quantitative trading strategies in r part 3 of 3

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Computational Finance and Risk Management

Quantitative Trading Strategies in R

Part 3 of 3

Guy YollinPrincipal Consultant, r-programming.org

Visiting Lecturer, University of Washington

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Outline

1 MACD example

2 MACD example extended to multiple assets

3 Optimizing the MACD trading system

4 RSI example

5 Bollinger band example

6 Summary

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Lecture references

TradeAnalytics project page on R-forge:http://r-forge.r-project.org/projects/blotter/

documents and demos for:

blotter packagequantstrat package

R-SIG-FINANCE:https://stat.ethz.ch/mailman/listinfo/r-sig-finance

Kent Russell’s Timely Portfolio blog:http://timelyportfolio.blogspot.com/

6-part quantstrat example

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Quantstrat demos

faber maCross bbands rsi macd faberMC

name='sigCrossover' Y Y Y N N Y

name='sigThreshold' N N N Y Y N

ordertype='market' Y Y Y Y Y Y

ordertype='stoplimit' N N N N Y N

type='enter' Y Y Y Y Y Y

type='exit' Y Y Y Y Y Y

type='risk' N N N N Y N

orderside='long' Y Y N Y Y Y

orderside='short' N N N Y N N

applyStrategy parameters N N Y Y Y N

index.class='Date' N Y Y Y Y N

index.class='POSIXt' Y N N N N N

multiasset Y N N Y N Y

multicurrency N N N N N Y

data adjusted N Y N N N N

updates Account N N N N N N

demos are located in ∼/R-2.13.1/library/quantstrat/demo

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Outline

1 MACD example

4 RSI example

6 Summary

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MACD (Moving Average Convergence-Divergence)

Trend-following momentum indicator

Published by Gerald Appel in the late 1970

MACD Calculation

MACD = 12-day EMA - 26-day EMAMACD Signal Line = 9-day EMA of MACDMACD histogram = MACD - Signal Line

Interpretation

Buy/Sell when MACD Signal Line crosses 0

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MACD system in TradeStation

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MACD code in EasyLanguage

EasyLanguage code

i n p u t s : Fas tLength ( 12 ) , SlowLength ( 26 ) , MACDLength( 9 ) ;v a r i a b l e s : MyMACD( 0 ) , MACDSig( 0 ) ;

MyMACD = MACD( Close , FastLength , SlowLength ) ;MACDSig = XAverage ( MyMACD, MACDLength ) ;

i f MACDSig c r o s s e s above 0 thenBuy ( ”MacdLE ” ) next bar at market ;

i f MACDSig c r o s s e s below 0 thenS e l l ( ”MacdLX” ) next bar at market ;

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MACD indicator from TTR

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Initialize currency and trading instruments

Initialize portfolio, account, orders,

strategy

Add indicators, signals, and rules

Generate performance reports

and graphs

Initialize currency and

instruments, and load historic data

Apply strategy to portfolio

InitializationBar-by-bar processing

Reporting

Update portfolio, account, equity

Define strategy Update

R Code:

> library(quantstrat)

> # inz currency and stocks

> dummy <- currency('USD')

> stock.str = c("XLF")

> for(symbol in stock.str)

stock(symbol, currency="USD",multiplier=1)

> # download stocks

> start.data <- as.Date("1998-12-22")

> end.data <- as.Date("2011-08-09")

> initDate <- start.data-1

getSymbols(symbol,from=start.data,to=end.data,adjust=T)

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Initialize portfolio, account, and orders object

strategy

and graphs

Reporting

R Code:

> # inz portfolio, account, orders, strategy

> strat.name <- "MACD"

> initEq=1000000

> trade.percent = 0.05

> dummy <- initPortf(name=strat.name,symbols=stock.str, initDate=initDate)

> dummy <- initAcct(name=strat.name,portfolios=strat.name,

initDate=initDate, initEq=initEq)

> initOrders(portfolio=strat.name,initDate=initDate)

> strat <- strategy(strat.name)

