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Modified and balanced FX carry

Jupyter Notebook

There are two simple ways to enhance FX carry strategies with economic information. The first increases or reduces the carry signal depending on whether relevant economic indicators reinforce or contradict its direction. The output can be called “modified carry”. It is a gentle adjustment that leaves the basic characteristics of the original carry strategy intact. The second method equalizes the influence of carry and economic indicators, thus diversifying over signals with complementary strengths. The combined signal can be called “balanced carry”. An empirical analysis of carry modification and balancing with economic performance indicators for 26 countries since 2000 suggests that both adjustments would have greatly improved the performance of vol-targeted carry strategies. Modified carry would also have improved the performance of hedged FX carry strategies.

A Jupyter notebook for audit and replication of the research results can be downloaded here. The notebook operation requires access to J.P. Morgan DataQuery to download data from JPMaQS, a premium service of quantamental indicators. J.P. Morgan offers free trials for institutional clients.

Also, there is an academic research support program that sponsors data sets for relevant projects.

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 FX carry needs quantamental enhancement

Forward-implied carry is the return on an FX forward contract if the spot exchange rate remained unchanged to maturity (view post on carry definitions). It can be calculated for standard and non-deliverable FX forward contracts. For convertible currencies, arbitrage typically keeps forward-implied carry close to the differential of risk-free interest rates of similar maturities. FX carry is a valid basis for trading strategies because it is often related to risk premia (riskier currencies need to offer positive real carry), monetary policy differences (more hawkish central banks set positive interest rate differentials), and divergences in economic growth and investment conditions (higher-growth countries pay higher real returns).

However, standard FX forward-implied carry is a crude signal that conflagrates the influences of risk premia, various fundamental divergences, and market distortions. There are many ways in which quantamental indicators can improve the plausibility and credibility of carry as a signal. In particular, quantamental information helps distinguish various causes of carry. A relevant example is a distinction between the impact of growth versus inflation differentials, since the former is typically a positive signal, but the latter is not. Another example is the distinction between implicit subsidies and standard risk premia, since the former is almost always a benefit, while the latter depends on the risk it insures.

Here, quantamental indicators are macro-fundamental real-time series that record the latest published information on economic states, such as growth and inflation measures, across countries. In particular, this post uses daily quantamental indicators of the J.P. Morgan Macrosynergy Quantamental System or “JPMaQS”. These indicators are daily information states based on concurrently available vintages of economic data series and are suitable for strategy backtesting.

How to enhance carry signals

This post focuses on the adjustment of FX carry by economic performance differentials. Economic performance is measured by output growth differentials and labour market performance differentials. This is just an example of quantamental enhancement. Other valid adjustment factors would include external balances, international investment positions, or economic overheating signals.

We consider two types of adjustment:

  • Modification reduces and enhances the original carry signal but does not override it by changing its sign.
  • Balancing adds to the original carry signal to give carry and quantamental information at pre-assigned (here equal) weights.

Upfront all carry measures have also been adjusted for short-term inflation expectations to obtain real or inflation-adjusted FX carry. Inflation expectations are taken from JPMaQS and are based on a formula that considers effective inflation targets and recent inflation performance. Inflation adjustment is a common-sense transformation that makes carry between high- and low-inflation countries more comparable. The mechanics and importance of this adjustment have been shown in a previous post and will not be discussed here.

Economic performance adjustment is applied to two types of carry signals that are realistically tradable:

