Economic growth differentials are plausible predictors of foreign exchange return trends because they are related to differences in monetary policy and return on investment. Suitable metrics for testing growth differentials as trading signals must replicate historic information states. Two types of such metrics based on higher-frequency activity data are [i] technical GDP growth trends, based on standard econometrics, and [ii] intuitive GDP growth trends, mimicking intuitive methods of market economists. Both types have predicted FX forward returns of a set of 28 currencies since 2000.

For simple growth differentials, the statistical probability of positive correlation with subsequent returns has been near 100% with a quite stable relationship across time. Excess growth trends, relative to potential growth proxies, would have been more appropriate predictors for non-directional (hedged) FX forward returns. Correlations with hedged returns have generally been lower but accuracy has been more balanced. Finally, balanced growth differentials that emphasize equally the performance of output and external balances are theoretically a sounder predictor. Indeed, these indicators post even higher and more stable correlations with subsequent directional returns than simple growth differentials.

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

This post ties in with this site’s summary on systemic value generation with macro trends.

## Why growth differentials matter for FX

Economic growth is related to both the monetary policy stance and the return on capital in a country. From the monetary policy angle __higher growth, particularly relative to its potential, typically gives rise to higher real policy rates and greater tolerance for currency strength__. That is why countries with positive growth differentials to funding currency areas often offer higher yields on local deposits and short-term bonds. From a real investment perspective, __higher economic growth is typically related to higher returns on real investment__ in the local capital stock and – often enough – an indication of improving supply conditions. Importantly, estimating economic growth trends in real-time is not trivial and outside the bandwidth and budget of many investment managers, leave alone other more sporadic market participants. Hence the information content of the estimated growth trend differential is unlikely to be priced in exchange rates fully, instantaneously, and consistently.

“In any economy, open or closed, the steady-state natural interest rate converges to the steady-state marginal product of capital net of depreciation… In an open economy, the steady-state marginal product of capital net of depreciation converges to an exogenous value, namely the natural external rate of interest and a baseline risk premium through net capital accumulation.” [Tanner]

## Two types of real-time growth metrics for trading strategies

__To measure the predictive power of economic growth trends on financial asset returns one needs historic real-time data of such trends that represent the information state of the market on each date__. They must be based on vintages (historic times series rather than currently available time series) and be aligned with the dates at which they were the latest current information, rather than at the time at which they occurred. This post uses data from the J.P. Morgan Macrosynergy Quantamental System (“JPMaQS”), which currently offers two types of such historic real-time indicators for a wide range of countries:

**JPMaQS technical real GDP trends**are real-time estimates of GDP growth, % over a year ago in 3-month moving averages, based on vintages of standard econometric (“technical”) estimates.__Historic and current estimation models are based on the simplest conventions and supervised learning__(view basic principles here). Thus models are rebuilt over time in light of preceding experience. This process reduces the contamination of estimates by hindsight, makes backtests more meaningful, and sets out clear rules for the generation of estimates in the future.

Annual growth rates are estimated for every new release of a set of “credible macroeconomic predictors” using their actual or estimated available data vintages at the time. “Credible macro indicators” are those that were plausibly watched by the market and that had explanatory power for concurrent (unreleased) GDP growth at least at some point during the data release cycle. The presence of predictive power is ascertained by using the “elastic net” earning method.

When aligning various predictors for recent observation periods, some values are usually missing. This reflects differences in release schedules and leads to a data structure that is called a “jagged edge”. It is a common inconvenience of economic data watching. The technical macro trend model estimates the missing data points (based on the available data) and then uses the estimated full recent data set to predict GDP trends.

__The credible macroeconomic predictors are chosen periodically by the learning algorithm from the full set of real activity indicators__**(“feature candidates”).**The feature candidates are those indicators that have been watched by the market according to the data release calendars of major market data services and that could plausibly have provided information prior to the release of the official national accounts.

