Exchange Rate Forecasting on a Napkin

This paper by Michele Ca’Zorzi and Michał Rubaszek claims to offer a formula for exchange rate forecasting so simple it can be calculated on the back of a napkin. The ‘back of a napkin’ adage is commonly used as a qualifier for trading strategies: if it is too complicated to write on the back of a napkin,  it is probably overfit, which is why this article piqued my interest. As an FX trader, a simple formula to forecast exchange rates is attractive but seems too good to be true.

By forming a model using two regularities in FX markets of advanced countries with flexible regimes, Ca’Zorzi and Rubaszek claim to have solved the in-sample vs. out-of-sample performance discrepancy of previous exchange rate predictive models. These regularities are 1) the fact that PPP (purchasing power parity) holds over the long run, and 2) the nominal exchange rate drives adjustment of the real exchange rate in flexible regimes.

The model identified as the strongest is a half-life (HL) model which assumes that real exchange rates are mean-reverting and that relative prices do not play a role in this adjustment. Using this model, exchange rate prediction involves two simple steps: 1) identify the approximate deviation of the real exchange rate from its sample mean, then 2) take the nominal exchange rate and use the appropriate time period adjuster to determine at which point the real exchange rate is in reversion to its mean. The authors note that the nominal exchange rate reverts 10% during the first six months, 20% in the first year, and exactly 50% after a period of 3 years. The HL model overwhelmingly outperforms a random walk model which is traditionally used as a benchmark for exchange rate reversion.

Read the full paper by Michele Ca’Zorzi and Michał Rubaszek, published as part of the ECB Working Paper Series.

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