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The add.signals function

quantstrat supports the following signal types:

sigCrossover crossover signal (”gt”, ”lt”, ”eq”, ”gte”, ”lte”)

sigComparison comparison signal (”gt”, ”lt”, ”eq”, ”gte”, ”lte”)

sigThreshold threshold signal (”gt”, ”lt”, ”eq”, ”gte”, ”lte”)

sigPeak peak/valley signals (”peak”, ”bottom”)

sigFormula signal calculated from a formula

R Code: The add.signals function

> args(add.signal)

function (strategy, name, arguments, parameters = NULL, label = NULL,

..., enabled = TRUE, indexnum = NULL, store = FALSE)

Main arguments:

strategy strategy object

name name of the signal (one of the 5 supported signals)

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The sigThreshold function

The sigThreshold function generates a threshold signal

R Code: The sigThreshold function

> args(sigThreshold)

function (label, data = mktdata, column, threshold = 0, relationship = c("gt",

"lt", "eq", "gte", "lte"), cross = FALSE)

Main arguments:

label text label to apply to the output

data data to apply comparison

column column name to apply comparison

threshold numeric threshold to compare

relationship relationship to test (”gt”, ”lt”, ”eq”, ”gte”, ”lte”)

cross if TRUE, then signal will be TRUE only for the firstobservation to cross the threshold

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Define indicators and signals

strategy

and graphs

Reporting

R Code:

> # indicators:

> strat <- add.indicator(strategy = strat, name = "MACD",

arguments = list(x=quote(Cl(mktdata))) )

> # signals:

> strat <- add.signal(strategy = strat, name="sigThreshold",

arguments = list(column="signal",relationship="gt",threshold=0,cross=TRUE),

label="signal.gt.zero")

> strat <- add.signal(strategy = strat,name="sigThreshold",

arguments = list(column="signal",relationship="lt",threshold=0,cross=TRUE),

label="signal.lt.zero")

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Define order sizing function

strategy

and graphs

Reporting

R Code:

> osPercentEquity <- function (timestamp,orderqty,portfolio,symbol,ruletype,...)

tempPortfolio <- getPortfolio(portfolio)

dummy <- updatePortf(Portfolio=portfolio,

Dates=paste('::',as.Date(timestamp),sep=''))

trading.pl <- sum(getPortfolio(portfolio)$summary$Net.Trading.PL)

assign(paste("portfolio.",portfolio,sep=""),tempPortfolio,pos=.blotter)

total.equity <- initEq+trading.pl

tradeSize <- total.equity * trade.percent

ClosePrice <- as.numeric(Cl(mktdata[timestamp,]))

orderqty <- sign(orderqty)*round(tradeSize/ClosePrice)

return(orderqty)

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Define entry and exit rules

strategy

and graphs

Reporting

R Code:

> # rules:

> strat <- add.rule(strategy = strat,name='ruleSignal',

arguments = list(sigcol="signal.gt.zero",sigval=TRUE, orderqty=100,

ordertype='market', orderside='long', osFUN='osPercentEquity'),type='enter')

arguments = list(sigcol="signal.lt.zero",sigval=TRUE, orderqty='all',

ordertype='market', orderside='long'),type='exit')

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Applying the strategy to a portfolio

strategy

and graphs

Reporting

R Code:

> # parameters:

> fastMA = 12

> slowMA = 26

> signalMA = 9

> maType="EMA"

> # apply strategy

> out<-try(applyStrategy(strategy=strat, portfolios=strat.name,

parameters=list(nFast=fastMA, nSlow=slowMA, nSig=signalMA,maType=maType),

verbose=F))

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Call updatePortf to update portfolio P&L

strategy

and graphs

Reporting

R Code:

> dummy <- updatePortf(Portfolio=strat.name,

Dates=paste('::',as.Date(Sys.time()),sep=''))

> if(sum(duplicated(index(getPortfolio(strat.name)$summary)))>0)

tempPortfolio <- getPortfolio(strat.name)

tempPortfolio$summary <- as.xts(aggregate(x=tempPortfolio$summary,

by=index(tempPortfolio$summary), FUN=sum))

assign(paste("portfolio.",strat.name,sep=""),tempPortfolio,pos=.blotter)

warning("duplicates removed after update")

