Great FAJ Article on Statistical Measure of Financial Turbulence Part 3

April 26, 2011
By

(This article was first published on Timely Portfolio, and kindly contributed to R-bloggers)

Building on posts Great FAJ Article on Statistical Measure of Financial Turbulence and Great FAJ Article on Statistical Measure of Financial Turbulence Part 2, I will now build a system incorporating a new correlation-based measure of turbulence and a simple relative strength technique.  First, the new correlation-based measure looks like this

From TimelyPortfolio
From TimelyPortfolio

Then if we build a system with just this new correlation-based turbulence, we get fairly good results.  However, if we take one step extra and apply a slope-based relative strength to choose S&P500 or CRB rather than equal-weight both, we get even better results.

From TimelyPortfolio

I always want more data in countries and years, but 1957 is pretty thorough.  Please let me know how you would improve this system.

 

R code:

require(quantmod)
require(PerformanceAnalytics)

#get data from St. Louis Federal Reserve (FRED)
getSymbols("GS20",src="FRED") #load 20yTreasury; 20y has gap 86-93; 30y has gap in early 2000s
getSymbols("GS30",src="FRED") #load 30yTreasury to fill 20y gap 86-93
getSymbols("BAA",src="FRED") #load BAA
getSymbols("SP500",src="FRED") #load SP500

#get CRB data from a csv file
CRB<-as.xts(read.csv("crb.csv",row.names=1))[,1]

#fill 20y gap from discontinued 20y Treasuries with 30y
GS20["1987-01::1993-09"]<-GS30["1987-01::1993-09"]

#do a little manipulation to get the data lined up on monthly basis
SP500<-to.monthly(SP500)[,4]
#get monthly format to yyyy-mm-dd with the first day of the month
index(SP500)<-as.Date(index(SP500))
#my CRB data is end of month; could change but more fun to do in R
CRB<-to.monthly(CRB)[,4]
index(CRB)<-as.Date(index(CRB))

#let's merge all this into one xts object; CRB starts last in 1956
assets<-na.omit(merge(GS20,SP500,CRB))
#use ROC for SP500 and CRB and momentum for yield data
assetROC<-na.omit(merge(momentum(assets[,1])/100,ROC(assets[,2:3],type="discrete")))

#get Correlations
corrBondsSp<-runCor(assetROC[,1],assetROC[,2],n=7)
corrBondsCrb<-runCor(assetROC[,1],assetROC[,3],n=7)
corrSpCrb<-runCor(assetROC[,2],assetROC[,3],n=7)
#composite measure of correlations between asset classes and roc-weighted correlations
assetCorr<-(corrBondsSp+corrBondsCrb+corrSpCrb+
    (corrBondsSp*corrSpCrb*assetROC[,2])+
    (corrBondsCrb*corrSpCrb*assetROC[,3])-
    assetROC[,1])/6
#sum of ROCs of asset classes
assetROCSum<-assetROC[,1]+assetROC[,2]+assetROC[,3]
#finally the turbulence measure
turbulence<-abs(assetCorr*assetROCSum*100)
colnames(turbulence)<-"Turbulence-correlation"

chartSeries(turbulence,theme="white",name="Correlation and % Change as Measure of Financial Turbulence")
abline(h=0.8)

chart.ACF(turbulence,main="Auto-correlation of Turbulence")

#wish I could remember where I got some of this code
#most likely candidate is www.fosstrading.com
#please let me know if you know the source
#so I can give adequate credit

#use turbulence to determine in or out of equal-weighted sp500 and crb
signal<-ifelse(turbulence>0.8,0,1)
#use slope of sp500/crb to determine sp500 or crb

signal<-lag(signal,k=1)
# Replace missing signals with no position
# (generally just at beginning of series)
signal[is.na(signal)] <- 0

#get returns from equal-weighted crb and sp500 position; Return.portfolio was causing problems, so did the hard way
ret<-(assetROC[,2]+assetROC[,3])/2
ret[1] <- 0

#get system performance
system_perf<-ret*signal
system_eq<- cumprod(1+ret*signal)

perf_comparison<-merge(lag((assetROC[,2]+assetROC[,3])/2,k=1),system_perf)
colnames(perf_comparison)<-c("Equal-weighted","System-with-turbulence-filter")

charts.PerformanceSummary(perf_comparison,ylog=TRUE,main="Turbulence-based System vs Equal-Weighted CRB and SP500")

#let's use basic relative strength to pick sp500 or crb
#know I can do this better in R but here is my ugly code
#to calculate 12 month slope of sp500/crb
width=12
for (i in 1:(NROW(assets)-width)) {
    model<-lm(assets[i:(i+width),2]/assets[i:(i+width),3]~index(assets[i:(i+width)]))
    ifelse(i==1,assetSlope<-model$coefficients[2],assetSlope<-rbind(assetSlope,model$coefficients[2]))
}
assetSlope<-xts(cbind(assetSlope),order.by=index(assets)[(width+1):NROW(assets)])
#use turbulence to determine in or out of equal-weighted sp500 and crb
signal<-ifelse(turbulence[(width):NROW(turbulence)]>0.8,0,1)

#use slope of sp500/crb to determine sp500 or crb
signal2<-ifelse(assetSlope>0,1,2)

signal<-lag(signal,k=1)
signal[1]<-0
signal2<-lag(signal2,k=1)
signal2[1]<-0

#get sp500 or crb return based on slope
ret<-ifelse(signal2==1,assetROC[(width):NROW(assetROC),2],ifelse(signal2==2,assetROC[(width):NROW(assetROC),3],0))

#get system performance
system_perf_rs<-ret*signal
system_eq_rs<- cumprod(1+ret*signal)

perf_comparison<-merge((assetROC[,2]+assetROC[,3])/2,assetROC[,2],assetROC[,3],system_perf,system_perf_rs)
colnames(perf_comparison)<-c("Equal-weighted","S&P500","CRB","System-with-turbulence-filter","System-with-turbulence-filter and RS")

charts.PerformanceSummary(perf_comparison,ylog=TRUE,main="Turbulence-based System with RS vs Equal-Weighted, CRB, and SP500")

To leave a comment for the author, please follow the link and comment on his blog: Timely Portfolio.

R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...



If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Tags: , , ,

Comments are closed.