Trading Long-Run FX Mean Reversion

May 2, 2023

Core Summary

  1. We predict medium-to-long-term equilibrium exchange rates for developed currencies and determine their deviation from fair value levels. We use a modified Behavioral Equilibrium Exchange Rate model (BEER) proposed by UniCredit in a 2013 research paper. We find that their reported results still hold since publication. A full pdf-report of our methodology and findings can be downloaded here.

  • We introduce systematic value strategies that are able to exploit fair valuedeviations and consistently achieve high Sharpe ratios out-of-sample.

  • We find that the dollar is overvalued in general. The more than a decade-long bull market in the Greenback has resulted in most currencies trading on the cheap side versus the Buck. The Scandies (NOK & SEK) are the most undervalued currencies. The Eastern European CZK seems most overvalued. (March ‘23)

1 Introduction

Future trends in foreign exchange rates are important to many different market participants. For instance, pension funds, insurance companies, and corporate clients often maintain significant holdings in foreign assets and actively seek to mitigate their currency risk. Market participants can use a variety of ways to estimate the long-term fair value of a currency.2In a research paper published in 2013, UniCredit performs an econometric analysis using a BEER (Behavioral Equilibrium Exchange Rate) model between exchange rates and a number o fmacroeconomic variables. They show that the deviation between model prediction and actual exchange rate helps forecast future price direction for G10 and CEE3 FX in the medium-to-long run. In this short study, we perform a BEER value analysis on the same currency universe for the period spanning April 1996 to March 2023. First, we apply a rolling fixed-effect panel regression using relative gross fixed capital formation as a share of GDP, and differentials of terms of trade, nominal interest rate, inflation, and productivity. We propose two promising value strategies that aim to exploit the BEER value predictions. Second, we replicate UniCredit's study by performing panel regression on the entire data period. We discover their findings still hold ten years after publication.

2 Data description

Our asset universe is comprised of G10 and CEE3 FX. We acquired monthly observations for 12 USD-denominated pairs spanning the period from April 1996 to March 2023. Note that we were only able to retrieve CEE3 data starting from January 2001. Table 1 summarizes our data:

Table 1. Summary of the selected asset universe.

Next, we outline our choice for macroeconomic variables. These were selected based on economic intuition and data availability. We provide a more thorough examination of our dataset in the pdf-version.


Log of the exchange rate. All exchange rates are expressed in dollars, for ease of interpretability and analysis. The quoted currency is USD, the base currency is the currency of the foreign country. So, a currency pair is always expressed in the number of units of dollars to one unit of the foreign currency.


Log of the relative terms of trade. This is the ratio of export to import prices. It is computed as the ratio of foreign terms of trade to terms of trade of the USA. It captures developments in the prices of exported and imported goods. Generally, a rise in this ratio would be supportive of a currency as importers demand less foreign FX, and foreign demand for domestic currency increases to cover higher export prices. Data is from Citigroup.

Log of relative gross fixed capital formation as % of GDP. Gross fixed capital is a measure for investment appetite in a country. Higher levels should indicate more investment opportunities. On average, higher relative levels should be supportive of the currency if some of the investments are financed by foreign demand. Data sourced from IMF.

Yield differential: 10y government yield foreign country minus 10y government yield USA. On average, countries with a positive yield differential should see a more positive impact on their nominal currency as speculative flows support the currency.  Data sourced from both Bloomberg and IMF.

Log of the relative CPI-index. The inflation differential is a measure of competitiveness.  Countries with open economies and lower inflation differentials have cheaper goods and services. On average, lower relative inflation should be supportive of the currency. Data sourced from IMF.

Log of relative productivity. The Balassa-Samuelson effect suggests that regions with high productivity experience support in their real exchange rates. Relative productivity is the labor productivity index divided by the labor productivity index in the USA. On average, higher relative productivity should be supportive of the currency. Data sourced from OECD.

In order to avoid lookahead bias (or data leakage) in our experiments, we shifted macroeconomic data forward in time by one month to create a conservative reporting lag.

3 Methodology and Findings

Unicredit’s research showed that fixed-effect panel regression is an effective tool for predicting future price direction for FX. We re-examine their BEER model findings on an extended data period using two different approaches:

  • First, we assess whether out-of-sample predictions - made by a rolling fixed-effect panel regression through time - can be used to devise sound systematic FX trading strategies.
    This is outlined in Section 3.1 of the full pdf-paper.
  • Second, similar to UniCredit in 2013, we use a fixed-effect panel regression and vector error correction model on the entire data period to assess whether the in-sample residuals (or price deviations from the predicted fair value) predict future mean reversion in exchange rates. This is outlined in Section 3.2 of the full pdf-paper.

3.1 BEER-Driven Systematic Value Strategies

We base our value strategies on predictions made by rolling (expanding) fixed-effect panel regressions. The first iteration uses a training window of five years after which it is continuously expanded by one month. For each iteration, we take the last month’s difference between the actual exchange rate and the predicted fair value. We then compute the rolling z-scores of these deviations using a lookback of five years. Note that this means that data for strategy implementation only starts in April 2006 for G10 currencies and January 2011 for CEE3 currencies. Window length was chosen arbitrarily and not optimized.

a) Strategy on Individual currency pairs (no portfolio):

  • Each month, long (short) currency when it is undervalued (overvalued) based on the z-score for that month. I.e. long EURUSD when the z-score is lower than minus one.
  • Hold position until the z-score crosses the value of zero. 