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Chart MACD system performance for XLF

strategy

and graphs

Reporting

R Code:

> source("chart_Posn.R")

> chart_Posn(Portfolio=strat.name,Symbol="XLF")

> plot(add_MACD())

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MACD system performance for XLF

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Outline

1 MACD example

4 RSI example

6 Summary

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Quantstrat/Blotter portfolios with multiple assets

While most of the quantstrat demos use a single asset, the real powerof the architecture is that it supports multiple assets

To use a multiple-asset portfolio, simply supply a symbol list whencalling initPortf

All functionality should simply work with the entire portfolio of assets

applying a strategy via applyStrategy will generate transactions forall assets according to the define trading rulescalculating portfolio P&L via updatePortf will accumulate the P&Lfor all assets

Due to the additional calculations required, working with multi-assetportfolios can be time consuming

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strategy

and graphs

Reporting

R Code:

> # clear out old portfolios and orders

> try(rm(list=ls(pos=.blotter),pos=.blotter),silent=TRUE)

> try(rm(list=ls(pos=.strategy),pos=.strategy),silent=TRUE)

> stock.str = c("XLF", "XLP", "XLE", "XLY", "XLV", "XLI", "XLB", "XLK", "XLU")

> # download stocks

> end.data <- as.Date("2011-08-09")

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strategy

and graphs

Reporting

R Code:

> strat.name <- "MACD"

> initEq=1000000

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The blotter_portfolio object

myPortfolio

--------------------

blotter_portfolio

symbols

--------------------

listsymbols

--------------------

listsymbols

--------------------

summary

--------------------

portfolio_summary xts

Long.Value

Short.Value

Net.Value

Gross.Value

Period.Realized.PL

Period.Unrealized.PL

Gross.Trading.PL

Txn.Fees

Net.Trading.PL

--------------------

transactions xts

--------------------

posPL xts

posPL.USD

--------------------

posPL xts

Pos.Qty

Con.Mult

Ccy.Mult

Pos.Value

Pos.Avg.Cost

Txn.Value

Period.Realized.PL

Period.Unrealized.PL

Gross.Trading.PL

Txn.Fees

Net.Trading.PL

Txn.Qty

Txn.Price

Txn.Value

Txn.Avg.Cost

Pos.Qty

Pos.Avg.Cost

Gross.Txn.Realized.PL

Txn.Fees

Net.Txn.Realized.PL

Con.Mult

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Symbols in the botter_portfolio object

R Code:

> macdPortfolio <- getPortfolio(strat.name)

> names(macdPortfolio)

[1] "symbols" "summary"

> length(macdPortfolio$symbols)

> names(macdPortfolio$symbols)

[1] "XLF" "XLP" "XLE" "XLY" "XLV" "XLI" "XLB" "XLK" "XLU"

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strategy

and graphs

Reporting

R Code:

> # indicators:

> strat <- add.indicator(strategy = strat, name = "MACD",

arguments = list(x=quote(Cl(mktdata))) )

> # signals:

arguments = list(column="signal",relationship="gt",threshold=0,cross=TRUE),

label="signal.gt.zero")

> strat <- add.signal(strategy = strat,name="sigThreshold",

arguments = list(column="signal",relationship="lt",threshold=0,cross=TRUE),

label="signal.lt.zero")

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Define order sizing function

strategy

and graphs

Reporting

R Code:

> osPercentEquity <- function (timestamp,orderqty,portfolio,symbol,ruletype,...)

tempPortfolio <- getPortfolio(portfolio)

dummy <- updatePortf(Portfolio=portfolio,

Dates=paste('::',as.Date(timestamp),sep=''))

trading.pl <- sum(getPortfolio(portfolio)$summary$Net.Trading.PL)

assign(paste("portfolio.",portfolio,sep=""),tempPortfolio,pos=.blotter)

total.equity <- initEq+trading.pl

tradeSize <- total.equity * trade.percent

ClosePrice <- as.numeric(Cl(mktdata[timestamp,]))

orderqty <- sign(orderqty)*round(tradeSize/ClosePrice)

return(orderqty)