Note: for full documentation see the section “Technical real GDP trends” on the JPMaQS site on J.P. Morgan markets.**JPMaQS technical intuitive GDP trends**are__real-time estimated recent GDP growth trends based on regressions that use the latest available national accounts data and monthly-frequency activity data__. The estimation relies on GLS regression with autocorrelated errors. Unlike standard academic models, the intention is to mimic intuitive methods of market economists.

Each day on which a new economic indicator is released a full new vintage of monthly-frequency GDP growth rates (% over a year ago) is being estimated. For the latest months of each vintage, for which national accounts data have not yet been published, GDP growth is estimated based on GLS (generalized least squares) regression. This r__egression predicts GDP growth for a month based on the relevant growth indicators that have so far been published and the autocorrelation effects of past error terms__. This means that the error of that same regression for the latest reported quarter carries over into subsequent months. Errors of linear predictions of GDP growth based on a select few growth indicators are often autocorrelated due to unobservable trends, typically related to sectors for which no higher-frequency data are available.

For the older history of each vintage, for which national accounts have already been released, the official quarterly-frequency GDP growth rates are decomposed into monthly-frequency growth rates using OLS regression based on monthly activity indicators.

The candidate monthly-frequency indicators are pre-selected according to markets’ popular economic release calendars and further narrowed down based on their predictive power prior to the point in time at which the selection must have been done. Thus, there is statistical pre-selection based on prior training data. In summary, this means that the set of explanatory monthly-frequency activity indicators changes over time according to (i) publication schedule and (ii) past predictive power.

Note: for full documentation see the section “Intuitive growth trends” on the JPMaQS site on J.P. Morgan markets.

## Stylized facts of economic growth differentials

Using technical and intuitive growth trends from JPMaQS __we compute growth differentials of 28 countries vis-à-vis their natural benchmark currency areas__. For most currencies, the benchmark is of course the dollar. However, for some European currencies (CHF, CZK, HUF, NOK, PLN, RON, SEK) the benchmark is the euro. And for GBP, TRY, and RUB an equally weighted basket of dollar and euro has been used. The choice of natural benchmark is important for the analysis of growth differentials because growth differentials to the U.S. have little importance for European countries that are closely integrated with the euro area and because their currencies’ fluctuations against the dollar are dominated by EURUSD.

__Technical and intuitive growth trends broadly track similar large and mini-cycles__. Annual averages of the two types of estimated trends post 82% linear correlation. However, they also display episodes of significant differences. In some emerging markets these differences have been persistent. During the COVID crisis intuitive growth differentials have on average been more volatile than technical growth differentials. On average since 20000 the growth differentials of the non-USD and non-EUR currencies have been positive thanks largely to the performance of EM economies.

Concurrently and over the longer term, there has been a strong correlation between recorded growth differentials and FX returns. Of course, this does not yet guarantee that growth differentials have sufficient leading predictive power to generate significant value in trading strategies.

## Stylized facts of FX returns

The target variables of this analysis are__ daily one-month FX forward returns of all liquid tradable and largely convertible currencies since 2000__. They are expressed in % of notional of the contract, assuming roll back to full 1-month maturity at the end of the month. For some currencies’ returns are partly based on non-deliverable contracts: BRL, CLP, IDR, INR, KRW, MYR, and TWD. CLP has become deliverable as of 2021. For this post, returns are calculated versus their respective dominant cross, which is USD or EUR or both. For some currencies the returns include periods of low liquidity and FX targeting. For the analysis in the subsequent sections, these periods have been blacklisted. Currencies that have been tightly managed throughout the past two decades, such as CNY and SGD, have been excluded.

