Pair trading strategy : how to use "PairTrading" package

October 25, 2011

(This article was first published on My Life as a Mock Quant in English, and kindly contributed to R-bloggers)

Mr.Ishikawa(my old friend) and I developed “PairTrading” package, and uploaded it on CRAN.

This article shows you how you can use it.

The pair trading is a market neutral trading strategy and gives traders a chance to profit regardless of market conditions. The idea of this strategy is quite simple.
 1 : Select two stocks(or any assets) moving similarly
 2 : Short out-performing stock, buy under-performing one
 3 : If “spread”(price difference between two stocks) converge, close your position.

So, Let’s start to explain how to use this package.
(This example is in PDF manual of this package)

0: Install & load package
You can install and load “PairTrading” package via CRAN in the same way as other packages.

> install.packages("PairTrading")
> library(PairTrading)

1: Load sample data
We prepared sample stock price data in our package. You can load it by using “data” command.

> #load sample stock price data
> data(stock.price)

2: Estimate parameters
Next, We extract two stock prices(from 31 Mar, 2008) and estimate parameters.

> #select 2 stocks
> price.pair <- stock.price[,1:2]["2008-03-31::"]
> #Estimate parameters & plot spread
> reg <- EstimateParameters(price.pair, method = lm)

At the moment, we have only normal linear regression method to estimate parameters, but we will develop more sophisticated method in the future.The estimation result contains the following contents.

> str(reg)
List of 3
$ spread :An ‘xts’ object from 2008-03-31 to 2011-08-05 containing:
Data: num [1:821, 1] 0.26 0.271 0.294 0.275 0.255 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr "7203"
Indexed by objects of class: [Date] TZ:
xts Attributes:
$ hedge.ratio: num 0.285
$ premium : num 6.34

The most important thing in this estimation is “spread”, then we try to plot it.

> plot(reg$spread)

And, you can check the stationarity of that by using “IsStationary” function.
This function return the result of two types unit root test.

> #check stationarity
> IsStationary(reg$spread, 0.1)
PP.test adf.test

( augmented Dickey–Fuller test (ADF) and Phillips-Perron test)

3: Estimate parameters for back-test
To run back-test, you have to estimate parameters historically by using “EstimateParametersHistoricallyfunction. This function do something like “rolling regression” to estimate parameters. This point is different from “EstimateParameter” function.

> #estimate parameters for back test
> params <- EstimateParametersHistorically(price.pair, period = 180)
> #create & plot trading signals
> str(params)
An ‘xts’ object from 2008-12-18 to 2011-08-05 containing:
Data: num [1:642, 1:3] 0.065 0.0577 0.0396 0.0136 0.021 ...
- attr(*, "dimnames")=List of 2
..$ : NULL
..$ : chr [1:3] "spread" "hedge.ratio" "premium"
Indexed by objects of class: [Date] TZ:
xts Attributes:

4: Create trading signal

Next, you create trading singal using estimated spread. “Simple” function give a very simple trading strategy(If The spread is more(less) than specified value, you will buy(sell))

> #create & plot trading signals
> signal <- Simple(params$spread, 0.05)
> barplot(signal,col="blue",space = 0, border = "blue",xaxt="n",yaxt="n",xlab="",ylab="")
> par(new=TRUE)
> plot(params$spread)

In this case, The trading signal is drawn as below.

Last, you can check the performance of pair trading by using “Return” function.

> #performance
> return.pairtrading <- Return(price.pair, lag(signal), lag(params$hedge.ratio))
> plot(100 * cumprod(1 + return.pairtrading))

In this case, our strategy seems to work correctly :-)

6: Conclusion and remarks

Pair trading is well-known trading strategy, and I introduced “PairTrading” package in this article.
We would like to modify this package to be more useful and fit in real-market.
If you have any suggestion, please let me know.
And we created a presentation slide to explain the basic concept of pair trading.

It may be useful for you to understand the basic concept of pair trading if you are interested in it.


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