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strategy

and graphs

Reporting

R Code:

> # rules:

arguments = list(sigcol="signal.gt.zero",sigval=TRUE, orderqty=100,

ordertype='market', orderside='long', osFUN='osPercentEquity'),type='enter')

arguments = list(sigcol="signal.lt.zero",sigval=TRUE, orderqty='all',

ordertype='market', orderside='long'),type='exit')

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strategy

and graphs

Reporting

R Code:

> # parameters:

> fastMA = 12

> slowMA = 26

> signalMA = 9

> maType="EMA"

> # apply strategy

verbose=F))

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strategy

and graphs

Reporting

R Code:

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Chart portfolio performance

strategy

and graphs

Reporting

R Code:

> library(PerformanceAnalytics)

> trading.pl <- getPortfolio(strat.name)$summary$Net.Trading.PL

> rets <- trading.pl/initEq

> charts.PerformanceSummary(rets,colorset = bluefocus,xlab="")

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MACD portfolio performance−

Net.Trading.PL Performance

1998−12−21 2000−07−03 2002−01−02 2003−07−01 2005−01−03 2006−07−03 2008−01−02 2009−07−01 2011−01−03

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Outline

1 MACD example

4 RSI example

6 Summary

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MACD optimization

The inventor of MACD suggests that the difference between a 12-dayand 26-day exponential moving average be calculated and thensmooth via a 9-day exponential moving average

Our research interest is to explore if other values provide superiorresults

We will try 3 different values for each of fastMA, slowMA, andsignalMA, 27 different settings

All testing will be done on the 9-asset portfolio of S&P Sector SelectETFs with data from Dec-1998 through Aug-2011

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The Omega performance measure

The Omega performance measure† is a reward-to-risk ratio that can beapplied to a time-series of returns

Ω(L) =

∫ bL (1 − F (r))dr∫ L

a F (r)drwhere L is some return threshold (e.g. 0)

Omega uses all of the information in the return series and is thus wellsuited for non-normal distributions

Omega is essentially the ratio of a call price to a put price

Omega performance measure is calculated by the Omega function inPerformanceAnalytics

Ω(L) =C (L)

†Shadwick and Keating. ”A Universal Performance Measure.”Journal of PerformanceMeasurement, Spring 2002

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The Omega performance measure

Portfolio Returns Cumulative Distribution Function

Omega Performance Measure

P/L Distribution

Density

Portfolio Returns Cumulative Distribution Function

R Tools for Portfolio Optimization26

-0.5 0.0 0.5 1.0

daily return

Density

-1.0 -0.5 0.0 0.5 1.0 1.5

-0.5 0.0 0.5 1.0

daily return

-0.5 0.0 0.5 1.0

daily return

a bLa bL

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MACD optimization

R Code:

> fastMA <- c(5,10,15)

> slowMA <- c(20,25,30)

> signalMA <- c(1,5,10)

> parm.comb <- expand.grid(fastMA=fastMA,slowMA=slowMA,signalMA=signalMA)

> head(parm.comb,12)

fastMA slowMA signalMA

1 5 20 1

2 10 20 1

3 15 20 1

4 5 25 1

5 10 25 1

6 15 25 1

7 5 30 1

8 10 30 1

9 15 30 1

10 5 20 5

11 10 20 5

12 15 20 5

> num.opts <- nrow(parm.comb)

> res.vec <- rep(NA,num.opts)

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Optimization loop

R Code:

> for(i in 1:num.opts)

# initialize portfolio and orders

try(rm(list=ls(pos=.blotter),pos=.blotter),silent=TRUE)

try(rm(list=ls(pos=.strategy),pos=.strategy),silent=TRUE)

dummy <- initPortf(name=strat.name,symbols=stock.str, initDate=initDate)

initOrders(portfolio=strat.name,initDate=initDate)

