Universal portfolio, part 11

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
ibm	IBM	IBM
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

library(logopt)
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")
grid()

# 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")

grid()

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.