Portfolio Construction using R
library(timeSeries)## Warning: package 'timeSeries' was built under R version 3.1.2## Loading required package: timeDate## Warning: package 'timeDate' was built under R version 3.1.2library(fPortfolio)## Warning: package 'fPortfolio' was built under R version 3.1.2## Loading required package: fBasics## Warning: package 'fBasics' was built under R version 3.1.2##
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## Rmetrics Package fBasics
## Analysing Markets and calculating Basic Statistics
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.org
## Loading required package: fAssets## Warning: package 'fAssets' was built under R version 3.1.2##
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## Rmetrics Package fAssets
## Analysing and Modeling Financial Assets
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.org
##
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## Rmetrics Package fPortfolio
## Portfolio Optimization
## Copyright (C) 2005-2014 Rmetrics Association Zurich
## Educational Software for Financial Engineering and Computational Science
## Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
## https://www.rmetrics.org --- Mail to: info@rmetrics.orglibrary(quantmod)## Warning: package 'quantmod' was built under R version 3.1.2## Loading required package: xts## Warning: package 'xts' was built under R version 3.1.2## Loading required package: zoo## Warning: package 'zoo' was built under R version 3.1.2##
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## Version 0.4-0 included new data defaults. See ?getSymbols.library(caTools)## Warning: package 'caTools' was built under R version 3.1.2library(timeDate)
library(knitr)## Warning: package 'knitr' was built under R version 3.1.2TickerList<-c("SPY","WWE","LNKD","AMZN","BOE","WMT","BABA","KO","BAC","FB","HD","HOG","TWTR")
ClosingPricesRead<-NULL
for (Ticker in TickerList)
ClosingPricesRead<-cbind(ClosingPricesRead,
getSymbols.yahoo(Ticker, from="1950-01-01",verbose=FALSE, auto.assign=FALSE)[,4])
#keep only the dates that have closing prices for all the tickers
ClosingPrices<-ClosingPricesRead[apply(ClosingPricesRead,1,function(x)all(!is.na(x))),]
#convert prices to daily returns
returns<-as.timeSeries(tail(ClosingPrices,-1)/as.numeric(head(ClosingPrices,-1))-1)
Frontier<-portfolioFrontier(returns)
#names(plot((Frontier)))
plot(Frontier,1) # Plot EF
plot(Frontier,2) # Min. Risk Portfolio
plot(Frontier,3) # Tangency Portfolio
plot(Frontier,4) # Risk/Return of Single Assets
plot(Frontier,5) # Equal Weights Portfolio
plot(Frontier,6) # Two Asset Frontiers(Long Only)
plot(Frontier,7) # Monte Carlo Portfolios
plot(Frontier,8) # MArkowitz PF Only
#get the means and covariance matrix of the price returns
#names(getStatistics(Frontier))
getStatistics(Frontier)$mean## SPY.Close WWE.Close LNKD.Close AMZN.Close BOE.Close
## 0.0005958962 -0.0019466564 0.0019450267 -0.0008530650 -0.0009477436
## WMT.Close BABA.Close KO.Close BAC.Close FB.Close
## 0.0018781501 0.0020260373 0.0003911629 0.0009501479 0.0006844107
## HD.Close HOG.Close TWTR.Close
## 0.0017801718 0.0008797936 -0.0045745298cor(returns)## SPY.Close WWE.Close LNKD.Close AMZN.Close BOE.Close
## SPY.Close 1.0000000 0.24899139 0.48436740 0.41305296 0.72241901
## WWE.Close 0.2489914 1.00000000 0.30133834 0.13835408 0.08138650
## LNKD.Close 0.4843674 0.30133834 1.00000000 0.46141464 0.32434108
## AMZN.Close 0.4130530 0.13835408 0.46141464 1.00000000 0.33182575
## BOE.Close 0.7224190 0.08138650 0.32434108 0.33182575 1.00000000
## WMT.Close 0.4248750 -0.07629585 0.10297325 0.39179731 0.24041028
## BABA.Close 0.4044309 0.29584219 0.34129413 0.20829848 0.31853948
## KO.Close 0.2567614 0.10069373 -0.03055834 0.03870129 0.05659792
## BAC.Close 0.7492623 0.25551614 0.26438661 0.23636029 0.56698639
## FB.Close 0.5533405 0.33492177 0.48346490 0.32291386 0.43152330
## HD.Close 0.6591608 0.04906058 0.31082645 0.39033258 0.55410273
## HOG.Close 0.6385693 -0.01388373 0.33405098 0.44031692 0.54462776
## TWTR.Close 0.3353428 0.29520744 0.36925097 0.27322641 0.24553190
## WMT.Close BABA.Close KO.Close BAC.Close FB.Close
## SPY.Close 0.42487500 0.4044309 0.25676135 0.7492623 0.55334053
## WWE.Close -0.07629585 0.2958422 0.10069373 0.2555161 0.33492177
## LNKD.Close 0.10297325 0.3412941 -0.03055834 0.2643866 0.48346490
## AMZN.Close 0.39179731 0.2082985 0.03870129 0.2363603 0.32291386
## BOE.Close 0.24041028 0.3185395 0.05659792 0.5669864 0.43152330
## WMT.Close 1.00000000 0.1199689 