There is often a strong case for hedging FX carry trades against unrelated global market factors. It is usually not difficult to hedge currency positions – at least partly – against global directional risk and against moves in the EURUSD exchange rate. The benefits of these hedges are [1] more idiosyncratic and diversifiable currency trades and, [2] a more realistic assessment of the actual currency-specific subsidy or risk premium implied by carry, by applying hedge costs to the carry measure. Empirical analysis suggests that regression-based hedging improves Sharpe ratios, reduces risk correlation and removes downside skews in the returns of global FX carry strategies. Hedging works well in conjunction with “economically adjusted” FX carry and even benefits the performance of relative FX carry strategies that have no systematic risk correlation to begin with.

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

The post is a sequel to FX carry strategies (part 1). For more detail, such as choice of currencies for the empirical analysis and the basics of carry calculation please refer to that post.

### Why and how to hedge FX carry positions?

We define carry positions as __normalized 1-month FX forward positions in 29 global currencies against USD or EUR, based on various measures of FX forward-implied carry__. Normalizing here means relative scaling of FX positions to the expected standard deviation of the S&P500. Carry measures include normalized nominal carry, corresponding to the position size, and normalized economically adjusted real carry, which strips out the estimated portion of carry that is due to expected inflation differentials and currency drifts that arise from external imbalance. For a further explanation of these points please view the previous post here.

If an FX forward position is taken to express a view on a specific currency, without views on other currencies or markets the overall market, it should principally be hedged against significant unrelated global factors. This has two benefits.

- First, the disturbing influence of global factors on the trade can be reduced. Generally,
__trades become more idiosyncratic and diversifiable__. - Second,
__the adjustment of FX carry for the cost of carry of the hedges gives a better measure of the true idiosyncratic risk premium__. For example, there is no point receiving a global cross-asset risk premium through an FX carry trade if other assets pay the same premium and more.

In particular, __a hedge is preferable if [1] the FX position is set up for a longer investment horizon__, which poses a greater risk of adverse market shocks along the way, __and if [2] the influence of global factors is significant and predictable__. Indeed, for most global FX forward contracts significant and predictable global influences are plausible and empirically evident. Specifically, most exchange rates are exposed to global equity and credit price changes (henceforth loosely called “directional risk”) and to EURUSD exchange rate moves. The former applies to all carry trades, which are a form of alternative risk premium strategy and depend on availability of leverage. EURUSD sensitivity arises for USD-based exchange rates of countries that have significant trade or financial transactions with the euro area.

In this analysis hedge ratios are estimated through weighted least squares regression at the end of each month and applied to trading positions for the subsequent month. Technically __hedge ratios are regression coefficients of relevant benchmarks, based on rolling windows of daily and weekly data__. In these regressions past observations carry exponentially decreasing weights backward in time. While daily data provide more observations, they also often understate the correlation of FX forwards due to time zone effects, i.e. incomplete overlap of trading hours during the day. Therefore we use a weighted average of a weekly-data estimate (26 weeks half time of lookback window) and a daily-data estimate (63 days half time of lookback window). This has been set a-priori based on expert judgment without any attempt of statistical optimization.

Importantly, hedge ratios have been estimated for normalized FX positions, i.e. positions that all target the standard deviation of the S&P500, based on recent relative volatility. Hence,__ the estimated beta mainly captures correlation, not relative standard deviations__ (while normally estimated regression coefficients capture both). The argument for this two-step procedure is that the relative standard deviation can be estimated based on daily data and short lookback windows, while correlation cannot. That is because relative standard deviations are less susceptible to non-overlapping trading hours. Once the relative normalization is out of the way the remaining beta is estimated with a longer lookback window and – predominantly – based on weekly returns.

### How effective has hedging been?

The __most obvious influence to be hedged against is global directional market risk__. In this section the market risk is approximated by a cross-asset basket, consisting equally of global equity index futures (11 countries) and credit default swaps (U.S. and euro area high-grade and high-yield indices).

