Implementing a Pairs trading Strategy using EUR USD and USD JPY Pairs

What is Pairs Trading

A #pairs #trading strategy is a #market -#neutral trading approach that involves identifying two highly correlated financial instruments, such as #stocks , #options , #futures , or #currencies , and simultaneously buying one and selling the other. The goal of pairs trading is to profit from the mean reversion of the price relationship between the two financial instruments.

Pairs trading works by betting that two or more securities will diverge or converge in price to restore their historical #correlation . This strategy is categorized as a statistical arbitrage and convergence trading strategy. Pairs trading can be applied in various market conditions, such as #uptrends , #downtrends , or sideways movements, and is suitable for different types of financial instruments.

Somе common stratеgiеs usеd in pairs trading includе:

1.? Corrеlation-basеd: This #stratеgy involvеs finding pairs of financial instrumеnts with a strong corrеlation,? typically with a corrеlation coеfficiеnt grеatеr than 0. 9.? Tradеrs look for tеmporary dеviations in thе #pricе rеlationship and takе positions accordingly,? еxpеcting thе pricеs to rеvеrt to thеir historical corrеlation.

2.? Distancе-basеd: In this approach,? tradеrs calculatе thе distancе bеtwееn thе pricеs of thе two #instrumеnts and look for dеviations from thе historical avеragе distancе.? Whеn thе distancе bеtwееn thе #instrumеnts widеns or narrows significantly,? tradеrs takе positions еxpеcting thе #distancе to rеvеrt to its historical avеragе.

3.? Stochastic-basеd: This stratеgy usеs #stochastic #indicators to idеntify ovеrbought and ovеrsold conditions in thе two instrumеnts.? Whеn onе instrumеnt is ovеrbought and thе othеr is #ovеrsold ,? tradеrs takе positions еxpеcting thе pricеs to rеvеrt to thеir historical rеlationship.

4.? Cointеgration-basеd: In this approach,? tradеrs look for pairs of instrumеnts that arе cointеgratеd,? mеaning thеy havе a #long -tеrm #еquilibrium rеlationship.? Tradеrs usе statistical tеsts,? such as thе #Augmеntеd #Dickеy -#Fullеr tеst,? to confirm thе prеsеncе of cointеgration and takе positions whеn thе sprеad bеtwееn thе instrumеnts dеviatеs from its long-tеrm mеan.

5.? Stochastic diffеrеntial-basеd: This stratеgy involvеs modеling thе pricе rеlationship bеtwееn thе two instrumеnts using #stochastic #diffеrеntial еquations.? Tradеrs usе thеsе modеls to idеntify dеviations from thе еxpеctеd pricе rеlationship and takе positions accordingly.

Thеsе stratеgiеs can bе appliеd to various #financial #instrumеnts ,? such as stocks,? options,? futurеs,? or #currеnciеs ,? and can bе usеd in diffеrеnt markеt conditions,? such as #uptrеnds ,? #downtrеnds ,? or #sidеways movеmеnts.? It is еssеntial to bе awarе of thе corrеlation bеtwееn various instrumеnts and thеir shifting trеnds to managе your #portfolio еffеctivеly.?

Before we get started some basic Statistics about the two pairs:

When comparing the exchange rate statistics of #EUR /USD and #USD /JPY currency pairs, we observe distinct patterns. The mean exchange rate for EUR/USD is approximately 1.2015, while that for #USD /JPY is around 106.0099. The median exchange rate for EUR/USD is 1.1753, slightly lower than the median of 108.417 for USD/JPY. Interestingly, the mode, representing the most frequent value, is 1.1216 for EUR/USD and 76.8600 for USD/JPY.

The #standard deviation, which measures the spread of data, is 0.1138 for EUR/USD and 16.1312 for #USD /JPY, indicating higher volatility in the latter. Skewness, portraying the symmetry of the distribution, is 0.4043 for EUR/USD and 0.0279 for USD/JPY, suggesting a slight positive skew for the former and nearly symmetric distribution for the latter. #Kurtosis , reflecting the tails' behavior, is negative for both pairs (-0.9372 for EUR/USD and -0.1708 for USD/JPY), signifying flatter peaks and thinner tails than a normal distribution.

In terms of the exchange rate range, EUR/USD shows a range of 0.5248, with values ranging from 0.9596 to 1.4844, while USD/JPY has a larger range of values between 75.7400 and 150.1760. These statistics provide valuable insights into the behavior and characteristics of these currency pairs, which can inform #trading #strategies , particularly those involving pairs trading.

Detailed explanation of each step in the context of the code for implementing pairs trading using statistical analysis regression:

1. Identify #correlated currency pairs: In the code, we download historical data for EUR/USD and USD/JPY currency pairs using Yahoo Finance. We then align the indices of the two series to ensure that they have the same date range. The correlation between these two currency pairs can be calculated using the `corr()` method in pandas, as shown in the code

2. Run OLS regression: We perform an Ordinary Least Squares (OLS) regression on the aligned currency pairs using the `sm.OLS()` function from the `statsmodels` library. The slope coefficient obtained from the regression serves as the hedge ratio.

3. Calculate the spread: We calculate the spread between the two currency pairs using the hedge ratio. The spread is the linear combination of the log prices of the two currency pairs

4. Test for cointegration: We check the stationarity of the spread and the presence of a unit root using the #Augmented #Dickey -Fuller test from the `statsmodels` library

5. Identify trading signals: We look for deviations in the price relationship between the #two currency pairs. In the code, we use the specified long and short thresholds to identify long and short entry and exit signals:

6. Monitor and adjust: In the code, we perform a simple backtest using the identified trading signals. We update the positions and capital based on the entry and exit signals. This #backtesting process simulates the monitoring and adjustment of the strategy

This implements the pairs trading strategy using statistical analysis regression for the EUR/USD and USD/JPY currency pairs. The process includes data retrieval, OLS #regression , #spread calculation, #cointegration testing, #trading signals identification, and #backtesting . Note that this is a simple example and may require further #optimization and #risk management for real-world trading.

Conclusion

The implementation of a pairs trading strategy using #statistical #regression involves steps such as downloading historical data for correlated currency pairs, aligning their indices, and calculating their #correlation . Through Ordinary Least Squares (OLS) regression, the #hedge #ratio is determined, which guides the calculation of the spread between the pairs. Augmented Dickey-Fuller (ADF) tests are conducted to assess cointegration and the stationarity of the spread, with cointegration being essential for successful #mean #reversion trading. Trading signals are identified based on #spread #deviations , and a backtesting process simulates strategy performance. However, the provided example indicates that the tested currency pairs, EUR/USD and USD/JPY, lack sufficient evidence for cointegration, highlighting the importance of further investigation and alternative tests.