Package PairTrading. February 15, 2013

Transcription

1 Package PairTrading February 15, 2013 Type Package Title classical pair trading based on cointegration in finance Version 1.1 Date Author Maintainer Shinichi This package gives classical trading strategy called Pair trading to you. you can easily specify pairs for trading and do back-test by this package. It s based on cointegration. Cointegration is a statistical feature of time series proposed by Engle and Granger. License BSD LazyLoad yes Depends R(>= ), xts, tseries Repository CRAN Date/Publication :04:29 NeedsCompilation no R topics documented: PairTrading-package EstimateParameters EstimateParametersHistorically IsStationary Return Simple stock.price Index 9 1

2 2 PairTrading-package PairTrading-package Classical pair trading methods based on cointegration analysis. This package gives classical trading strategy called "Pair trading". You can easily specify pairs for trading and do back-testing. Analysis are based on the idea of Cointegration that is a statistical feature of time series proposed by Engle and Granger. Package: PairTrading Type: Package Version: 1.1 Date: License: BSD LazyLoad: yes Maintainer: Shinichi Takayanagi<shinichi.takayanagi@gmail.com> References Engle, Robert F. and C.W.J. Granger, 1987, Co-integration and error correction: Representation, estimation, and testing, Econometrica 55, Granger, C.W.J., 1986, Developments in the study of cointegrated economic variables, Oxford Bulletin of Economics and Statistics 48, #Estimate parameters & plot spread reg <- EstimateParameters(price.pair, method = lm) str(reg) plot(reg$spread)

3 EstimateParameters 3 #check stationarity IsStationary(reg$spread, 0.1) #estimate parameters for back test params <- EstimateParametersHistorically(price.pair, period = 180) #create & plot trading signals signal <- Simple(params$spread, 0.05) barplot(signal,col="blue",space = 0, border = "blue",xaxt="n",yaxt="n",xlab="",ylab="") par(new=true) plot(params$spread) #performance return.pairtrading <- Return(price.pair, lag(signal), lag(params$hedge.ratio)) if(!all(is.na(return.pairtrading))){ plot(100 * cumprod(1 + return.pairtrading)) } EstimateParameters Estimate parameters at any point. Estimate parameters(spread, premium, cointegration coefficient) at any point by regression(default linear regression). EstimateParameters(price.pair, method = lm) price.pair method pair stock price (xts object) estimation method.(see also) Value "method" is any regression method which returns a result with "$coef" attribute. "$coef[1]" should be regression intercept(means premium) and "$coef[2]" should be regression coefficient(headge.ratio). return a list consisting of elements below. spread hedge.ratio premium xts object. "residual" in regression scalar value. "coefficient" in regression scalar value. "intercept" in regression

4 4 EstimateParametersHistorically #Estimate parameters & plot spread reg <- EstimateParameters(price.pair, method = lm) str(reg) plot(reg$spread) EstimateParametersHistorically Estimate parameters historicall for back test. Estimate parameters(spread, premium, cointegration coefficient) at any point by regression(default linear regression). EstimateParametersHistorically(price.pair, period, method = lm) price.pair period method pair stock price (xts object) width of rolling window(see details) estimation method.(see details) "method" is any regression method which returns a result with "$coef" attribute. "$coef[1]" should be regression intercept(means premium) and "$coef[2]" should be regression coefficient(headge.ratio).

5 IsStationary 5 Value return a list consisting of elements below. spread hedge.ratio premium xts object. "residual" in regression scalar value. "coefficient" in regression xts object. "intercept" in regression #Estimate parameters & plot spread reg <- EstimateParameters(price.pair, method = lm) str(reg) plot(reg$spread) IsStationary Check the stationarity of time series (especially spread) Check the stationarity of time series by Phillips-Perron Test for Unit Roots and Augmented Dickey- Fuller Test. IsStationary(spread, threshold) spread threshold checked time series object(xts) threshhold value of p-value Value the vector which have the result of each test passed or not.

6 6 Return #Estimate parameters & plot spread reg <- EstimateParameters(price.pair, method = lm) #check stationarity IsStationary(reg$spread, 0.1) Return Calculate return of back-test Calculate the performance of pair trading by specified trading signal and hedge ratio Return(price.pair, signal.lagged, hedge.ratio.lagged) price.pair pair stock price (xts object) signal.lagged lagged signal(see details) hedge.ratio.lagged hedge ratio created by EstimateParametersHistorically function(see details) You have to consider "lag" to signal, because you can not trade when you calculate your trade position at that time. hedge.ratio.lagged is too. We defined "return" as following that [Return of (Buy-Sell)portfolio = (Return of Price1) * (Investmentratio of Price1) + (Return of Price2) * (Investment ratio of Price2) In this equation, as you know, "Return" is calculated as "Change ratio of price between two period". We defined "Investment ratio" as following that. [(Investment ratio of Price1) = 1 / (1 + abs(hedge ratio))], [(Investment ratio of Price2) = hedge ratio / (1 + abs(hedge ratio))]

7 Simple 7 Value performance data(not price but return) as xts object & estimate parameters params <- EstimateParametersHistorically(price.pair, period = 180) #create trading signals signal <- Simple(params$spread, 0.05) #Performance of pair trading return.pairtrading <- Return(price.pair, lag(signal), lag(params$hedge.ratio)) if(!all(is.na(return.pairtrading))){ plot(100 * cumprod(1 + return.pairtrading)) } Simple Create trading Signal Create trading signal by the spread of stock pair. This function provide you the simplest method to create signal in the meaning that it just create signals according to whether spread is over a threshold or not. Simple(spread, spread.entry) spread spread.entry the spread of stock pair. an xts object Entry level of spread. single scalar.

8 8 stock.price This function generates trading singal by spread and it s threshold. #estimate parameters for back test params <- EstimateParametersHistorically(price.pair, period = 180) #create & plot trading signals signal <- Simple(params$spread, 0.05) stock.price sample stock price data This data set gives 3 stock prices data from to as xts object. stock.price Format xts object

9 Index Topic EstimateParametersHistorically EstimateParametersHistorically, 4 Topic EstimateParameters EstimateParameters, 3 Topic IsStationary IsStationary, 5 Topic Return Return, 6 Topic Simple Simple, 7 Topic datasets stock.price, 8 Topic package PairTrading-package, 2 Topic signal Simple, 7 EstimateParameters, 3 EstimateParametersHistorically, 4 IsStationary, 5 PairTrading (PairTrading-package), 2 PairTrading-package, 2 Return, 6 signal (Simple), 7 Simple, 7 stock.price, 8 9