For most of the below analyses, __the focus is on volatility-targeted returns, to make currency performances more comparable across countries __with varying openness and tolerance for exchange rate fluctuations. Positions are scaled to a 10% vol target based on standard deviations for exponential moving averages with a half-time of 11 days. Positions are rebalanced at the end of each month. Also, a maximum leverage ratio of 5 (of implied notional to cash position) is imposed

Some analyses below use hedged FX forward returns to strip out the market directional influences on currency returns through a position in a global directional risk basket that includes equity, credit, and FX contracts. __Both vol-targeted and hedged FX forward returns display pronounced medium-term drifts__. For many EM and carry currencies there has been an upward drift in the 2000s followed by flat or negative performance in the 2010s. Three currencies THB. TWD and RON) posted directional trends for almost two decades. Hedged returns have on average been much lower than unhedged returns since the majority of currencies qualify as carry or EM currencies have displayed positive risk market beta and incurred costs related to shorts in equity and credit positions.

## Stylized facts of relations between growth differentials and FX returns

### Simple growth trend differentials

The expected predictive power of growth differentials for subsequent FX forward returns has been borne out by the empirical evidence since 2000. The analysis below is based on monthly frequencies, but findings are broadly similar for weekly and quarterly data:

- For
**technical growth trend differentials,**Pearson and Kendall correlation coefficients (parametric and non-parametric metrics respectively) point to the probability of positive relation with subsequent monthly returns of above 99%. A positive correlation has been observed in 69% of all years and 66% of all currencies.

Balanced accuracy (weighing equally the precision of hitting positive and negative returns correctly) has been 51.8% on a monthly and per-currency basis.

N.B.: Standard unweighted accuracy has been higher at 53.1% but this standard metric has been flattered by the long bias of the signal (67%) in conjunction with the prevalence of positive returns (55% since 2000). As a result, the positive precision of the signal, i.e. the ratio of correct hits of the long signals has been impressive at 54.5%, while the negative precision was just 47.6%. - In the case of
**intuitive growth differentials,**correlation with subsequent returns has been higher with a__positive correlation probability near 100%.__A positive correlation of this indicator was observed in 75% of all years and -again- 66% of all countries. Also,__balanced accuracy has been notably higher than for technical growth differentials at 52.7%,__with both positive and negative signals producing better precision.

A naive PnL is calculated for simple monthly rebalancing using a z-score with a mean of zero, based on the full trailing panel up to the signal calculation date, and trimmed at 2 standard deviations to avoid data outliers. Positions are taken across 28 currencies at the beginning of the month based on the information status at the end of the previous month, although it is assumed that it takes one day to trade in and out of positions. Positions are scaled so that one unit of the signal corresponds to one unit of vol-based risk in a specific forward. Neither transaction costs have not been nor compounding effects have been considered.

The long-term Sharpe ratio based on technical growth differentials has been just below 0.5, while the ratio based on intuitive growth has been just below 0.7. Both strategies suffered large drawdowns in the wake of the global financial crisis and pronounced seasonality.

Naïve growth differential strategies would also have suffered from a notable deterioration in performance from 2012. This resembles the performance of carry strategies, but mainly because both simple growth and carry strategies have historically involved a long bias in carry and EM currencies, and the latter performed poorly after 20102. Importantly, __the deterioration of PnL generation from 2012 has not been due to declining predictive powe__r. Indeed, signal correlation with subsequent monthly returns has improved from 2012. Yet this improvement has not been enough to offset the impact of poor performance in many carry and EM currencies in conjunction with the long bias of a simple growth differential signal.

The most obvious problem with direct and exclusive use of growth differential is the absence of penalty for any other drawbacks and risk factors. Indeed, high growth often coincides with high currency sensitivity to global risk markets, due to capital flows, and external trade deficits.

### Excess growth trend differentials

__Excess growth differentials conceptually single out the effect of growth differentials on exchange rates through the monetary policy channel__ as opposed to the long-term natural rate of interest. Here excess growth is defined as an estimated technical or intuitive GDP growth trend minus a 5-year rolling median of real GDP growth, based on a concurrent vintage of actual national account reports. The rolling multi-year medians are regarded as a simple objective estimate for what markets or central banks might consider as a normal or potential growth rate.

