FX forward returns for 29 floating and convertible currencies since 1999 provide important empirical lessons. First, the long-term performance of FX returns has been dependent on economic structure and clearly correlated with forward-implied carry. The carry-return link has weakened considerably in the 2010s. Second, monthly returns for all currencies showed large and frequent outliers beyond the borders of a normal random distribution. Simple volatility targeting would not have mitigated this. Third, despite large fundamental differences, all carry and EM currencies have been positively correlated among themselves and with global risk benchmarks. Fourth, relative standard deviations across currencies have been predictable and partly structural. Hence, they have been important for scaling FX trades across small currencies.

*This post is based on SRSV proprietary research.*

### Basic points

An FX forward contract is an over-the-counter derivative through which parties agree to purchase or sell a set amount of a foreign currency at a specified price and settlement date in the future. In the absence of market frictions, the forward exchange rate depends on the spot exchange rate and relevant interest rate differential between the two currency areas. Under normal market conditions __a short-dated FX forward contract is most sensitive to spot exchange rate fluctuations and much less sensitive to changes in the interest rate differential__.”

The empirical analysis of forward returns is based on a panel that comprises 9 developed market currencies and 20 emerging market currencies from 1999 to 2017. The starting date has been chosen in accordance with the replacement of most European currencies with the euro and the expansion of floating exchange rate regimes in emerging markets. To be eligible for this analysis 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).

When currencies are temporarily pegged or their markets disrupted, particularly due to convertibility restrictions, they are excluded from the analysis for the length of the disruption period.

Generic FX forward returns are calculated based on regular forward contracts or, where appropriate, non-deliverable forwards with initial maturity of just over one month. The contracts are “rolled” at the beginning of each month of the approximate initial maturity. __The contracts are based on the exchange rate of the specified local currency versus the U.S. dollar for most cases, except for some European currencies that naturally trade against the euro__ (i.e. CHF, HUF, NOK, PLN, RON, SEK) and some currencies of the European periphery that are benchmarked against an equal basket of U.S. dollar and euro (i.e. GBP, RUB, TRY).

### Log-term returns across currencies

__Long-terms cumulative returns of developed market currencies have been diverse__. The commodity currencies, i.e. the Australian dollar (AUD), Canadian dollar (CAD, Norwegian krone (NOK), and New Zealand dollar (NZD) all posted positive returns since 1999, albeit this positive performance ceased with the turnaround in the commodity cycle in the 2010s. JPY posted negative returns. The remaining European currencies recorded no meaningful long-term returns. __Emerging markets FX forward positions have almost all rendered positive returns__ since 1999, with the Taiwanese dollar being the only exception. The highest return, close to 150% over 17 years have been accrued by the Brazilian real.

Over the full sample period and particularly in the 2000s, difference in returns across currencies have been clearly correlated with simple forward-implied carry.

However, that carry-return relation weakened noticeably in the 2010s. For example, the Swiss franc, a currency with negative carry, posted the highest return of all global currencies in the sample, while the Turkish lira, a high-carry currency, posted a negative cumulative return.

### The distribution of monthly FX returns

Monthly FX returns have displayed great differences in variance. The average monthly standard deviation across all currencies has been 2.8%, and ranged between 1.4% for the Taiwanese dollar and 5.1% for Brazilian real.

What FX forward returns all have in common is __a tendency towards large and ample outliers relative to a normal distribution__ and given their historical standard deviations. Statistical measures of kurtosis have been positive for every one of the 29 currencies and highest for the Indonesian rupiah and the Swiss franc (even excluding the 2016 break of the franc’s de-facto peg). An intuitive way of illustrating the “fat tails issue” is to compare the trading range in quiet times with extreme monthly returns: the inner 50% of returns has been in a +/- 1.5% range on average, while the average maximum upside and downside returns have been around 10%.

Unlike equity returns, __FX forward forward returns have no strong tendency towards negative skewness__. While carry currencies mostly display some negative skewness it has been small and some EM currencies, such as the Indonesian rupiah and the Philippine peso, even post positive skewness.

### Volatility targeting

The proclivity of FX forward returns to large outliers has supported the practice of volatility targeting in discretionary trading and algorithmic strategies. The principle of volatility targeting is to scale positions overtime such that the expected variation of their individual PnL accords with a target. The aim is to keep the actual volatility of positions close to that target.

We have simulated a simple and practical version of such volatility targeting based on the following parameters: [1] the targeted annualized standard deviation of each FX forward position is set to 10%, [2] the basis for position adjustment is a historic exponential moving averages of returns with a half-time of 11 days (in accordance with risk management standards), [3] positions are rebalanced once a month at the beginning of the month to contain trading costs. The purpose of the analysis is to see whether such a simple procedure helps reducing currencies’ proclivity to outliers.

In developed FX markets, estimated annualized standard deviations have indeed varied considerably overtime. Normal ranges have 5-10% annualized, but volatility easily doubled in times of turmoil and soared 4-5-fold increase during the global financial crisis. The EMFX space experienced even more dramatic surges in standard deviations overtime.