# apply strategy

fastMA = parm.comb[i,"fastMA"]

slowMA = parm.comb[i,"slowMA"]

signalMA = parm.comb[i,"signalMA"]

out<-try(applyStrategy(strategy=strat, portfolios=strat.name,

verbose=F))

# calculate performance matric

dummy <- updatePortf(Portfolio=strat.name,

trading.pl <- getPortfolio(strat.name)$summary$Net.Trading.PL

rets <- trading.pl/initEq

omega <- as.numeric(Omega(rets))

res.vec[i] <- omega

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Optimization

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Optimization summary

Performed a true multi-parameter grid search on a multi-assetportfolio

Functionality not supported within TradeStation or similar packages

Optimal values:

fastMA = 15 (default = 12)slowMA = 25 (default = 26)signalMA = 10 (default = 9)

Process ran for approximately 8.5 hours on the RStudio cloud

Embarrassingly parallel problem that would be idea for any of R’sparallel computing capabilities (e.g. snow, NetWorkSpaces etc.)

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Outline

1 MACD example

4 RSI example

6 Summary

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RSI (Relative Strength Index)

Momentum oscillator (value between 0 and 100)

Published by Welles Wilder in the late 1970

RSI Calculation

RSI = 100 − 100

1 + RS

RS =mean(up changes)

mean(down changes)

typical lengths are 14-days, 9-days, or 25-days

Interpretation

Trade reversals between thresholds (e.g. 70/30)Trade break-outs above/below thresholds (e.g. 70/30)

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Semiconductor HOLDR stocks

HOLDRS are ETFs that represent a basket of stocks in a specificindustry segment

The Semiconductor HOLDR includes large-cap semiconductormanufacturers as well as semiconductor equipment manufacturers

We’ll apply the RSI system to 5 components of the semiconductorHOLDR ETF

INTC - IntelTXN - Texas InstrumentAMAT - Applied MaterialsADI - Analog DevicesALTR - Altera

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strategy

and graphs

Reporting

R Code:

> stock.str = c("INTC","TXN","AMAT","ADI","ALTR")

> # download stocks

> end.data <- as.Date("2011-08-09")

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strategy

and graphs

Reporting

R Code:

> strat.name <- "RSI"

> initEq=1000000

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strategy

and graphs

Reporting

R Code:

> # indicators:

> strat <- add.indicator(strategy = strat, name = "RSI",

arguments = list(price = quote(getPrice(mktdata))), label="RSI")

> # signals:

arguments = list(threshold=70, column="RSI",relationship="gt", cross=TRUE),

label="RSI.gt.70")

arguments = list(threshold=30, column="RSI",relationship="lt",cross=TRUE),

label="RSI.lt.30")

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Define short entry and exit rules

strategy

and graphs

Reporting

R Code:

> # rules:

> strat <- add.rule(strategy = strat, name='ruleSignal',

arguments = list(sigcol="RSI.gt.70", sigval=TRUE, orderqty=-1000,

ordertype='market', orderside='short', osFUN='osPercentEquity', replace=FALSE),

type='enter', path.dep=TRUE)

arguments = list(sigcol="RSI.lt.30", sigval=TRUE, orderqty='all',

ordertype='market', orderside='short', replace=FALSE),

type='exit', path.dep=TRUE)

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Define long entry and exit rules

strategy

and graphs

Reporting

R Code:

> # rules:

arguments = list(sigcol="RSI.lt.30", sigval=TRUE, orderqty= 1000,

ordertype='market', orderside='long', osFUN='osPercentEquity', replace=FALSE),

type='enter', path.dep=TRUE)

arguments = list(sigcol="RSI.gt.70", sigval=TRUE, orderqty='all',

ordertype='market', orderside='long', replace=FALSE),

type='exit', path.dep=TRUE)

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strategy

and graphs

Reporting

R Code:

> # apply strategy

parameters=list(n=2),verbose=F))

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strategy

and graphs

Reporting

R Code:

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strategy

and graphs

Reporting

R Code:

> chart_Posn(Portfolio=strat.name,Symbol="AMAT",Dates="2009::2011")

> plot(add_RSI())

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AMAT performance for RSI strategy

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RSI portfolio performance0.