  • Volatility-targeted real carry: The signal is a 5-day rolling median of inflation-adjusted FX carry on a forward position that is scaled to target a 10% annualized standard deviation of returns on the underlying risk capital. The targeting is based on recently realized volatility of the forward contract using an exponential lookback window with a half-time of 11 days. Volatility targeting serves two essential purposes: it balances the exposure across currencies and contains the risk of the overall portfolio. Without volatility targeting or some other forms of risk control carry strategies are not practical, allowing the concentration of risk in a few currencies and outsized PnL swings in crisis time. Positions are rebalanced at the end of each month. Also, a maximum leverage ratio of 5 (of implied notional to cash position) has been imposed. The latter also serves to make the carry signal more realistic for practical trading.
  • Hedged real carry: Again, the basis for a contract-specific signal is a 5-day rolling median of inflation-adjusted FX carry. However, now the carry is calculated on a position that is hedged against the influences of global directional market risk in order to focus strategy performance on idiosyncratic currency features and to (partly) immunize it from events in other markets. The global directional risk basket contains equal volatility-weighted positions in equity index futures, CDS indices and FX forwards. For details see the related page of the JPMaQS documentation site. The carry of that basket is multiplied by the hedge ratio of the FX contracts and subtracted from the FX carry.N.B.: Hedge ratios are calculated based on historical “beta”, i.e. rolling OLS regression coefficients of past forward returns with respect to global directional risk basket returns. The estimate uses two regressions. One is based on monthly returns with an exponentially-weighted lookback of 24 months half-time. The other is based on daily returns with an exponentially-weighted lookback of 63 trading days. The usage of the two lookbacks strikes a balance between timeliness of information and structural relations

The above carry metrics and related position returns have all been taken from JPMaQS. For the below analysis, we use FX forward contracts of 26 developed and emerging currencies against their dominant benchmarks, which is typically USD, except for European currencies, which trade either mainly against EUR or against both (GBP, RUB and TRY). The sample period is 23 years, 2000 to 2022. For a full list of currencies and symbols used see Annex 1 at the bottom of the post. Not all markets were properly functioning during the sample periods we exclude periods of inconvertibility, illiquidity, and tight exchange rate pegs.

Modified carry signal: the basic idea

Modified carry is a signal that preserves carry as the dominant signal, with all its advantages and faults, but manages the strength of the signal strength by using macro-quantamental information. This is accomplished through a modifying coefficient.

Technically, modification is performed in two steps.

  1. We calculate a metric of difference between a quantamenal indicator, say relative growth, and the carry signal. For this purpose, both are first converted to z-scores around logical neutral values beforehand. In order to de-emphasize large outliers, the scores are winsorized (limited by a boundary) at 4 standard deviations. Then, the z-score difference is taken.
  2. We transform this difference, which can be positive or negative, into a modification coefficient, with values between 0 and 2. A value of zero means that the carry signal is completely devalued because of its inconsistency with the fundamental signal. A value of 2 means that the carry signal is doubled because the fundamental signal is even much stronger that the carry signal alone, either in a positive or negative direction.

Mathematically, the transformation from z-score difference to modification coefficient is accomplished by using the former as an argument of a logistic function.

The formula for the modification coefficient (coef) in terms of the z-score difference (zsd) is:

coef = 2 / (1 + exp( – zsd))

This logistic (or sigmoid) function reaches 0 when the z-score difference hits its most negative (- 8 standard deviations) and 2 when the z-score difference reaches its most positive (+ 8 standard deviations). Moreover, the shape of this function implies that a 2 standard deviation difference between the carry score and the performance score reduces the carry signal by 75%. Similarly, a 2 SD difference between the performance and the carry scores increases the carry signal by 75%. The function has not been optimized in any way but uses unit parameters. Optimization would be the domain of statistical learning and could increase performance, but is not required for the below proof of concept.

The multiplication of the coefficient depends on the sign of the carry signal, because strong quantamental scores should increase positive signals but reduce negative signals. For a positive carry signal the carry is simply multiplied by the coefficient. For a negative signal the coefficient is subtracted from 2 and then carry is multiplied by this difference. The relation between modified carry signal (crm)  and outright carry signal (crr) can be summarized in Python lingo:

for crr > 0:

crm = coef * crr


crm = (2 – coef) * crr

As a basis for modification, we use the quantamental indicators of relative economic growth and relative labour market performances.

