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rollingPortfolios.r
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rollingPortfolios.r
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# rollingPortfolios.r Examples of rolling analysis of portfolios
#
# author: Eric Zivot
# created: November 26, 2006
# updated: November 16, 2008
#
# notes:
# 1. requires portfolio functions in portfolio.r
# 2. data are imported from singleIndexPrices.csv
# which contains monthly closing prices on the following assets
#
# sp500, sbux, msft, nord, boeing
#
# over the period 10/98 - 10/03
#
library(zoo)
singleIndexPrices.df = read.csv("C:/finBook/EXCEL/singleIndexPrices.csv",
stringsAsFactors=F)
colnames(singleIndexPrices.df)
#
# 2. Create zooreg object from data and dates in singleIndexPrices.df
#
singleIndexPrices.z = zooreg(data=singleIndexPrices.df[,-1],
start=c(1998,10), end=c(2003,10),
frequency=12)
plot(singleIndexPrices.z)
#
# 3. create returns
#
si.z = diff(log(singleIndexPrices.z))
si.df = as.data.frame(coredata(si.z))
# returns excluding market
ret.mat = as.matrix(si.df[,-1])
# plot returns over full sample
plot(si.z)
# estimate parameters of constant expected return
# model
options(digits=4)
nobs = length(si.z[,1])
muhat.vals = colMeans(ret.mat)
sigmahat.vals = apply(ret.mat,2,sd)
cov.mat = var(ret.mat)
cor.mat = cor(ret.mat)
se.muhat = sigmahat.vals/sqrt(nobs)
se.sigmahat = sigmahat.vals/sqrt(2*nobs)
mu.lower = muhat.vals - 2*se.muhat
mu.upper = muhat.vals + 2*se.muhat
sigma.lower = sigmahat.vals - 2*se.sigmahat
sigma.upper = sigmahat.vals + 2*se.sigmahat
plot(sigmahat.vals, muhat.vals, type="n",
xlab = "sigma", ylab="mu",
xlim=range(c(sigma.lower,sigma.upper)),
ylim=range(c(mu.lower,mu.upper)))
text(sigmahat.vals[c(1,4)], muhat.vals[c(1,4)],
labels=names(muhat.vals[c(1,4)]))
#
# compute efficient portfolios
#
# global minimum variance portfolio
gmin.4 = globalMin.portfolio(er=muhat.vals,cov.mat=cov.mat)
gmin.4
# efficient portfolio with target return = 0.015
eport.015 = efficient.portfolio(er=muhat.vals,cov.mat=cov.mat,
target.return=0.015)
eport.015
plot(eport.015)
# compute efficient frontier
ef.4 = efficient.frontier(er=muhat.vals,cov.mat=cov.mat)
ef.4
plot(ef.4, plot.assets=T)
#
# rolling global min portfolios
#
rollGmin = function(x) {
mu.hat = colMeans(x)
cov.hat = var(x)
gmin = globalMin.portfolio(er=mu.hat,cov.mat=cov.hat)
ans = c(gmin$er,gmin$sd,gmin$weights)
names(ans)[1:2] = c("er","sd")
ans
}
rollefficient = function(x,target=0.015) {
mu.hat = colMeans(x)
cov.hat = var(x)
eport = efficient.portfolio(er=mu.hat,cov.mat=cov.hat,
target.return=target)
ans = c(eport$er,eport$sd,eport$weights)
names(ans)[1:2] = c("er","sd")
ans
}
# rolling global minimum variance portfolios
roll.gmin = rollapply(si.z[,-1],width=24,
by.column=F,align="right",
FUN=rollGmin)
plot(roll.gmin[,3:6],main="Rolling weights in global min portfolio",
plot.type="single", col=1:4, lwd=3, ylab="weight")
abline(h=0)
legend(x="bottomleft",legend=colnames(si.z[,-1]),
lty=rep(1,4),col=1:4,lwd=3)
plot(roll.gmin[,1:2],plot.type="single",ylab="percent",
main="Rolling means and sds on global min portfolio",
col=c("black","orange"),lwd=3)
abline(h=0)
legend(x="topleft",legend=colnames(roll.gmin[,1:2]),
lty=rep(1,2),col=c("black","orange"),lwd=3)
# rolling efficient portfolios with target = 0.015
roll.eport = rollapply(si.z[,-1],width=24,
by.column=F,align="right",
FUN=rollefficient)
plot(roll.eport[,3:6],main="Rolling weights in efficient portfolio with target=0.015",
plot.type="single", ylab="weight", col=1:4,lwd=3)
abline(h=0)
legend(x="bottomleft",legend=colnames(si.z[,-1]),
lty=rep(1,4),col=1:4,lwd=3)
plot(roll.eport[,1:2], plot.type="single", ylab="percent",
main="Rolling means and sds on efficient portfolio with target=0.015",
col=c("black","orange"),lwd=3)
abline(h=0)
legend(x="topleft",legend=colnames(roll.eport[,1:2]),
lty=rep(1,2),col=c("black","orange"),lwd=3)