonality in performance. Correlation with a global directional risk basket has been small at just above 10%. There has been no meaningful skew in the distribution of this PnL.

The probability of positive correlation of relative economically-adjusted real normalized carry with subsequent relative normalized returns has likewise been close to 100% on a 1-3 month horizon. Intertemporal correlation of relative economically-adjusted carry with subsequent 3-month relative normalized returns has been positive in 12 of 15 currencies and, thus, has been more prevalent than for unadjusted carry. Likewise, cross-sectional correlation of carry with subsequent 3-month returns has been positive in 13 of 17 years.

Naive PnLs based on the values and signs or relative real normalized carry have produced Sharpe ratios of 0.6-0.7 with just above 10% global risk market correlation and a slight positive skew. Value generation has been more even than for relative nominal carry.

#### Relative carry signals and value generation for 20 EM currencies

A relative normalized position here means a long/short normalized position in one of the 20 eligible EM currencies (versus their natural base currencies) against an opposite-sign position in the EM currencies basket. __The aim is approximate neutrality to an EM currency shock that pushes all EM currencies up or down by multiple of their standard deviations__. Importantly, the relative position is not necessarily uncorrelated with global directional market risk or USD risk. Different currencies can and plausibly will overtime have different correlation with these sources of risk.

Compared to simple normalized carries, relative normalized nominal carries are more similar in variance, but display similar pronounced differences in long-term mean. Thus, a relative nominal carry signal is similarly prone to long-term one-sided positioning as a directional carry signal.

Adjustment for inflation greatly reduces the heterogeneity in mean of the relative inflation signal, with the distance between maximum and minimum means declining to 2.0 panel standard deviations from 3.5 standard deviations. That means that the inflation adjustment reduces the long-term bias in positioning.

Comparing the economically adjusted real relative carry with the nominal real carry shows that the character of signal has changed significantly. In particular, nominal carry longs in BRL, IDR, INR, RUB and TRY turn into more balanced positions.

The naive PnL based on relative nominal normalized carry posts long-term Sharpe ratios of just below 0.6, with positive 24-27% correlation with global directional risk. Balanced intertemporal accuracy has been 53%, higher than for the case of directional carry strategies.

As for the carry currencies, __the economic adjustment makes a significant positive difference__. Sharpe ratios of naive PnLs based on digital and proportionate relative economically-adjusted normalized carry signals have been 0.8 and 0.9 respectively, with about 22% global directional risk correlation. Performance was disproportionately strong during periods of high equity volatility, such as 2013, 2008/09 and 2011. Partly this just reflects that Value-at-Risk of such a naive strategy is higher in those periods and also the carry signals are larger. Performance would plausibly have been less uneven with some additional risk management or partial volatility targets. All country strategies based on the proportionate strategy posted positive long-term performance, except for CLP and ZAR.