Relative economic growth

  • Relative intuitive GDP growth: This is the difference between quantamental indicators of the estimated GDP growth trend in the reference currency area and the natural benchmark area, i.e. the U.S. or the euro area. Growth trend here means the latest estimable percent change over a year ago in 3-month moving averages (to mitigate monthly volatility). It is based on JPMaQS technical intuitive GDP trends, which are sequential real-time estimates based on regressions that use the latest available national accounts data and monthly-frequency activity data. See the relevant documentation on the JPMaQS site.
  • Relative industrial production growth: This is the difference between quantamental indicators of reported industrial output trends in the reference currency area and the natural benchmark country. Production trend is again measured as % over a year ago in 3-month moving averages. Industrial production focuses on tradable goods, for which the exchange rate is particularly important. See also the related documentation on the JPMaQS site l

Relative labour market performance

  • Relative employment growth: This is the difference between quantamental indicators of reported employment trends in the reference currency area and the natural benchmark country. Again, the growth trends are measured as % over a year ago in 3-month moving averages. In some countries, employment data are only available at a quarterly frequency and those values are used instead of 3-month averages. See the related documentation on the JPMaQS site.
  • Relative unemployment gaps: This is the difference between quantamental indicators of reported unemployment gaps in the reference currency area and the natural benchmark country. An unemployment gap here means the difference between the latest unemployment rate, seasonally adjusted and as 3-month rolling average or quarterly values, and its 5-year moving average. It is put in negative terms, as low unemployment means economic strength, and, unlike employment growth, is a measure of labour market tightness. See the relevant documentation on the JPMaQS site.

All relative economic performance indicators are being z-scored, i.e. divided by standard deviations around their zero values on a rolling basis. This means that at each point in time we only use past information. Standard deviations are re-estimated based on the overall panel of 26 currencies and at a monthly frequency at the end of each month. The scores are winsorized at 4 standard deviations to mitigate outliers, which are extreme values, typically related to economic disruptions or statistical distortions, and can be seem in some countries of the above panel. Then we calculate z-score differences of quantamental indicators and carry, as explained above.

For easier viewing of results, we combine the modification coefficients for growth and labour market performance and for overall economic performance. Combining here means averaging the coefficients, except for periods where only one coefficient could be calculated.

Remember that the actual adjustment is dependent on both the sign and the magnitude of the carry signal, and – hence – can be quite different for unhedged and hedged carry, if they have different signs. For example, a strong growth performance increases a positive real carry signal but would reduce a negative signal.

Modified carry signal: evidence of benefits

Below we simulate performance statistics for real carry strategies that rebalance positions on a monthly basis at the beginning of each month based on the signal at the end of the previous month and with a trading slippage of one working day. The signals are all normalized and winsorized at 4 standard deviations. We do not incorporate trading costs, as those depend on position sizes, but differences in trading costs between outright and modified carry strategies are unlikely to be significant, as signal fluctuations have been roughly similar.

Although carry modification never affects the direction of FX forward positions, all modifications of vol-targeted real carry signals lead to significantly higher value generation.

Modifying vol-targeted real carry

A vol-targeted real carry strategy takes volatility-targeted positions across all tradable FX forwards markets at a monthly frequency. For overall strategies with similar PnL volatility, the modification would mainly change the relative strength of signals across currencies.

Note that “straight lines” in the below charts represent periods where a market was untradable and so signals were not calculated for the days between the beginning and end of the disruption period. No positions could be taken during these times.

The modification does not affect the accuracy (ratio of the correctly predicted signs of subsequent returns) of monthly currency-specific signals, which is 54.6%. However, the Pearson correlation coefficient between signals and returns increases from 4.2% before modification to 7% after modification, using an average economic performance modifier.

More importantly, simulated PnLs of modified vol-adjusted carry strategies are substantially better. Sharpe and Sortino ratios increase from 0.23 and 0.37 respectively without modification to 0.6 and 0.91 using the average of growth and labour market modification. This means volatility-adjusted returns have more than doubled thanks to modification. For labour market modification alone the Sharpe ratio would have been just below 0.7.

Modifying hedged real carry

A hedged real carry strategy takes both FX forward and hedge basket positions for trades across all tradable FX forwards markets at a monthly frequency. As for vol-targeted carry, modification changes mainly relative signal strength, but also seems to enhance signal stability, which suggests that it will probably save some transaction costs. Hedged carry alone has been more prone to outliers due to instability in estimated hedge ratios.

Again, monthly accuracy is unaffected and 54% for both unmodified and modified signals. The correlation coefficient of signals with subsequent monthly returns increases from 6.6% without modification to 7.7% with growth and labour market modification.