0.36897638 0.3400061 0.23506166
## BABA.Close 0.11996887 1.0000000 -0.13165589 0.2972917 0.30788080
## KO.Close 0.36897638 -0.1316559 1.00000000 0.2185564 -0.01513403
## BAC.Close 0.34000608 0.2972917 0.21855639 1.0000000 0.38113965
## FB.Close 0.23506166 0.3078808 -0.01513403 0.3811396 1.00000000
## HD.Close 0.51102822 0.2667712 0.10749395 0.5757504 0.45958061
## HOG.Close 0.29112534 0.2385422 -0.16274569 0.5382613 0.41192386
## TWTR.Close 0.12214179 0.3180954 0.10209176 0.1073537 0.55352305
## HD.Close HOG.Close TWTR.Close
## SPY.Close 0.65916081 0.63856934 0.3353428
## WWE.Close 0.04906058 -0.01388373 0.2952074
## LNKD.Close 0.31082645 0.33405098 0.3692510
## AMZN.Close 0.39033258 0.44031692 0.2732264
## BOE.Close 0.55410273 0.54462776 0.2455319
## WMT.Close 0.51102822 0.29112534 0.1221418
## BABA.Close 0.26677120 0.23854216 0.3180954
## KO.Close 0.10749395 -0.16274569 0.1020918
## BAC.Close 0.57575036 0.53826135 0.1073537
## FB.Close 0.45958061 0.41192386 0.5535231
## HD.Close 1.00000000 0.63833023 0.2913843
## HOG.Close 0.63833023 1.00000000 0.1949419
## TWTR.Close 0.29138426 0.19494193 1.0000000#to plot annualized return and risk
#convert from daily to annual returns and risk
#EF using annualized risk and return
riskReturnPoints<-frontierPoints(Frontier) #risk and return points on the EF
annualizedPoints<-data.frame(targetRisk=riskReturnPoints[,"targetRisk"]*sqrt(252),
targetReturn=riskReturnPoints[,"targetReturn"]*252)
plot(annualizedPoints)
#plot Sharpe ratios for each point on the EF
riskFreeRate<-0
plot((annualizedPoints[,"targetReturn"]-riskFreeRate)/annualizedPoints[,"targetRisk"], xlab="point on EF", ylab="Sharpe Ratio")
#plot the allocation to each stock for each point on the efficient frontier
weightsPlot(Frontier)
#(weightsPlot(Frontier))$minRisk
allocations <-getWeights(Frontier@portfolio)# get allocations for each stock
colnames(allocations)<-TickerList
barplot(t(allocations),col=rainbow(ncol(allocations)+2),legend=colnames(allocations))
#write.csv(annualizedPoints, file="annualReturns.csv")
#getwd() #the location of file
#examine the efficient frontier for portfolios with different constrants
constraints<-"minW[1:length(TickerList)]=-1"
Frontier<-portfolioFrontier(returns ,constraints=constraints)
Frontier.LongOnly<-portfolioFrontier(returns)
riskReturnPoints<-frontierPoints(Frontier)
annualizedPoints<-data.frame(targetRisk=riskReturnPoints[,"targetRisk"]*sqrt(252),
targetReturn=riskReturnPoints[,"targetReturn"]*252)
riskReturnPoints.LongOnly<-frontierPoints(Frontier.LongOnly)
annualizedPoints.LongOnly<-data.frame(targetRisk=riskReturnPoints.LongOnly[,"targetRisk"]*sqrt(252),
targetReturn=riskReturnPoints.LongOnly[,"targetReturn"]*252)
xlimit<-range(annualizedPoints[,1],annualizedPoints.LongOnly[,1])
ylimit<-range(annualizedPoints[,2],annualizedPoints.LongOnly[,2])
plot(annualizedPoints.LongOnly,xlim=xlimit,ylim=ylimit,pch=16,col="blue")
points(annualizedPoints, col="red", pch=16)
legend("right",legend=c("long only","constrained"),col=c("blue","red"), pch= 14)
#red allows both long and short positions
#other type of constraints
constraints<-c("minW[1:length(TickerList)]=-1.0","maxW[1:length(TickerList)]=.60")
Frontier<-portfolioFrontier(returns ,constraints=constraints)
Frontier.LongOnly<-portfolioFrontier(returns)
riskReturnPoints<-frontierPoints(Frontier)
annualizedPoints<-data.frame(targetRisk=riskReturnPoints[,"targetRisk"]*sqrt(252),
targetReturn=riskReturnPoints[,"targetReturn"]*252)
riskReturnPoints.LongOnly<-frontierPoints(Frontier.LongOnly)
annualizedPoints.LongOnly<-data.frame(targetRisk=riskReturnPoints.LongOnly[,"targetRisk"]*sqrt(252),
targetReturn=riskReturnPoints.LongOnly[,"targetReturn"]*252)
xlimit<-range(annualizedPoints[,1],annualizedPoints.LongOnly[,1])
ylimit<-range(annualizedPoints[,2],annualizedPoints.LongOnly[,2])
plot(annualizedPoints.LongOnly,xlim=xlimit,ylim=ylimit,pch=16,col="blue")
points(annualizedPoints, col="red", pch=16)
legend("right",legend=c("long only","constrained"),col=c("blue","red"), pch= 14)
#New Allocations
allocations <-getWeights(Frontier@portfolio)# get allocations for each stock
colnames(allocations)<-TickerList
barplot(t(allocations),col=rainbow(ncol(allocations)+2),legend=colnames(allocations))
#Long Only Allocation Chart
Frontier<-portfolioFrontier(returns)
allocations <-getWeights(Frontier@portfolio)# get allocations for each stock
colnames(allocations)<-TickerList
barplot(t(allocations),col=rainbow(ncol(allocations)+2),legend=colnames(allocations))