__Risk betas of normalized FX forward returns have been predominantly positive across time for almost all currencies__, with only three exceptions: CHF, JPY and EUR. CHF and JPY have been funding currencies for carry trades and EUR has been both funding and carry currency in the past. Directional risk betas of al other developed market currencies have consistently been positive. The estimated betas of EM currencies have also almost always been positive. All this suggest that direction risk betas have been partly predictable.

Since the directional betas refer to return series that have been approximately equalized in volatility they are indicative of the directionality of various currencies, i.e. the strength of the influence of global risk factors, as opposed to idiosyncratic price factors. By that metric, __the MXN has been the “most directional” currency over the full sample period__, corresponding to a common view among currency traders that the Mexican currency is often used as a proxy for equity exposure.

There has been a consistent positive link between FX carry and FX “risk beta”. In each year since 2000 the currencies with higher normalized carry have displayed greater sensitivity to global directional market risk. This __suggests that FX carry contains a premium for taking directional risk, not unlike the risk premium proposed by the Capital Asset Pricing Model__ for non-diversifiable market risk.

__If we hedge FX positions against global directional risk, average absolute correlation with global risk across all currencies drops by about 48%__ out of sample. Risk correlation has been reduced for all currencies, even for EUR and JPY, whose beta has historically been harder to predict. At the same time hedging has reduced the standard deviation of returns only by about 9%. Estimation errors and related basis risk plausibly increased variation.

Exchange rates of small countries are sensitive to exchange rates between larger currencies. A particularly strong case can be made for hedging against EURUSD changes, which confound the idiosyncratic returns on currency positions in virtually all other countries, in dependence upon their natural trading benchmark. __Currencies that trade against USD should plausibly be correlated positively with EURUSD__ and the more so the stronger their economic ties with the euro area. This is borne out by the predominantly positive sign of estimated betas of non-European currencies in the past.

Despite some instability of estimated betas, __EURUSD hedging has reduced average absolute correlation of FX forward positions return with EURUSD returns by about 40%.__ This means that the influence of EURUSD on other currency positions would be reduced significantly. In the case of AUD, NZD and ZAR the reduction was about 70%. For European currencies the benefit of this hedging has been a lot smaller. Indeed for SEK, EURUSD hedging has led to an increase in absolute EURUSD correlation.

In the below sections we investigate empirically the performance of FX carry strategies based on positions that have been “double hedged”, against global directional risk and – subsequently – against EURUSD exchange rate moves. This method implies that the sporadic communal variations in the two hedge benchmarks have been allocated to global directional risk.

### Have hedged FX carry strategies generated value?

As shown in a previous post, the naïve PnL of a 29-currency __directional unhedged FX carry strategy (based on normalized positions and carry) has generated a positive return, but not a reliable and sustained one__. Correlation of the FX carry PnL with global directional risk has been roughly 80%, monthly PnLs have been skewed towards the negative side and value generation effectively ceased in the 2010s.

__If instead we base the FX carry strategy on “double hedging”, both the strategy signals (now “hedged carries”) and the returns of the target positions (hedged positions) change__. Thus, hedging has a profound impact on level and dynamics of FX carry. In times of financial turmoil high beta and hedging costs can drastically reduce the carry signal. The impact is strongest on developed market currencies. Also, double-hedging reduces the differences between mean carry signals across sections in terms of panel standard deviations. The tendency of the carry signal to produce long-term long and short positions is a bit reduced through hedging.

Simulating a naïve PnL where the double-hedged normalized nominal carries are applied as signal to double-hedged normalized positions shows that hedging has historically mitigated two of three problems of the unhedged nominal carry strategy. First, __correlation with global directional risk has been reduced to 20% from 80%__ and, hence, crisis related drawdowns no longer “break” the long-term performance. Second, the __negative skew in monthly return distribution gives way to a small positive skew__. However, hedging does not prevent value generation of a nominal carry strategy from decaying in the 2010s. As a principal guide for directional trading, nominal carry has failed over the past 10 years

In the post “FX carry strategies (part 1)”, we have argued that simple nominal carry is just a very rough measure of the risk premia and implicit subsidies that actually justify carry trades. __Reasonably, nominal carry should at least be adjusted for expected inflation differentials, currency drifts associated with external balances and interest rate drifts associated with economic growth trends__. If we apply the “double hedge” to an economically adjusted real normalized carry, the signal profile changes again. In particular, the carry signal becomes more homogeneous, i.e. it displays less long-term differences in mean and variation across currencies.