The hedged real carry strategies generally produce higher volatility-adjusted returns. Nevertheless, modification still increases the hedged carry strategy’s Sharpe and Sortino ratios from 0.55 and 0.82 to 0.7 and 1.05. Thus modification would have increased vol-adjusted returns by about a quarter. As explained below, our simple balancing of hedged carry is conceptually a bit flawed, as it does not consider the costs of the hedge.

Balanced carry signal: the basic idea

The purpose of carry balancing is to calculate trading signals that consider both carry and fundamental indicators at pre-defined weights. Thus, balanced carry does not necessarily cling to carry as the dominant strategy characteristic and can lead to positioning that is opposite to simple trading strategies.

Here we simply equalize the carry and fundamental influences. In principle, the weights of these two could be optimized sequentially, but for the proof of concept of value enhancement of trading strategies by means of quantamental balancing the simplest version has more credibility. Therefore, the empirical results should not be seen as the best value that can be accomplished with a balanced signal.

The basic quantemantal z-scores are the same that are used for modification. This means we have again two relative economic growth and two relative labour market performance z-scores. For the empirical analysis we combine the scores into growth, labour and real carry z-scores. Combination here means averaging of the constituent scores, except when one is missing for a country and the group score is based only on the remaining indicator. We also define an economic performance z-score, which is simply the average of the growth and labour z-score.

Balanced carry signal: evidence of benefits

Balancing carry also leads to better strategy performance. Indeed, it more than triples the returns of a vol-adjusted carry strategy. The improvement is less impressive for the hedged strategy, however. This plausibly reflects that the economic performance scores interfere with the incorporation of directional hedging implied in the signal.

Balancing vol-targeted real carry

Balancing changes both the magnitude and direction of signals. Thus, it has a more profound effect on the overall characteristics of a carry strategy, effectively mixing it with a complementary signal.

Balancing slightly improved the monthly accuracy of the vol-targeted real carry signal from 54.6% to 55.6%. Its impact on correlation was much stronger. The Pearson correlation coefficient increases from 4.2% for the outright vol-adjusted carry signal to as high as 9.6%.

Also, PnL performance statistics substantially improve through balancing. Sharpe and Sortino ratios rise from 0.23 and 0.37 respectively to 0.8 and 1.21. This means volatility-adjusted returns increase more than three times through balancing.

Balancing hedged real carry

Again balancing affects both the magnitude and direction of the carry signal.

Balancing hedged carry leads to a slight increase in monthly accuracy from 53.9% to 54.2% for an average of the growth and labour market score. The Pearson correlation coefficient of the signal with subsequent returns would increase from 6.6% for the outright hedged real carry signal to 7.8% for the balanced hedged carry signal.

PnL performance metrics improve only slightly as consequence of balancing. The Sharpe and Sortino ratios increase from 0.55 and 0.82 for the outright hedged carry signal to 0.6 and 0.88 for the balanced one. An apparent issue is that the balancing interferes with the efficiency of the hedging. While the hedged carry considers the costs of the hedge, the quantamental z-score does not. This means that, relative to the pure hedged real carry strategy, the balanced real carry systematically increases the weight of positions with high hedging costs, such as longs in currencies with high sensitivity to global market risk. Principally, this could be avoided by balancing the carry measure before incorporating the hedging cost. However, this requires significant model enhancement, which is beyond the scope of this post.

Annex 1: Currencies and tickers used in the post

The currency names are in alphabetical order: AUD (Australian dollar), BRL (Brazilian real), CAD (Canadian dollar), CHF (Swiss franc), CLP (Chilean peso), CNY (Chinese yuan renminbi), COP (Colombian peso), CZK (Czech Republic koruna), GBP (British pound), HKD (Hong Kong dollar), HUF (Hungarian forint), ILS (Israeli shekel), JPY (Japanese yen), KRW (Korean won), MXN (Mexican peso), MYR (Malaysian ringgit), NOK (Norwegian krone), NZD (New Zealand dollar), PEN (Peruvian sol), PHP (Philippine peso), PLN (Polish zloty), RON (Romanian leu), RUB (Russian ruble), SEK (Swedish krona), SGD (Singaporean dollar), THB (Thai baht), TRY (Turkish lira), TWD (Taiwanese dollar), ZAR (South African rand).


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