FX forward-implied carry is a popular ingredient in currency trading strategies because it is related to risk premia and implicit policy subsidies. Its signal value can often be increased by considering inflation differentials, hedging costs, data outliers, and market restrictions. However, even then, FX carry is an imprecise and noisy signal, and previous research has shown the benefits of enhancements based on economic performance (view post here). This post analyses the adjustment of real carry measures by currency over- or undervaluation. As a reference point, it uses point-in-time metrics of purchasing power parity-based valuation estimates that are partly or fully adjusted for historical gaps. The adjustment is conceptually compelling and has historically increased the performance of carry signals across a variety of 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. It ties in with this site’s summary of implicit subsidies in financial markets.

## Common-sense modifications of FX forward-implied carry

Forward-implied foreign exchange carry is the annualized percent difference between spot and forward exchange rates, defined as the value of the local currency in units of a base currency. __FX carry is the theoretical return that is earned on a long position in the local currency if the spot exchange rate remains unchanged over the forward period__. Arbitrage usually aligns FX carry with the differential between local and benchmark short-term interest rates, a relation that is called “covered interest parity”. While this parity can at times be compromised (view post here) a positive carry for the local currency mostly means that local short-term interest rates are higher than in the base currency area.

This post uses FX carry metrics from the J.P. Morgan Macrosynergy Quantamental System (JPMaQS) for 25 developed and emerging market currencies since 2000 (view documentation here). The exchange rates that serve as a basis for the forward contracts are local currency against the “dominant benchmark”, i.e., the currency it is naturally trading against. Mostly, this is the USD, but for some European currencies, the reference currency is the euro, and for two currencies (GBP and TRY), an equally weighted basket of EUR and USD has been used; for the full list of currencies and tickers, see the Annex at the bottom of the post.

__FX carry is a popular and valid basis for trading strategies because positive interest rate differentials are related to risk premia and implicit subsidies__. For example, central banks often maintain high real local short-term interest rates and engage in FX interventions to reduce inflation and attract capital flows. Also, corporates and financial institutions in smaller, higher-risk currency areas often hold positions in international reserve currency assets as protection against funding pressure. Even if forward-implied carry deviates from the interest rate differential, this “FX basis” itself is typically indicative of risk premia or subsidies and, hence, valuable as a trading signal.

However, carry is a very “dirty” or “noisy” measure of such premia and subsidies. Hence a range of standard adjustments should be applied, some of which come “out of the box” from the JPMaQS database:

**Inflation differential adjustment**: It is most important to adjust the FX carry of differences in inflation expectations. Only real carry or real interest rate differentials are plausible indicators of differences in policies and premia.__The practical challenge is to estimate inflation expectations point-in-time__. Neither inflation derivatives nor surveys offer reliable data history across many countries. Hence, JPMaQS provides real-time estimates of inflation expectations for various forward horizons based on a formula that uses (i) vintages or recent adjusted inflation and (ii) the estimated effective long-term inflation target of the monetary authorities (view documentation here). A critical assumption of this formula is that after adjusting past under- or overperformance, the inflation target always retains some credibility. If inflation expectations have become evidently “unanchored” and hyperinflation is a distinct possibility, the formulaic approach would not be appropriate. In this post,__we use JPMaQS’ measure of real carry, which is based on 1-year ahead inflation expectation differentials__.**Hedging cost adjustment**: Standard carry measures ignore differences in the “market beta” of currencies, i.e., sensitivities of global risk asset markets. Currencies with high beta should command higher premia and require a higher carry to be attractive propositions. Similarly, FX positions that are hedged against global market sensitivities can be more suitable for extracting value from FX premia alone. JPMaQS implements an appropriate adjustment by calculating carry of FX forward positions that are hedged against directional market risk. The latter is represented by a weighted basket of equity index futures, credit default swap indices, and FX carry currencies (view documentation here). The hedging cost of an FX forward position is the carry of the hedge basket times the beta of the positions (view documentation here).__Carry excluding this cost conceptually better indicators of non-directional premia and subsidies__, albeit at the expense of adding estimation risk.**Smoothing and winsorization**: JPMaQS records carry at the end of the local trading day. Sometimes, these records can be distorted by a single trade or reflect market conditions that compromise the information value of the data or do not allow trading at the recorded price. Therefore, we smooth all daily FX carry series in the form of a 5-day moving median and contain the absolute value of real carry at 25%, positive or negative.**Convertibility and liquidity requirements**: We exclude episodes when individual currencies were temporarily not convertible, flexible, or liquid enough for trading in size for all analyses and backtesting (as we must for live trading). This is done based on JPMaQS tradability and flexibility indicators (view documentation here).

The below panel shows the smoothed history of real FX carry, with and without hedging cost adjustment. __Real carry has been highly autocorrelated with limited volatility, cyclical fluctuations, and longer-term trends__. Adjusting for hedging costs greatly reduces the carry of many emerging market countries and increases volatility, which reflects volatility in beta estimates.

