# Pairs Trading Strategy: 6-Month Analysis Of The EUR/USD And GBP/USD

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by: Discount Fountain

## Summary

With cointegration existing between the EUR/USD and GBP/USD, arbitrage opportunities may exist between these currency pairs.

Over the last 24 trading days, a long EUR/USD - short GBP/USD strategy would have proven profitable.

The 10-day standard deviation of the EUR/USD and GBP/USD have recently reached their highest levels in the past six months.

In this article, I am going to describe how a forex arbitrage trading strategy across both the EUR/USD and GBP/USD can be executed using the principles of stationarity and cointegration. When two time series are cointegrated, it means that their mean values may deviate in the short-term but will ultimately converge in the long-term. If two time series show cointegration, this means that while the two time series are non-stationary, a linear combination of these time series are stationary. By the very nature of a time series, we expect that if two time series are cointegrated, then the linear combination must be stationary since the mean, variance and autocorrelation of the time series are consistent.

However, there will invariably be periods where the trends of two time series can diverge, and this creates a potential profit opportunity. Here, I demonstrate how such a trading strategy could have been used to make profit by taking a long position on the EUR/USD and a short position on the GBP/USD.

Stationarity and Cointegration Testing

Using 179-day trading data expressed in ln (natural logarithmic) form, we first wish to test for stationarity across both real-time and first-differenced datasets. From the results below, we see that while the Dickey-Fuller test does not reach the 5% level of significance for real-time data, it is significant in both cases when the data is first-differenced. This means that we have a cointegrated time series according to the Engle-Granger procedure.

Sources: Author's Calculations

Additionally, a scatter plot of residuals shows a clear trend in real time, whereas our residuals are random when we use first differences:

Sources: Author's Calculations

In running our OLS regression on ln data, we see that for every 1% change in the GBP/USD currency pair, we have a 2.11% change in the EUR/USD currency pair.

Source: Author's Calculations

This marks an arbitrage opportunity, because we see that a converging time series shows a significant deviation in returns. Over the past 24 trading days, we can see from the graph below that the 10-day standard deviation of the EUR/USD and GBP/USD reached their highest levels in the past six months.

Source: Author's Calculations

Up till this point, the EUR/USD had been down -17.85% since the beginning of the time period and the GBP/USD had fallen -0.16%. With the assumption that the two currencies must eventually converge to a similar level, a possible trading strategy over the past 24 days could have been long EUR/USD and short GBP/USD. At the time of writing, the EUR/USD had appreciated 3.61% and the GBP/USD had depreciated -0.16%. As we can see, we would have made profit on both sides of the trade because we are making the assumption that as standard deviation decreases, the returns on the two currencies will converge.

I will be quite interested in seeing how this strategy plays out going forward. With the UK General Election approaching, the consensus is that with the prospect of a hung parliament we will see the GBP depreciate further against the USD. According to this model, we can expect the EUR/USD to appreciate; assuming low standard deviation as the two currencies must converge. However, we could also find that standard deviation increases for the month of April, at which point any appreciation in the GBP/USD after the election could be matched by depreciation in EUR/USD as the two series converge. On the assumption that the GBP/USD will decrease this month and begin an increase after the election, a possible trade based on this data is long EUR/USD - short GBP/USD for the month of April and short EUR/USD - long GBP/USD for the month of May.

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