Universal portfolio, part 11

September 23, 2012

(This article was first published on logopt: a journey in R, finance and open source, and kindly contributed to R-bloggers)

First an apology, the links to the Universal Portfolio paper have stopped working.  This is because the personal webpage of Thomas Cover at Stanford has been taken down, but fortunately the content moved elsewhere.  The new link is Universal Portfolio and hopefully this one will be stable.

Note that there are many available copies on the web but most (like this one) are for something that seems to be a slighly reworked version dated October 23 1996.  The text appears mostly identical to the published version, but it does not include the figures.

In the rest of this post, I discuss the data used by Cover.  That data is included in logopt as nyse.cover.1962.1984.  It contains the relative prices for 36 NYSE stocks between 1962 and 1984.

> range(index(nyse.cover.1962.1984))
[1] “1962-07-03″ “1984-12-31″

> colnames(nyse.cover.1962.1984)
 [1] “ahp”    “alcoa”  “amerb”  “arco”   “coke”   “comme”  “dow”    “dupont” “espey”  “exxon”  “fisch”  “ford”   “ge”     “gm”     “gte”    “gulf”   “hp”    
[18] “ibm”    “inger”  “iroqu”  “jnj”    “kimbc”  “kinar”  “kodak”  “luken”  “meico”  “merck”  “mmm”    “mobil”  “morris” “pandg”  “pills”  “schlum” “sears” 
[35] “sherw”  “tex” 
The names are not stickers, some guessing and with some help from an other person using the series gives the table below (and if anybody knows about the one without expansion yet. please post a comment).

Abbreviation Company name Current ticker
ahp ? ?
alcoa Alcoa AA
amerb American Brands
aka Fortune Brands
arco ? ?
coke Coca-Cola KO
comme Commercial Metals CMC
dow Dow Chemicals DOW
dupont DuPont DD
espey Espey Manufacturing ESP
exxon Exxon Mobil XOM
coke Coca-Cola KO
fisch Fischbach Corp
ford Ford F
ge General Electric GE
gm General Motors GM*
gte GTE Corporation
gulf Gulf Oil (now Chevron) CVX
hp Hewlett-Packard HPQ
inger Ingersoll-Rand IR
iroq Iroquois Brands
jnj Johnson & Johnson JNJ
kimbc Kimberly-Clark KMB
kinar Kinark?
kodak Eastman Kodak EKDKQ
luken Lukens?
meico ? ?
merck Merck MRK
mmm 3M MMM
mobil Exxon Mobil XOM
morris Philip Morris PM
pandg Procter & Gamble PG
pills Pillsbury, now part of General Mills
schlum Schlumberger SLB
sears Sears Holdings SHLD
sherw Sherwin-Williams SHW
tex Texaco, now Chevron CVX

There is a lot of diversity across the different stocks, we saw that in two ways:

  • by showing the global time evolution of all stocks in time
  • by showing the growth rate at two times separated by N market days (shown as a price relative between the two dates).

# Some statistics on the NYSE series

x <- coredata(nyse.cover.1962.1984)
w <- logopt:::x2w(x)
nDays <- dim(x)[1]
nStocks <- dim(x)[2]
Days <- 1:nDays
iWin <- 1 ; plot(1:10)
Time <- index(nyse.cover.1962.1984)

# for each stock calculate:
# - min, max
# - average geometric return

MaxFinal <- max(w[nDays,])
MinFinal <- min(w[nDays,])
MaxAll <- max(w)
MinAll <- min(w)

if(length(dev.list()) < iWin) { x11() } ; iWin <- iWin + 1 ; dev.set(iWin) ;
plot(Time, w[,1], col="gray", ylim=range(w), log="y", type="l")
for (i in 1:nStocks) {
lines(Time, w[,i], col="gray")
if (w[nDays,i] == MaxFinal) { cat(sprintf("Stock with best final value: %s finishing at %.2f\n", colnames(w)[i], MaxFinal)) ; iMax <- i }
if (w[nDays,i] == MinFinal) { cat(sprintf("Stock with worst final value: %s finishing at %.2f\n", colnames(w)[i], MinFinal)) ; iMin <- i }
if (max(w[,i]) == MaxAll) { cat(sprintf("Stock with best peak value: %s at %.2f\n", colnames(w)[i], MaxAll)) }
if (min(w[,i]) == MinAll) { cat(sprintf("Stock with worst valley value: %s at %.2f\n", colnames(w)[i], MinAll)) }

lines(Time, w[,iMax], col="green")
lines(Time, w[,iMin], col="red")
lines(Time, apply(w,1,mean), col="blue")

# do a summary across n quotes
nDelta <- 1200
wD <- w[(nDelta+1):nDays,] / w[1:(nDays-nDelta),]
Time <- Time[1:(nDays-nDelta)]
MaxDAll <- max(wD)
MinDAll <- min(wD)
if(length(dev.list()) < iWin) { x11() } ; iWin <- iWin + 1 ; dev.set(iWin) ;
plot(Time, wD[,1], col="gray", ylim=range(wD), log ="y", type="l")
for (i in 1:nStocks) {
lines(Time, wD[,i], col="gray")
if (max(wD[,i]) == MaxDAll) { cat(sprintf("Stock with best gain on %s days: %s at %.2f\n", nDelta, colnames(w)[i], MaxDAll)) }
if (min(wD[,i]) == MinDAll) { cat(sprintf("Stock with worst lost on %s days: %s at %.2f\n", nDelta, colnames(w)[i], MinDAll)) }
lines(Time, apply(wD,1,mean), col="blue")


This gives the following textual answer and graphs.  Note that there are many alternate ways to present this information, in particular the package PerformanceAnalytics.

Stock with worst final value: dupont finishing at 3.07
Stock with worst valley value: meico at 0.26
Stock with best final value: morris finishing at 54.14
Stock with best peak value: schlum at 90.12
Stock with best gain on 1200 days: espey at 15.84
Stock with worst lost on 1200 days: meico at 0.07

This sequence forms a nice reference covering a long period of time, and has been used in many studies of portfolio selection algorithms.  But the series has a number of serious problems:
  • Survivorship bias
  • The time range corresponds to a time where quotes were not yet decimal.

To leave a comment for the author, please follow the link and comment on their blog: logopt: a journey in R, finance and open source.

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