1998−12−21 2000−07−03 2002−01−02 2003−07−01 2005−01−03 2006−07−03 2008−01−02 2009−07−01 2011−01−03

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Outline

1 MACD example

4 RSI example

6 Summary

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Bollinger bands

Bollinger bands are a volatility-sensitive price channel

Published by John Bollinger in the early 1980s

RSI Calculation

Calculate a simple moving average (typically 20 days) of the C (eitherthe close or weighted-close)Upper band: MA + N × StdDev(C )Lower band: MA− N × StdDev(C )N typically in the range of 2 to 3

Interpretation

Trade reversals between the upper and lower bandsTrade break-outs above/below the bands

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Oil services HOLDR stocks

HOLDRS are ETFs that represent a basket of stocks in a specificindustry segment

The oil services HOLDR includes companies specifically involved in oildrilling and related services

We’ll apply the Bollinger band system to 5 components of the oilservices HOLDR ETF

SLB - SchlumbergerRIG - TransoceanHAL - HaliburtonBHI - Baker HughesDO - Diamond Offshore

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strategy

and graphs

Reporting

R Code:

> stock.str = c("SLB","RIG","HAL","BHI","DO")

> # download stocks

> end.data <- as.Date("2011-08-09")

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strategy

and graphs

Reporting

R Code:

> strat.name <- "BBANDS"

> initEq=1000000

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strategy

and graphs

Reporting

R Code:

> # indicators:

> strat <- add.indicator(strategy = strat, name = "BBands",

arguments = list(HLC = quote(HLC(mktdata)), maType='SMA'))

> # signals:

> strat <- add.signal(strat,name="sigCrossover",

arguments = list(columns=c("Close","up"),relationship="gt"),

label="Cl.gt.UpperBand")

arguments = list(columns=c("Close","dn"),relationship="lt"),

label="Cl.lt.LowerBand")

arguments = list(columns=c("High","Low","mavg"),relationship="op"),

label="Cross.Mid")

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strategy

and graphs

Reporting

R Code:

> # rules:

> strat <- add.rule(strat,name='ruleSignal',

arguments = list(sigcol="Cl.gt.UpperBand",sigval=TRUE, orderqty=-100,

ordertype='market', orderside=NULL, threshold=NULL),type='enter')

arguments = list(sigcol="Cl.lt.LowerBand",sigval=TRUE, orderqty= 100,

ordertype='market', orderside=NULL, threshold=NULL),type='enter')

arguments = list(sigcol="Cross.Mid",sigval=TRUE, orderqty= 'all',

ordertype='market', orderside=NULL, threshold=NULL),type='exit')

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strategy

and graphs

Reporting

R Code:

> # parameters:

> SD = 2

> N = 20

> # apply strategy

parameters=list(sd=SD,n=N),verbose=F))

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strategy

and graphs

Reporting

R Code:

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strategy

and graphs

Reporting

R Code:

> chart_Posn(Portfolio=strat.name,Symbol="DO",Dates="2009::2011")

> plot(add_BBands())

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DO performance for BBands strategy

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Bollinger bands portfolio performance0.

1998−12−21 2000−07−03 2002−01−02 2003−07−01 2005−01−03 2006−07−03 2008−01−02 2009−07−01 2011−01−03

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Outline

1 MACD example

4 RSI example

6 Summary

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Summary of blotter and quantstrat

Transaction infrastructure for defining instruments, transactions,portfolios and accounts for trading systems and simulation. Providesportfolio support for multi-asset class and multi-currency portfolios.Still in heavy development.

Despite beta-status, software is used everyday by hearty workingprofessions in asset management

Inherent flexibility provided by R allows analysis that is stillunavailable in some dedicated commercial packages

Although the software is free, be prepared to pay some dues in terms oftime and effort to get things working

R-SIG-FINANCE is your friend

quantitative trading strategies in r part 3 of 3

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