Utility Spread and Financial Turbulence

May 23, 2011
By

[This article was first published on Timely Portfolio, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)
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THIS IS NOT INVESTMENT ADVICE.  YOU ARE RESPONSIBLE FOR YOUR OWN GAINS AND LOSSES.

In Long XLU Short SPY Part 2 (More History), I explored the defensive nature of the spread and its potential as a bond substitute in troublesome periods for stocks.  I thought it would be interesting to see what happens if we use the spread as our cash position in the Great FAJ Article on Statistical Measure of Financial Turbulence Part 3 system.  Unfortunately, the use of the spread on price returns as cash does not benefit the system as much as bonds as cash, but I still thought it might encourage some additional reader thought on the spread and its potential uses.

From TimelyPortfolio

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
#now Dow Jones Indexes
getSymbols(“DJIA”,src=”FRED”) #load daily Dow Jones Industrial
getSymbols(“DJUA”,src=”FRED”) #load daily Dow Jones Utility

DJUADJIA<-DJUA/DJIA

#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]
DJUADJIA<-to.monthly(DJUADJIA)[,4]
#get monthly format to yyyy-mm-dd with the first day of the month
index(SP500)<-as.Date(index(SP500))
index(DJUADJIA)<-as.Date(index(DJUADJIA))
#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,DJUADJIA))
#use ROC for SP500 and CRB and momentum for yield data
assetROC<-na.omit(merge(momentum(assets[,1])/100,ROC(assets[,2:4],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<-ifelse(signal==1,(assetROC[,2]+assetROC[,3])/2,assetROC[,4])
ret[1] <- 0

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

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

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

signals_and_returns<-merge(signal,signal2,assetROC,turbulence)
#get sp500 or crb return based on slope or use bonds as cash
ret<-ifelse(signals_and_returns[,2]==1,signals_and_returns[,4],ifelse(signals_and_returns[,2]==2,signals_and_returns[,5],signals_and_returns[,3]))
#get sp500 or crb return based on slope or use utility spread as cash
ret_util<-ifelse(signals_and_returns[,2]==1,signals_and_returns[,4],ifelse(signals_and_returns[,2]==2,signals_and_returns[,5],signals_and_returns[,6]))
ret[1]<-0
ret_util[1]<-0

#get system performance
system_perf_rs<-signals_and_returns[,1]*ret
system_perf_rs_util<-ret_util
system_eq_rs<- cumprod(1+signals_and_returns[,1]*ret)
system_eq_rs_util<- cumprod(1+ret_util)

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

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

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