The importance of common-sense adjustments for the success of FX carry strategies has been illustrated in a previous research note (view post here). The benefits of further quantamental adjustments, for example, by considering economic performance differences, have also been illustrated for simple cases (view post here). This post goes a step further and considers exchange rate valuation adjustment.

## Overvaluation adjustment based on purchasing power parity

On its own, real FX carry disregards whether a currency is apparently over- or undervalued. This is a critical conceptual flaw. A high carry for an undervalued currency is more likely to indicate risk premia and central bank subsidies than a high carry for an overvalued currency. The latter combination often indicates a downside skew in the risk around a currency’s value.

There is no simple standard for measuring FX value but purchasing power parity (PPP) is a popular starting point. PPP is an economic theory that suggests that in the absence of trade barriers, identical goods or services should have the same price when expressed in a common currency. Therefore, __PPP proposes that exchange rates between two currencies should adjust to close price differentials for a given basket of goods and services__.

In practice, __PPP exchange rates are local currency prices in USD that equate the value of price baskets across currency areas.__ They are sometimes used as reference for long-term equilibrium exchange rates, following the “law of one price”. Technically, they are ratios of prices in the local currency area to prices in the United States. There are two official sources of estimation of annual PPP exchange rates: the OECD for its member states and the World Bank for non-OECD countries. Methods and release conventions of the sources differ; more importantly, revisions can be huge.

Fortunately, __JPMaQS provides point-in-time information states of PPP exchange rates__ that combine annual official PPP exchange rate releases and CPI-based estimates of monthly changes up to the latest month for which CPIs have been released for both the local economy and the United States (view documentation here). Based on these estimated PPP exchange rates, JPMaQS also calculates PPP overvaluation ratios, i.e., ratios of the market-based USD value of the local currency and the PPP value.

For the purpose of adjusting carry by valuation, we transform these overvaluation ratios into suitable adjustment factors in four steps:

First, we translate the overvaluation ratios of the 25 currencies in our analysis to __overvaluation percentages, as % of the PPP value and against the dominant benchmark currencies__ rather than the USD alone. The below box-and-whisker chart shows the ranges of these valuation percentages and conveys a well-known reality: PPP-based overvaluation and undervaluation are persistent, and ranges of countries with different governance and stages of development may never overlap. Put differently, __the strict law of one price does not hold, even over multiple decades__. This makes intuitive sense, as nothing is perfectly tradable, and countries with lower productivity should have lower prices for local content, such as services.

Second, we adjust overvaluation ratios for long-term median values to account for structural differences in purchasing power. In particular, we calculate for each date a median overvaluation percentage since inception (typically early 1990s) based on available data up to that date and subtract this median from the concurrent overvaluation metric. The outright overvaluation and the long-term trailing medians are displayed in the panel below.

Looking at overvaluation relative to a long-term median removes the persistent directional bias of the indicator. However, this crude tackle of structural gaps disregards that, in the long run, there may be convergence for some countries. Hence, __we calculate both a full adjustment for the median and a partial (50%) adjustment__ and consider both in subsequent analyses. The partial adjustment leaves large persistent differences in the overvaluation estimates, but this finding is with hindsight and does not disprove the notion that, in the long run, there is some convergence trend across economies that share a common global economy.

Finally, we make plausible assumptions about how overvaluation affects a carry signal. It is based on the notion of medium-term partial correction for overvaluation. In particular, we assume that 50% of overvaluation is expected to be corrected linearly over the coming 3-6 years. This means we subtract either one-sixth or one-twelfth of the overvaluation from the annualized real carry metrics. Both versions are considered in subsequent analyses. The below panel shows smoothed real FX and the effects of adjustments for a 3-year horizon. The importance of valuation is greater for countries with modest carry size and volatility.

## Performance of simple real carry strategies with valuation adjustment

We estimate predictive relations and stylized PnLs for real carry signals. As targets of the analysis, we use generic JPMaQS FX forward returns (view documentation here). These returns assume that the trader takes positions in 1-month FX forwards at the beginning of a calendar month and rolls positions at the end of that month.

For the full panel of developed and emerging market currencies since 2000, real FX carry has been a highly significant positive predictor of FX forward returns, both at monthly and quarterly frequencies. Similarly, PPP-based overvaluation metrics have been significant (negative predictors), and hence, real carry metrics that have been adjusted for such overvaluation show a somewhat higher predictive correlation with returns than simple real carry.

We __estimate the economic value of enhanced FX carry strategies based on a standard naïve PnL methodology__ used in many previous research posts. This PnL is calculated for simple monthly rebalancing in accordance with the carry score, normalized, and winsorized at two standard deviations at the end of each month. The end-of-month score is the basis for the positions of the next month under the assumption of a 1-day slippage for trading. The naïve PnL does not consider transaction costs or compounding. For the chart below, the PnL has been scaled to an annualized volatility of 10%.

