Which FX Valuation Models Work Best?

While most markets like equities and bonds have well-established valuation models, FX markets often baffle people. What anchors the value of a currency? Well, there are a number of valuation approaches: Purchasing Power Parity (PPP), Behavioural Equilibrium Exchange Rate (BEER), and the Macroeconomic Balance (MB). But which is best? A new ECB paper, The predictive power of equilibrium exchange rate models, puts these three to the test. It finds that the simplest, PPP, is probably the winner, while the more complex and much favoured MB is the least useful.

The Three Models in Detail

Purchasing Power Parity (PPP)

PPP is the simplest and most enduring FX model. It states that currencies should move in a way that neutralises changes in price indices (inflation) between countries.

PPP is typically estimated for a currency by taking the average of the real exchange rate over a historical period (the sample). If today’s real exchange rate is above or below that average, then the currency is deemed overvalued or undervalued respectively.

In this paper, the authors apply the Consumer Price Index (CPI) to the spot exchange rates to compute the real exchange rate between 1975 and 2018. And rather than looking at bilateral exchange rates, they calculate trade-weighted exchange rate baskets. They find that the sample average for most currencies is stable except for the Swedish krona (SEK), Swiss franc (CHF), and the New Zealand dollar (NZD) (Figure 1).

As for the latest valuations, their estimates suggest that the USD, NZD, CHF, and Australian dollar (AUD) are overvalued. Meanwhile the SEK, Japanese yen (JPY), Norwegian krone (NOK), British pound (GBP), and Canadian dollar (CAD) are undervalued. The euro (EUR) is moderately overvalued (Figure 1).

Figure 1: PPP Based Equilibrium Exchange Rates

Source: Page 32, The Predictive Power of Equilibrium Exchange Rate Models

Behavioural Equilibrium Exchange Rate (BEER)

PPP implicitly assumes that the real exchange rate is mean-reverting around the sample average. But at least in theory, there are reasons that the real exchange rate could exhibit a trend. FX models that attempt to find economic indicators explaining these trends are typically called Behavioural Equilibrium Exchange Rate (BEER) models.

The most common economic indicators used are productivity (GDP per capita used in this paper), net foreign assets, and terms of trade (export prices divided by import prices). Increases in the three variables would normally lead to a higher “equilibrium” or valuation for the currency.

The authors run regressions with the exchange rate on one side and these variables on the other side to arrive at the equilibrium values. They find that productivity and terms of trade have the expected sign (positive) but not net foreign assets. Moreover, they find that as time goes in their sample, the size of the coefficients for all three variables declines, which suggest BEER model estimates would start to converge to PPP estimates.

As for the latest estimates (end-2018), they find that USD, CHF, EUR, and NZD are overvalued, while SEK, GBP, NOK, AUD, and CAD are undervalued. JPY is about fairly valued.

Figure 2: BEER Based Equilibrium Exchange Rates

Source: Page 34, The Predictive Power of Equilibrium Exchange Rate Models

Macroeconomic Balance (MB/FEER)

MB, or the fundamental equilibrium exchange rate (FEER) model as it is elsewhere known, is an altogether different approach to FX valuation. Here we need to solve a system of equations to find the level of the real exchange rate compatible with the dual goal of achieving internal and external balance. Put simply, what move in the exchange rate could bring the current account back into “equilibrium”?

To do this, you must work out what the level of the current account would be if the output-gaps in each country were closed. We would also need to determine a target current account, which would be the “equilibrium” level. Finally, we would need to estimate the relationship between real exchange rates and the current account. This means estimating import and export elasticities to the exchange rate. Armed with this knowledge, we can determine how much of an exchange rate move is required to move from the output-gap adjusted current account to the target “equilibrium” current account.

In the paper, the authors simply use the current value of the current account rather than the output-gap adjusted current account as the starting point. For the target current account, they use a forecast for the current account based on productivity, net foreign asset, and terms of trade (they run a regression for this). Then, for the relationship between the exchange rate and the current account, they use import and export shares of GDP (for the size of the trade sector), assuming the export elasticity is zero (exporters take the world price) and the import elasticity is one.

The resultant FX valuation estimates are much more volatile than either the PPP or the BEER versions. In some instance they are even more volatile than the real exchange rate itself. As for the latest values, they show that CAD, GBP, and NOK are overvalued, and that EUR is undervalued. USD, AUD, JPY, NZD, and SEK are fairly valued.

Figure 3: MB Based Equilibrium Exchange Rates

Source: Page 36, The Predictive Power of Equilibrium Exchange Rate Models

Predictive Power of the Models

The big question is which models are best to forecast currencies? The authors approach this question this using in-sample and out-of-sample data. They look at four different time horizons: 3 months, 1 year, 3 years, and 5 years. For the sake of simplicity, I focus on their 3-year results.

In-sample

They find that across all currencies 60% of the PPP models’ mis-valuations are corrected within three years, 72% of the BEER mis-valuations, and 26% of the MB’s. On that metric, BEER wins, closely followed by PPP, and MB lags far behind.

For individual currencies – PPP is the winner for GBP and NOK; BEER is the winner for AUD, CAD, EUR, JPY, NZD, SEK, and USD; MB has no winners

Out-of-sample

Here, the authors compare the cumulative forecast errors of the model using out-of-sample model estimates. They compare these to a random walk model – i.e. using today’s estimate as the best forecast for the future (a bit like tossing a coin). They see how much better the models can perform relative to the random walk model.

On this metric, they find that the PPP and BEER models are joint winners, while MB loses out again. On an individual currency basis, they find that the BEER model does best for commodity currencies (AUD, NZD, and CAD) as well as for JPY (a major oil importer), while PPP does best for USD, GBP, EUR, and NOK. MB does best for SEK, though only marginally outperforms the random walk (Figure 4).

Figure 4: Outperformance vs Random Walk

Source: Macro Hive

Bottom Line

The results conform to the work I’ve done over the years. For valuations, simplicity is best. PPP is the best bet in most cases except for commodity-affected currencies where BEER outperform. But the more complex (and much loved by economists) MB (or FEER) models are terrible for forecasting. This is unsurprising given the number of assumptions and estimates required for them. MB’s only consolation is that it may have some predictive power for the Swedish krone – the one currency that most valuation models fail on.