When I saw the answer to this Stack Overflow question, I immediately remembered working on my old post Clustering with Currencies and Fidelity Funds and just had to try to apply this technique. As I should have guessed, it worked with only a minimal amount of changes. Hoping to incrementally improve, I added a couple of slight modifications.
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| From TimelyPortfolio |
R code from GIST (select raw to copy/paste):
Since I explored the relationship between the Japanese Yen and the US 10y Treasury Yield on Friday, I thought it might be worthwhile to extend the exploration to a much broader range of currencies. I personally am most interested on how Asian Central Bank manipulation has affected the US 10y yield, and how if that changes what might be the impact to world markets. Please let me know your thoughts.
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| From TimelyPortfolio |
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| From TimelyPortfolio |
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.
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| From TimelyPortfolio |
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| 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.
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| 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.
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| From TimelyPortfolio |
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| From TimelyPortfolio |
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| 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)
After the very nice Convore reply
@timelyportfolio some of your posts include "eigenvalue ratio plots" -- kindly tell us what they show and how they might be useful in constructing a portfolio.
I felt like I should at least attempt to offer a little more detail on eigenvectors, which allow us to visually see similarity between variables (in my mind, time series of asset classes, indexes, stocks, or other financial prices). In other posts, I have used the fAssets package function assetsCorEigenPlot for Long XLU Short SPY and Russell Napier, ASIP in FT Says Emerging Market Currencies. Michael Friendly’s wonderful paper does a very fine job of explaining eigenvalues and their use in sorting for helpful visualizations of correlation. Wikipedia also gives a decent introduction in these two articles http://en.wikipedia.org/wiki/Principal_component_analysis and http://en.wikipedia.org/wiki/Eigenvector. Also, I’m anxious to read the following book whose authors run http://factominer.free.fr/classical-methods/index.html.
Really, the closer the variables in distance and angle, the more closely they are related. I thought some currency data from the St. Louis Fed would provide a nice example. Similar to milktrader’s Chop, Slice and Dice Your Returns in R, I also wanted to show multiple ways in R of achieving a plot of eigenvalues with fAssets, SciViews, and corrgram. This analysis does not yield any real surprises—Mexican Peso and Brazilian Real are closely related, but both are least related to the Japanese Yen.
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| From TimelyPortfolio |
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| From TimelyPortfolio |
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| From TimelyPortfolio |
Since I used Michael Friendly’s paper so much in writing this article, I wanted to show a corrgram of the currency data. The corrgram package offers lots of potentially useful variations of this visualization.
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| From TimelyPortfolio |
The second part of the Convore question is how can we use eigenvalues to construct a portfolio. Maybe I can answer that in one of my next posts…
R code:
#explain basics of principal component analysis
#by showing the various methods of charting eigenvalues
#of currency data #give specific credit to Michael Friendly
#and his paper http://www.math.yorku.ca/SCS/Papers/corrgram.pdf
#another example of similar techniques used for both
#baseball and finance #for additional information on principal component analysis (PCA)
#see http://en.wikipedia.org/wiki/Principal_component_analysis 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")
#get daily percent changes
currencies<-currencies/lag(currencies)-1 #using fAssets
require(fAssets)
assetsCorEigenPlot(as.timeSeries(currencies)) #using techniques from corrgram package documentation
#get correlation matrix
(currencies.cor <- cor(currencies,use="pair"))
#get two largest eigenvectors
(currencies.eig<-eigen(currencies.cor)$vectors[,1:2])
e1 <- currencies.eig[,1]
e2 <- currencies.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 Asian
and American Currencies (corrgram)")
arrows(0, 0, e1, e2, cex=0.5, col="red", length=0.1)
text(e1,e2, rownames(currencies.cor), cex=0.75)
#run an interesting corrgram chart
require(corrgram) #do not need for previous eigenvector plot
df1 <- data.frame(cbind(index(currencies),coredata(currencies)))
corrgram(df1, order=TRUE,
main="Currency data PC2/PC1 order",
lower.panel=panel.shade, upper.panel=panel.pie,
text.panel=panel.txt) #using techniques from SciViews package
#do principal component analysis
require(SciViews)
(currencies.pca <- pcomp(~Korea + Malaysia + Singapore + Taiwan +
China + Japan + Thailand + Brazil + Mexico + India +
USDOther + USDBroad,
data = currencies))
#make the chart
plot(currencies.pca, which = "correlations",
main="Plot of 2 Largest Eigenvectors for Various Asian
and American Currencies (SciViews)")
#more SciViews fun
#summary(currencies.pca)
#screeplot(currencies.pca)
#currencies.ldg<-loadings(currencies.pca)
#(currencies.cor <- correlation(currencies.pca))
#plot(currencies.pca, which = "scores", cex = 0.8)
#pairs(currencies.pca) #compare 2 largest eigenvectors from the sciview and corrgram
cbind(loadings(currencies.pca)[,1],e1,loadings(currencies.pca)[,2],e2)