All real carry-based strategies have produced positive long-term PnLs. However, they have also been highly seasonal, with the 2000s up until the great financial crisis marking an exceptionally favorable period for both FX carry strategies. Since then, however, value generation has almost ceased.

All __valuation-adjusted PnLs have outperformed the simple real carry strategy__. Moreover, valuation-adjusted strategies proved less seasonal and, __unlike the unadjusted carry strategies, continued to produce positive PnLs in the 2010s and 2020s__. The long-term (24-year) Sharpe ratios of the valuation-adjusted carry PnLs ranged from 0.53 to 0.62 versus 0.47 for unadjusted real carry. The Sortino ratios of the valuation-adjusted carry PnLs registered between 0.80 and 0.96 versus 0.7 for unadjusted real carry. Also, the average correlation of valuation-adjusted PnLs has been lower with respect to the S&P500 returns and EURUSD returns.

## Performance of relative real carry strategies with valuation adjustment

An alternative application of the adjusted carry signal is for trades across small-country currencies rather than against the USD or EUR. This takes out some of the correlation within the overall portfolio by reducing the dependence on common USD- and EUR-specific influences and typically reduces the directionality of the portfolio. The__ trades use each local currency’s FX forward position against benchmark currencies, vol-targeted to 10% annualized, and against the 25-currency basket of these positions__. Vol-targeting makes position-related risk comparable across currencies.

The correlation of relative real carry with subsequent relative returns has also been positive and highly significant, if somewhat lower than in the directional case. As for directional real carry, any type of __valuation adjustment increases forward correlation strength__, whether measured in parametric or non-parametric terms.

The __returns of strategies based on valuation-adjusted relative real carry have been a lot stronger and more consistent than the performance of simple relative real carry__. The 24-year Sharpe ratios of the adjusted relative carry strategies range from 0.67 to 0.78 versus 0.48 for the unadjusted strategy. The Sortino ratios of the adjusted strategies reach 1.09-1.27, compared to 0.76 for their unadjusted benchmark.

## Performance of hedged real carry strategies with valuation adjustment

A final version of the real carry strategy uses the real carry adjusted for hedge costs (as explained above) as a signal to set up hedged FX forward positions, i.e., positions in portfolios with an FX forward versus benchmark currencies as the main leg and position in the hedge basket determined by the FX forward’s estimated beta up to the day as the secondary leg.

For the full panel of monthly or quarterly data, the forward correlation of hedged carry with subsequent hedged returns has generally been higher than for their unhedged counterparts and highly significant. The __adjustment for PPP-based overvaluation adds further to the strength of the predictive relation__.

Value generation, according to naïve PnLs, has been particularly strong for hedged positions. This reflects the partial immunization of trades against global market influence and, hence, the concentration on country-specific forces and performances. It should be noted, however, that hedged trades typically require higher leverage and incur greater transaction cost per unit value of risk than simpler carry strategy. The actual advantage versus unhedged trades depends a lot on position size and skill of execution.

__Valuation adjustment has further enhanced naïve PnL performance for most adjustment versions__. However, the benefit of adjustment has been less obvious than for the simple carry strategies. Sharpe ratios of valuation-adjusted strategies ranged from 0.64 to 0.87 versus 0.71 for the simple hedged real carry strategy. Similarly, the Sortino ratios for adjusted hedged carry have been between 1.0 and 1.32, compared to 1.09 for the unadjusted hedged carry strategy.

The more modest average incremental improvement through adjustment probably reflects two circumstances.

- First, hedging creates a target portfolio, and the concept of overvaluation does not apply to the hedge basket part of that portfolio. In other words. hedging waters down the relevance of the adjustment.
- Second, hedged carry strategies rely predominantly on the quality of the beta estimation, and the “simple” hedged real carry metric of JPMaQS is already a strong trading signal in its own right. Even if valuation adjustment gives it more solidity and consistency, it also dilutes the purity of the approach and makes the hedge ratio quality a bit less relevant.

The important lesson is that composite trading signals, while potentially powerful value generators, quickly become complicated, and the way to combine different aspects is an important area of quantamental strategy know-how.

Finally, __one can apply overvaluation adjustment to hedged cross-currency strategies,__ i.e., relative positions in the local currency forward versus the dominant benchmark and versus a 25-currency basket of these positions *and* hedged against global directional market risk. This means we apply hedged relative real carry with respect to hedged relative positions.

Once again, the __valuation-adjusted relative hedged carry signals outperform the unadjusted benchmark by modest margins__. The long-term Sharpe ratios of the adjusted strategies ranged between 0.76 and 0.89, compared to 0.74 for the unadjusted strategy. The adjusted Sortino ratios were recorded between 1.17 and 1.36 versus 1.11 for the unadjusted carry.

## Annex:

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), SEK (Swedish krona), THB (Thai baht), TRY (Turkish lira), ZAR (South African rand).