Over the past 20 years the positive correlation probability of economically-adjusted real normalized carry with corresponding subsequent returns has been close to 100% for a 1-month or 3-month forward horizon. Reliability of this correlation has been high across currencies and time.

The long-term naive PnL of an FX carry strategy based on double-hedged normalized economically-adjusted real carry measure has produced Sharpe ratios of 0.9-1.0 for digital and proportional signals respectively. Directional risk correlation has been 17-30% and the distribution of monthly PnLs has displayed a modest positive skew. __Importantly, value generation did not cease in the 2010s, as was the case without economic adjustment__.

### Should relative FX carry strategies be hedged?

Economically-adjusted carry has been a valid and successful basis for relative carry trades across EM and traditional carry currencies. __While relative positions have on aggregate less exposure to global directional risk and EURUSD risk, sporadically there can still be considerable dependence of PnLs on these benchmarks__.

Hence, the question is this: “should residual directional exposure of relative FX positions be hedged?” There is no clear theoretical case here. On the one hand, directionality is undesirable. On the other, betas of relative positions are harder to predict and, hence, hedge ratios are a lot less reliable.

Empirical analysis for two groups of relative FX carry strategies suggests that reduction of directionality is small and, hence, for a given signal double hedging of relative positions does not seem to be essential. However, the combination of position hedging and adjustment of carry for hedging costs (which is a proxy for correlation risk premium) does seem to improve the quality of the trading signal and deliver somewhat better performance statistics.

**Relative EM FX trades**

The __directional betas of relative positions have been less stable and one-sided than those of absolute positions__. Estimated betas have often flipped signs overtime. It would be plausible that betas of relative normalized positions are more sporadic than betas of outright positions, because structural volatility differences and the beta of the whole peer group have no influence.

__Average absolute correlation with global directional risk declines only slightly after hedging, by around 6%.__ Thus, on average hedging has been a lot less productive in the relative case compared to the absolute case. This suggests that the estimation error is high relative to the benefit of hedging. Across currencies the importance of hedging has been very different, ranging from 37% reduction of correlation (CZK) to 45% increase (ILS). EURUSD hedging has been more successful. __On average the EURUSD hedge reduced EURUSD correlation of directionally hedged normalized positions by about 15%__, with the greatest impact on TRY.

At the same time, the impact of double-hedging on relative economically-adjusted real carry in the EM FX space has been quite subtle. Neither sign nor dynamics have changed in a graphically conspicuous way over the past 19 years.

Despite the rather subtle effect of double hedging on return correlation and signal in the EMFX space, __the hedged version of the relative normalized and economic adjusted real carry strategy has produced higher Sharpe ratios of around 1.1__ versus 0.8-0.9 for the unhedged version. Moreover, the positive skewness of the monthly returns doubled after hedging.

**Relative carry currencies’ FX trades **

The impact of hedging on relative normalized carry currencies’ trades was similar to the impact on relative EMFX trades. Hedging against the directional risk basket reduced absolute average correlation of currency positions directional risk only by 5%. However, the incremental EURUSD hedge has reduced absolute average EURUSD correlation of directionally hedged normalized positions by about 21%. The reduction was more than 50% for AUD and TRY.

Similar to the EM space, the impact of hedging on relative carry signals for carry currencies has been small. However, __the Sharpe ratio of a naïve PnL based on the hedged version of the relative normalized economically adjusted carry signal increased to 0.8-0.9 __(for digital proportional signals respectively) , from 0.5-0.7 for the unhedged signal. Also, as in the EM FX case, the positive skewness of monthly returns doubled.