__In the developed market space active volatility-targeting has provided very modest benefits in terms of preventing outsized PnL moves__. The boxplot below compares returns on position with average 10% annualized standard deviation (light blue) and those that actively adjust position sizes (dark blue) to accomplish the target. On balance, the actively targeted positions post fewer and smaller outliers, and average kurtosis of returns (tendency towards outliers) declines. However, the evidence is not strong and varies across countries. For the Japanese yen outliers increase in size after volatility targeting. Also, negative skewness slightly increases. In particular, __for the commodity carry currencies volatility targeting did a better job in reducing upside outliers than reducing downside outliers__.

__Active volatility targeting has been even less successful in the EM space__. Average kurtosis has actually increased and outliers of targeted returns have been larger in a number of countries. In particular, __volatility targeting of some low-volatility countries has produced some of the largest historical outliers of FX forward returns__, exceeding 20% or two annualized standard deviations in a single month.

### Correlations

With the exceptions of the Swiss franc, the Japanese yen, and – occasionally – the euro, FX forward returns are positively correlated with each other and with major risk benchmarks.

Cross-correlations of developed market FX returns have been diverse. There has been high correlation across the commodity currencies and between the Norwegian krone and the Swedish krona. Also, the euro has posted high correlation with commodity currencies. The Swiss franc has been correlated negatively with commodity currencies. The Japanese yen posted little correlation with other currencies.

Similarly, the correlation of developed market exchange rates with benchmark returns has been mixed. __The USD-based commodity currencies posted over 50% correlation with a global directional risk basket returns__ (1/3 equity, 1/3 credit and 1/3 FX, labelled GLB_DRB_XR in the graphic), U.S./ euro area equity returns (USD_EQ_XR and EUR_EQ_XR) and global commodity returns (GLB_COM_XR). They posted negative correlation with U.S. treasury returns (USD_T10Y_XR), but not with euro area or German treasury returns (EUR_T10Y_XR). The Scandies and the British pound displayed a similar pattern, but weaker correlation. The euro posted positive correlation with risk and commodities as well but, correlation with treasury returns has been positive. This means the euro benefited directly from declines in U.S. yields even if these declines were often triggered by negative risk shocks. Conversely, the euro posted clear negative correlation with euro area yields.

The Swiss franc has historically benefited from negative risk shocks, except for the time of the EUR-CHF floor (2011-2016). __The franc displayed mostly opposite correlation to the commodity currencies:__ correlation with global risk, equities and commodities returns has been negative, while correlation with U.S. and euro area government bond yields has been positive. The __risk correlation of JPY has been similar__, except for a slight positive correlation with global commodities, which probably reflects that both JPY and commodity currencies benefit from idiosyncratic USD weakness.

Cross-correlation for all EM currencies have been positive, despite huge differences in carry and country ratings. This holds also true if one looks at the 2010s alone. The highest cross-correlations have been observed within regions. Benchmark correlations have also been similar across countries. Importantly, __all EM currencies displayed positive correlation with the global directional risk basket, G2 equity markets, and commodity prices, even commodity importers__.

### Relative volatility adjustment

Relative volatility-adjusted returns of currencies can be calculated by normalizing positions such that their expected return variance is equal to that of a benchmark. Here we chose the S&P 500 equity index as such benchmark and historical standard deviation ratios as the basis of position calibration. Unlike for outright volatility, it is not evident whether short or longer-term lookback windows are better for estimating relative future standard deviations, as relative volatility is more prone to short-lived outliers, such as elections, and less aligned with sustained shifts in the global financial environment. Hence, we chose two equally-weighted lookback windows for calibration, a monthly-frequency return window with a half-time of two years (medium-term perspective) and a daily-frequency return window with a half-time of 11 days (short-term perspective).

The __empirical experience suggests that adjusting for relative volatility is essential for calibrating relative FX trades__. For example, in the developed market space the relative standard deviations of the Australian dollar and the New Zealand dollar have consistently been above the other currencies, while those of the Scandinavian currencies has consistently been on the low side.

Also, in the EM space there have also been clear and persistent differences in relative volatility across currencies. However, there has been a greater proclivity towards instability and sudden bouts of idiosyncratic volatility.

Open economies tended to have lower currency volatility consistently across all years, corroborating the notion of structural differences.

In both developed and emerging markets calibrated returns become a lot more similar in distribution after adjustment. Unlike volatility targeting calibrating relative returns has delivered a clear intended effect on the distribution of ex-post returns. The box-whisker plot below suggests that calibration leads to convergence of the normal range of distribution, rather than preventing outliers.

### Autocorrelation curiosities

In the developed world, there has been consistent and significant negative autocorrelation of Australian dollar and Canadian dollar FX forward returns in both the 2000s and 2010s. In the emerging world, our data show strongly negative daily autocorrelation in Central Europe (Czech koruna, Hungarian forint, Polish zloty, Romanian leu). Meanwhile, there has been consistent significant positive autocorrelation in the Andean currencies, Chilean peso and Colombian peso.