Clustering with Currencies and Fidelity Funds

Great news came yesterday with the release of the R In Finance 2011 Presentations.  I must attend next year after seeing all that I missed.  The Iacus: Statistical Analysis of Financial Time Series and Option Pricing in R (pdf) presentation offered a different method of clustering than that shown in yesterday’s post Eigen-who? How Can I Write About Eigen-anything and Expect You to Read?, so I thought it would be fun to quickly run his Markov Operator Distance example on the currency data from yesterday. As always, please comment liberally and point out any errors.  Mr. Iacus does not use the change but rather price in his analysis.  Knowing far less about these methods, I think using percentage change makes more sense.  I’ll use price first and then show results using percentage change.

From TimelyPortfolio

From TimelyPortfolio

As I said above, price is used, but I thought I should run on price change also.  These results make more sense to me since I know that the Chinese Yuan has been closely pegged to the US Dollar over the analysis period.

From TimelyPortfolio

A very good friend of mine has a 401k with various Fidelity mutual funds, so let’s run the same techniques on his set of Fidelity Fund options.  To avoid repetition, I will only run on price change rather than price.  I only included the equity fund options, so FPURX Fidelity Puritan with only 60% equities makes sense that it is all alone.

From TimelyPortfolio

From TimelyPortfolio

From TimelyPortfolio

R code:

#extends post on principal component analysis with MODist
#using example from http://www.rinfinance.com/agenda/2011/StefanoIacus.pdf
#on currency data and fidelity mutual fund data   require(quantmod)   #get currency data from the FED FRED data series
Korea  <-  getSymbols("DEXKOUS",src="FRED",auto.assign=FALSE) #load Korea
Malaysia  <-  getSymbols("DEXMAUS",src="FRED",auto.assign=FALSE) #load Malaysia
Singapore  <-  getSymbols("DEXSIUS",src="FRED",auto.assign=FALSE) #load Singapore
Taiwan  <-  getSymbols("DEXTAUS",src="FRED",auto.assign=FALSE) #load Taiwan
China  <-  getSymbols("DEXCHUS",src="FRED",auto.assign=FALSE) #load China
Japan  <-  getSymbols("DEXJPUS",src="FRED",auto.assign=FALSE) #load Japan
Thailand  <-  getSymbols("DEXTHUS",src="FRED",auto.assign=FALSE) #load Thailand
Brazil  <-  getSymbols("DEXBZUS",src="FRED",auto.assign=FALSE) #load Brazil
Mexico  <-  getSymbols("DEXMXUS",src="FRED",auto.assign=FALSE) #load Mexico
India  <-  getSymbols("DEXINUS",src="FRED",auto.assign=FALSE) #load India
USDOther  <-  getSymbols("DTWEXO",src="FRED",auto.assign=FALSE) #load US Dollar Other Trading Partners
USDBroad  <-  getSymbols("DTWEXB",src="FRED",auto.assign=FALSE) #load US Dollar Broad       #combine all the currencies into one big currency xts
currencies <- merge(Korea, Malaysia, Singapore, Taiwan,
	China, Japan, Thailand, Brazil, Mexico, India,
	USDOther, USDBroad)
currencies <- na.omit(currencies)
colnames(currencies) <- c("Korea", "Malaysia", "Singapore", "Taiwan",
	"China", "Japan", "Thailand", "Brazil", "Mexico", "India",
	"USDOther", "USDBroad")       #use MODist package as described in the fine presentation
#http://www.rinfinance.com/agenda/2011/StefanoIacus.pdf
require(sde)   currencies <- as.zoo(currencies)
d  <-  MOdist(currencies)
cl  <-  hclust( d )
groups  <-  cutree(cl, k=4)
plot(currencies, col=groups, main="Various Asian and American Currencies
	1995-Current")
cmd  <-  cmdscale(d)
colnames(cmd)  <-  c("first coordinate","second coordinate")
plot( cmd, col=groups, main="MODist of Various Asian and American Currencies
	1995-Current" )
text( cmd, labels(d) , col=groups)   #struggling with whether price or percent change works better
#run again with percentage change
currencies <- ROC(currencies,1,type="discrete")
currencies[1,1:NCOL(currencies)] <- 0
currencies <- as.zoo(currencies)
d  <-  MOdist(currencies)
cl  <-  hclust( d )
groups  <-  cutree(cl, k=4)
cmd  <-  cmdscale(d)
colnames(cmd)  <-  c("first coordinate","second coordinate")
plot( cmd, col=groups, main="MODist of Various Asian and American Currencies
	Percentage Change 1995-Current" )
text( cmd, labels(d) , col=groups)     #do the same MODist for some Fidelity Funds
#except just use price change rather than price
tckr<-c("FBGRX","FCNTX","FDGFX","FEQIX","FEXPX",
	"FFTYX","FFIDX","FDGRX","FDEGX","FLCSX",
	"FMCSX","FOCPX","FDVLX","FSLSX","FIVFX",
	"FOSFX","FRESX","FSEMX","FSTMX","FPURX")
start<-"1990-01-01"
end<- format(Sys.Date(),"%Y-%m-%d") # yyyy-mm-dd   # Pull tckr index data from Yahoo! Finance
getSymbols(tckr, from=start, to=end, adjust=TRUE)   fidelity<-na.omit(merge(to.weekly(FBGRX)[,4],to.weekly(FCNTX)[,4],
	to.weekly(FDGFX)[,4] ,to.weekly(FEQIX)[,4],
	to.weekly(FEXPX)[,4] , to.weekly(FFTYX)[,4],
	to.weekly(FFIDX)[,4] , to.weekly(FDGRX)[,4],
	to.weekly(FDEGX)[,4] , to.weekly(FLCSX)[,4],
	to.weekly(FMCSX)[,4] , to.weekly(FOCPX)[,4],
	to.weekly(FDVLX)[,4] , to.weekly(FSLSX)[,4],	
	to.weekly(FIVFX)[,4] , to.weekly(FOSFX)[,4],
	to.weekly(FRESX)[,4] , to.weekly(FSEMX)[,4],
	to.weekly(FSTMX)[,4] , to.weekly(FPURX)[,4]))   colnames(fidelity) <- substr(colnames(fidelity),1,5)   fidelity <- ROC(fidelity,1,type="discrete")
fidelity[1,1:NCOL(fidelity)] <- 0
fidelity <- as.zoo(fidelity)   d  <-  MOdist(fidelity)
cl  <-  hclust( d )
groups  <-  cutree(cl, k=5)
plot(fidelity, col=groups, main="Various Fidelity Mutual Funds
	1998-Current")
cmd  <-  cmdscale(d)
colnames(cmd)  <-  c("first coordinate","second coordinate")
plot( cmd, col=groups, main="MODist of Various Fidelity Mutual Funds
	1995-Current" )
text( cmd, labels(d) , col=groups)   #get plot of eigenvalues since we have not done in any
#previous posts
#using techniques from corrgram package documentation
#get correlation matrix
(fidelity.cor <- cor(fidelity,use="pair"))
#get two largest eigenvectors
(fidelity.eig <- eigen(fidelity.cor)$vectors[,1:2])
e1 <- fidelity.eig[,1]
e2 <- fidelity.eig[,2]
#make the chart
plot(e1,e2,col='white', xlim=range(e1,e2), ylim=range(e1,e2),
	main="Plot of 2 Largest Eigenvectors for Various Fidelity Funds")
arrows(0, 0, e1, e2, cex=0.5, col=groups, length=0.1)
text(e1,e2, rownames(fidelity.cor), cex=0.75, col=groups)

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