Since 2000 __excess growth differentials as trading signals would have called for a short bias rather than a long bias for positions in non-USD and non-EUR currencies__. Only about 40% of all monthly signals have been positive since 2000, contrasting 55% of positive monthly returns. This illustrates natural myopia of excess growth differentials as stand-alone trading signals. As they serve signals for many carry and EM they implicit only focus on policy differentials and do not consider the risk premia that are paid on many of them

Indeed, with respect to subsequent directional monthly FX returns both accuracy and correlation have been weaker than for outright growth differentials.

- In the case of
**excess technical growth differentials**, the positive correlation probability with respect to subsequent directional returns would have been just 82%. Balanced accuracy would not have deteriorated much at 51.2%, but the short bias of the signal means that it would have failed to generate significant value. - For
**excess intuitive growth differentials,**forward correlation with returns would also have receded compared to the simple directional relation. However, the probability of positive correlation with subsequent returns would still have been near 98%, while balanced accuracy would have held up at 51.5%.

By contrast, __excess growth differentials perform a lot better in predicting the non-directional portion of FX forward returns,__ as proxied by returns on forward positions that are hedged against global direction risk beta. This is no surprise, as excess growth has no conceptual basis as a tracker of directional risk and focuses on temporary biases in monetary policy.

- In the case of
**technical excess growth differentials,**forward correlation with hedged returns would have displayed an average positive correlation probability of just 85%. However, balanced accuracy would have been 52%, with both positive and negative precision near 52%. - For
**intuitive excess growth differentials**forward correlation with monthly hedged returns points to a positive correlation probability of over 99%. Balanced accuracy would have been stronger than for the directional growth differential signal at 52.3%, with positive and negative precision both above 52%. Thus, this strategy signal is equally good in hitting the up and down months, a notable difference from the directional simple growth differential, which recorded negative precision of below 50%.

The performance of a hedged FX strategy based on excess growth differentials would have posted only half the Sharpes of the directional strategy, between 0.3 and 0.4. However, this strategy has had a short bias in carry and EM currencies since 2000 and, by construction, does never take intentional market directional exposure. It is therefore a valid diversifier for currency and global macro portfolios.

### Balanced growth trend differentials

A strong theoretical case can be made for combining and balancing the different aspects of growth differentials for the purpose of an FX forward trading signal. For example, we can create a combined z-score (around a natural zero level and calculated sequentially out-of-sample) based on three sub-scores:

- the simple expected growth trend differential,
- the excess growth trend differential, and
- the dynamics in external balances, which penalizes rising external trade deficits.

A simple plausible composite would be the __average of growth differentials and external balances’ changes__ (both in z-scores). As a signal, it gears positions towards currencies with a good trade-off between relative growth and external balance dynamics. This is __related to the concept of macroeconomic competitiveness__. Typically, currency areas with improved competitiveness either post strong relative growth without much deterioration in external balance ratios or shifts external balances towards surpluses that do not require a significant underperformance of domestic demand and production. The balanced growth differential of this type is then used as a signal for directional volatility-targeted FX returns.

- In the case of
**technical balanced growth differentials,**probability of positive correlation with subsequent monthly FX returns has been very close to 100%. Positive correlation was recorded for 73% of all cross-sections and 72% of all years since 2000. Balanced accuracy has been 52.2%, - In the case of
**intuitive balanced growth differentials,**the statistical probability of positive correlation with subsequent monthly returns has likewise been nearly 100%. Positive correlation prevailed in 80% of all years and 71% of all cross-sections. Balanced accuracy has been 52.4% across currencies and months since 2000.

Naïve PnL generation was quite different for technical and intuitive growth differentials, which Sharpe ratios of 0.7 and 0.3 respectively. This difference reflected partly that the signal based on technical growth displayed almost no long bias, while the signal based on intuitive growth recorded a 58% long bias. However, both naïve PnLs showed fairly consistent value generation with limited market directionality since the mid-2000s (when growth trend estimates improved in quality for many countries).