Hurst as Relative Strength

June 21, 2011
By

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

THIS IS NOT INVESTMENT ADVICE AND COULD EASILY RESULT IN SIGNIFICANT LOSSES.

As an extension to Testing Hurst with Multiple Indexes and Exploring the Market with Hurst, we also might employ our new Hurst signal as a relative strength determinant.  Let’s pick the index from S&P 500, German Dax, and the Nikkei 225 with the strongest Hurst signal as long as the signal also meets our original condition of >1 and at least one other index has a signal > a less severe 0.75.

From TimelyPortfolio

Certainly not the best I have seen but not bad.

From TimelyPortfolio

And this is a perfect example how standard deviation misrepresents a very significant risk reduction.


From TimelyPortfolio

R code (click to download):

#check Hurst exponent system as a potential relative strength signal
#this code is ugly and not very flexible
#I will continue to refine   require(quantmod)
require(PerformanceAnalytics)
require(FGN)   #sort of random mix for additional testing
indexes<-c("GSPC","GDAXI","N225")
getSymbols(paste("^",indexes,sep=""),
from="1900-01-01",to=format(Sys.Date(),"%Y-%m-%d"))
for (i in 1:length(indexes)) {
#set monthly index to first day of the month
assign(indexes[i],to.monthly(get(indexes[i]))[,4])
#has to be a cleaner way than this to set the index
assign(indexes[i],as.xts(coredata(get(indexes[i])),
order.by=as.Date(index(get(indexes[i])))))
}
#get monthly changes
retGSPC<-ROC(GSPC,n=1,type="discrete")
retGDAXI<-ROC(GDAXI,n=1,type="discrete")
retN225<-ROC(N225,n=1,type="discrete")
index(retGSPC) <- as.Date(index(retGSPC))
index(retGDAXI) <- as.Date(index(retGDAXI))
index(retN225) <- as.Date(index(retN225))   hurstKGSPC <- apply.rolling(retGSPC, FUN="HurstK", width = 12)
hurstKGDAXI <- apply.rolling(retGDAXI, FUN="HurstK", width = 12)
hurstKN225 <- apply.rolling(retN225, FUN="HurstK", width = 12)   serialcorrGSPC <- runCor(cbind(coredata(retGSPC)),cbind(index(retGSPC)),n=12)
serialcorrGDAXI <- runCor(cbind(coredata(retGDAXI)),cbind(index(retGDAXI)),n=12)
serialcorrN225 <- runCor(cbind(coredata(retN225)),cbind(index(retN225)),n=12)
serialcorrGSPC <- as.xts(serialcorrGSPC,order.by=index(retGSPC))
serialcorrGDAXI <- as.xts(serialcorrGDAXI,order.by=index(retGDAXI))
serialcorrN225 <- as.xts(serialcorrN225,order.by=index(retN225))   autoregGSPC <- runCor(retGSPC,lag(retGSPC,k=1),n=12)
autoregGDAXI <- runCor(retGDAXI,lag(retGDAXI,k=1),n=12)
autoregN225 <- runCor(retN225,lag(retN225,k=1),n=12)   signalUpTrendGSPC <- runMean(hurstKGSPC+serialcorrGSPC+autoregGSPC,n=6) +
(GSPC/runMean(GSPC,n=12)-1)*10
signalUpTrendGDAXI <- runMean(hurstKGDAXI+serialcorrGDAXI+autoregGDAXI,n=6) +
(GDAXI/runMean(GDAXI,n=12)-1)*10
signalUpTrendN225 <- runMean(hurstKN225+serialcorrN225+autoregN225,n=6) +
(N225/runMean(N225,n=12)-1)*10   #merge returns and lagged signal into one xts for evaluation
ret_signals <- merge(na.omit(merge(retGSPC,retGDAXI,retN225)),
lag(na.omit(merge(signalUpTrendGSPC,signalUpTrendGDAXI,signalUpTrendN225)),k=1))   #get return from the strongest Hurst exponent
retSys <- ifelse(ret_signals[,4]>ret_signals[,5]&ret_signals[,4]>ret_signals[,6]&ret_signals[,4]>1&(ret_signals[,5]>0.75|ret_signals[,6]>0.75),1,0)*ret_signals[,1]+
ifelse(ret_signals[,5]>ret_signals[,4]&ret_signals[,5]>ret_signals[,6]&ret_signals[,5]>1&(ret_signals[,4]>0.75|ret_signals[,6]>0.75),1,0)*ret_signals[,2]+
ifelse(ret_signals[,6]>ret_signals[,4]&ret_signals[,6]>ret_signals[,5]&ret_signals[,6]>1&(ret_signals[,4]>0.75|ret_signals[,5]>0.75),1,0)*ret_signals[,3]   #fill NAs from beginnning periods with no signal with 0
retSys[is.na(retSys)] <- 0   retCompare <- merge(retSys,ret_signals[,1:3])
colnames(retCompare) <- c("Hurst RS System","SP500","DAX","N225")
#jpeg(filename="HurstRS.jpg",quality=100,width=6.25, height = 5,
# units="in",res=96)
charts.PerformanceSummary(retCompare[19:NROW(retCompare),],ylog=TRUE,cex.legend=1.25,
colorset=c("cadetblue","darkolivegreen3","purple","gray70"))
#dev.off()     #for some risk return comparison
#jpeg(filename="HurstRSRiskReturn.jpg",quality=100,width=6.25, height = 5,
# units="in",res=96)
chart.RiskReturnScatter(retCompare[19:NROW(retCompare),],
main="Risk Return of Hurst RS System and Indexes")
#dev.off()   #for some ggplot2 risk bar charts
require(ggplot2)
#jpeg(filename="HurstRSRisk.jpg",quality=100,width=6.25, height = 5,
# units="in",res=96)
downsideTable<-melt(cbind(rownames(table.DownsideRisk(retCompare)),table.DownsideRisk(retCompare)))
colnames(downsideTable)<-c("Statistic","Portfolio","Value")
ggplot(downsideTable, stat="identity", aes(x=Statistic,y=Value,fill=Portfolio)) +
geom_bar(position="dodge") + coord_flip()
#dev.off()

Created by Pretty R at inside-R.org

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