Each currency might have an optimal z-score threshold to drive this strategy. We ran the strategy in-sample for the period until 2014 (ex). The optimal in-sample z-thresholds per currency are outlined in Appendix 5.2 in the pdf-paper. The following table shows the out-of-sample results using in-sample optimal thresholds for the period spanning January 2014 to March 2023.

It seems that the model is able to predict when a currency is under- or overvalued. We were able to achieve positive Sharpe ratios for 6 out of 8 currencies that had trade signals out-of-sample. Certain currencies were not traded as their z-scores were not extreme enough during the evaluation period. Note that the inferior results in NOKUSD could have been avoided as the strategy performed poorly in-sample as well. In reality, this would have led to not deploying the strategy on this currency. The following figure details trades placed by the strategy on HUFUSD for the entire out-of-sample period:

Figure 1. Strategy one trades and returns out-of-sample (CHFUSD).

b) Currency portfolio strategy: long-short

Instead of trading individual currencies, the second strategy considers a currency portfolio where we long (short) the top three most undervalued (overvalued) currencies based on their z-scores. Rebalances happen each month. The following figure shows the equity curve for this simple strategy from 2014 to March 2023. The obtained Sharpe ratio equals 0.71.

Figure 2. Strategy equity curve (long/short FX value) out-of-sample vs long EURUSD.

The currency allocations through time are fairly steady and can be found in the next figure:

Figure 3. Portfolio weight allocations through time.

Note that the three most overvalued currencies today seem to be PLNUSD, CZKUSD, and CHFUSD. The three most undervalued currencies are SEKUSD, NZDUSD, and NOKUSD. At this point, we know that currencies tend to mean-revert differently under the BEER model. The strategy could therefore be extended to deal with individual currency peculiarities to optimize entries and exits.

3.2 BEER-Predictions and FX Mean-Reversion

We estimate the long-run equilibrium fair value for each currency pair using fixed-effect panel regression together with cointegration tests. Subsequently, we tested (using a vector error correction model) if deviations from fair level lead to significant future movements in the actual exchange rate. We refer to Appendix 5.3-5.6 of the pdf for implementation details.

We find no evidence of significant mean-reversion on monthly time-frames, but find very significant evidence of mean-reversion on time-frames longer than four months. For a given deviation from fair-value (a shock), we find that a currency on average:

  • mean-reverts around 7% of the shock in the next quarter.
  • mean-reverts around 35% of the shock in the next year.
  • mean-reverts around 67% of the shock in the next two years.
  • mean-reverts around 100% of the shock in the next four years on average.

In table 3 we report the deviations versus long-term equilibrium fair-value levels for our 12 currencies today. The deviation is expressed in both percentage and z-score. A positive deviation points to potential overvaluation versus fair value and vice versa. The z-score illustrates the normalized magnitude versus history. The currencies are ranked on z-score deviation.

Tabe 3. FX deviation from fair value


In figure 4, we provide an example chart of EURUSD which visualizes: 

  • The actual fx-level versus the long-run equilibrium fair value (in-sample and out-of-sample).
  • The percent deviation versus fair value.
  • The deviation in z-score.

Figure 4. EURUSD exchange rate, BEER predictions, and fair value deviations through time.

Appendix 5.7 in the full pdf-paper contains the same chart for all other currencies

4 Conclusion

We computed long-term equilibrium levels for 12 developed currencies (G10+CEE3) using fixed-effect panel regression. The vector error correction model uncovers evidence of significant mean-reversion potential in the mid to long term. Visually eyeballing the charts will confirm this. This fortifies previously reported results from UniCredit's 2013 study.

We introduced two straightforward strategies that try to systematically exploit deviations in fair value. The first strategy trains a model for optimal in-sample z-thresholds per currency and tests out-of-sample. We discovered significant large Sharpe ratios for most currencies except two. The second strategy goes long (short) the three cheapest (three most expensive) currencies and rebalances monthly. This resulted in a Sharpe ratio of 0.7.

We note that for discretionary fixed income and global macro players, FX valuation alone should not be the only factor that determines positioning. It remains extremely important to add additional analysis by factoring in: 

  • Geopolitical analysis
  • Momentum, trend en sentiment (COT)
  • Central bank analysis (expected policy paths, guidance,…)
  • Carry versus volatility

However, currencies with large undervaluation might have the best potential if enough positive catalysts from above are present. In that regard market participants should closely watch the most undervalued currencies such as NOK, SEK, EUR, GBP, NZD for bullish signs and CZK for signs of bearish reversal.

An interesting research topic would be to analyze if BEER-models beat some of the other well-known cross-sectional value signals on currencies: deviations from FEER (Fundamental Equilibrium Exchange Rate), deviations from PPP (Purchasing Power Parity), and deviations from the REER (Real Exchange Rate).