Universal portfolio, part 3

After the theoretical analysis, section 8 of Universal Portfolios provides examples.  We now use logopt and R to reproduce them, the first three in this post.

The examples of Universal Portfolios use a long time series of relative stock prices on the NYSE originally accumulated by Cover himself.  This series has been reused by many authors to allow for comparisons of algorithms, and the series is available in logopt itself (originally downloaded from this website).

The two first figures introduce two specific stocks (8.1), then a series of CRP and Universal Portfolio for these two stocks (8.2).  Each figure is drawn using a standalone snippet of code.

	# figure 8.1 of Cover "Universal Portfolios"
	library(logopt)
	data(nyse.cover.1962.1984)
	x <- coredata(nyse.cover.1962.1984)
	xik <- x[,c("iroqu","kinar")]
	nDays <- dim(xik)[1]
	Days <- 1:nDays
	pik <- apply(xik,2,cumprod)
	plot(Days, pik[,"iroqu"], col="blue", type="l",
	ylim=range(pik), main = '"iroqu" and "kinar"', ylab="")
	lines(Days, pik[,"kinar"], col="red")
	grid()
	legend("topright",c('"iroqu"','"kinar"'),
	col=c("blue","red"),lty=c(1,1))

view raw fig8.1.R hosted with ❤ by GitHub

Performance of Iroquois brands and Kin Ark

	# fig 8.2 of Cover "Universal Portfolios"
	library(logopt)
	data(nyse.cover.1962.1984)
	x <- coredata(nyse.cover.1962.1984)
	xik <- x[,c("iroqu","kinar")]
	nDays <- dim(xik)[1]
	Days <- 1:nDays
	alphas <- seq(0,1,by=0.05)
	crps <- alphas
	for (i in 1:length(crps)) {
	crps[i] <- crp(xik, c(alphas[i], 1-alphas[i]))[nDays]
	}
	plot(alphas, crps, col="blue", type="l", ylab="",
	main='20 Year Return vs. mix of "iroqu" and "kinar"',
	xlab='Fraction of "iroqu" in Portfolio')
	points(alphas, crps, pch=19, cex=0.5, col="red")
	abline(h=mean(crps), col="green")
	text(0.5,mean(crps)*1.05,labels="Return from Universal Portfolio")
	grid()

view raw fig8.2.R hosted with ❤ by GitHub

Performance of rebalanced portfolio

	# fig 8.3 of Cover "Universal Portfolios"
	library(logopt)
	data(nyse.cover.1962.1984)
	x <- coredata(nyse.cover.1962.1984)
	xik <- x[,c("iroqu","kinar")]
	nDays <- dim(xik)[1]
	Days <- 1:nDays
	pik <- apply(xik,2,cumprod)
	alphas <- seq(0,1,by=0.05)
	universal <- xik[,1] * 0
	for (i in 1:length(alphas)) {
	universal <- universal + crp(xik, c(alphas[i], 1-alphas[i]))
	}
	universal <- universal/length(alphas)
	plot(Days, pik[,"iroqu"], col="blue", type="l", ylim=range(pik, universal),
	main = 'Universal Portfolios with "iroqu" and "kinar"', ylab="")
	lines(Days, pik[,"kinar"], col="red")
	lines(Days, universal, col="green")
	legend("topleft",c('"iroqu"','"kinar"','"universal"'),
	col=c("blue","red","green"),lty=c(1,1,1))
	grid()

view raw fig8.3.R hosted with ❤ by GitHub

Performance of universal portfolio

Updated on 2012/07/25 to correct code errors and use github:gist as repository for the code examples.