# Bonds Risk and Return by Rating

June 27, 2011
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(This article was first published on Timely Portfolio, and kindly contributed to R-bloggers)

As an extension to the Bond Market as a Casino Game series and Historical Sources of Bond Returns-Comparison of Daily to Monthly, I thought a ggplot of risk and return by decade and Moody’s Rating might be helpful.  Anyone who has read those other posts know that my opinion of bonds Guaranteed Failure with Bonds is not very favorable, and this is just another illustration that bond returns 1980-2011 are extremely abnormal and are mathematically impossible now.

 From TimelyPortfolio

`#do everything twice to compare monthly average to daily    require(RQuantLib)require(quantmod)require(PerformanceAnalytics) require(ggplot2)   getSymbols("AAA",src="FRED") # load Moody's AAA from Fed Fred getSymbols("BAA",src="FRED") # load Moody's BAA from Fed Fred    #Fed monthly series of yields is the monthly average of daily yields#set index to yyyy-mm-dd format rather than to.monthly mmm yyy for better merging laterindex(AAA)<-as.Date(index(AAA))index(BAA)<-as.Date(index(BAA))AAApricereturn<-AAABAApricereturn<-BAA   AAApricereturn[1,1]<-0BAApricereturn[1,1]<-0colnames(AAApricereturn)<-"PriceReturn-monthly avg AAA"colnames(BAApricereturn)<-"PriceReturn-monthly avg BAA"#use quantlib to price the AAA and BAA bonds from monthly yields#AAA and BAA series are 20-30 year bonds so will advance date by 25 yearsfor (i in 1:(NROW(AAA)-1)) {  AAApricereturn[i+1,1]<-FixedRateBondPriceByYield(yield=AAA[i+1,1]/100,issueDate=Sys.Date(),     maturityDate= advance("UnitedStates/GovernmentBond", Sys.Date(), 25, 3),    rates=AAA[i,1]/100,period=2)[1]/100-1} for (i in 1:(NROW(BAA)-1)) {  BAApricereturn[i+1,1]<-FixedRateBondPriceByYield(yield=BAA[i+1,1]/100,issueDate=Sys.Date(),     maturityDate= advance("UnitedStates/GovernmentBond", Sys.Date(), 25, 3),    rates=BAA[i,1]/100,period=2)[1]/100-1}   #total return will be the price return + yield/12 for one monthAAAtotalreturn<-AAApricereturn+lag(AAA,k=1)/12/100colnames(AAAtotalreturn)<-"TotalReturn-monthly avg AAA" BAAtotalreturn<-BAApricereturn+lag(BAA,k=1)/12/100colnames(BAAtotalreturn)<-"TotalReturn-monthly avg BAA"   charts.PerformanceSummary(merge(AAApricereturn,AAAtotalreturn,BAApricereturn,BAAtotalreturn),ylog=TRUE,	colorset=c("cadetblue","darkolivegreen3","purple","goldenrod"),	main="Simulated Returns from Moody's AAA and BAA Yield")mtext("Source: Federal Reserve FRED",side=1,adj=0)   AAA_BAA <- na.omit(merge(AAAtotalreturn,BAAtotalreturn))#get df for ggplotdf <- as.data.frame(cbind(index(AAA_BAA),coredata(AAA_BAA[,1:2])))df[,1] <- paste(substr(format(as.Date(df[,1]),"%Y"),1,3),0,sep="")colnames(df) <- c("Decade","AAA","BAA")dfmelt <- melt(df,id.vars=1)colnames(dfmelt) <- c("Decade","Moodys_Rating","TotalReturn")dfsum <- ddply(dfmelt, .(Decade,Moodys_Rating), summarise,	mean = mean(TotalReturn),	sd = sd(TotalReturn))jpeg(filename="risk and return by rating.jpg",quality=100,width=6.25, height = 5,  units="in",res=96)ggplot(dfsum, aes(x=sd,y=mean,label=factor(Decade))) + geom_point(aes(colour=Moodys_Rating)) +	geom_line(aes(x=sd,y=mean,colour=Moodys_Rating)) + geom_text(aes(colour=Moodys_Rating)) +	opts(title="Risk (sd) and Return (mean) by Moodys Rating since 1919")dev.off()     ####some other experimentation but not part of blog postgetSymbols("DJTA",src="FRED")getSymbols("DJIA",src="FRED")#convert to monthly and get monthly returnsDJTA <- ROC(to.monthly(DJTA)[,4],n=1,type="discrete")DJIA <- ROC(to.monthly(DJIA)[,4],n=1,type="discrete")#set index to yyyy-mm-dd format rather than to.monthly mmm yyy for better merging laterindex(DJTA)<-as.Date(index(DJTA))index(DJIA)<-as.Date(index(DJIA))   #merge AAA,BAA,DJTA,DJIAassetReturns <- na.omit(merge(AAAtotalreturn,BAAtotalreturn,DJTA,DJIA))   charts.PerformanceSummary(assetReturns,ylog=TRUE,	colorset=c("cadetblue","darkolivegreen3","purple","goldenrod"),	main="DJIA, DJTA, and Simulated Returns from Moody's AAA and BAA Yield")mtext("Source: Federal Reserve FRED",side=1,adj=0)   chart.RiskReturnScatter(assetReturns["1950::1959",])`

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