With Size, Does Risk–>Return?

A basic tenet in finance is that higher risk should lead to higher return as the time horizon stretches to infinity.  However, in bonds, higher risk has not meant higher return with either credit risk (high-yield) or long duration risk (maturity > 15 years).  Based on some quick analysis of Kenneth French’s dataset on returns by market capitalization, it appears theory might better explain reality but not in a linear fashion.  For those more interested in risk and return on small caps, see this fascinating revelation refuting a basic tenet of finance About That Small Cap Effect: Oops!

From TimelyPortfolio

From TimelyPortfolio

From TimelyPortfolio

R code from GIST:

	#use Ken French market cap series
	#http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/Portfolios_Formed_on_ME.zip
	require(PerformanceAnalytics)
	require(quantmod)
	my.url="http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/ftp/Portfolios_Formed_on_ME.zip"
	my.tempfile<-paste(tempdir(),"\\frenchsize.zip",sep="")
	my.usefile<-paste(tempdir(),"\\Portfolios_Formed_on_ME.txt",sep="")
	download.file(my.url, my.tempfile, method="auto",
	quiet = FALSE, mode = "wb",cacheOK = TRUE)
	unzip(my.tempfile,exdir=tempdir(),junkpath=TRUE)
	#read space delimited text file extracted from zip
	french_size <- read.table(file=my.usefile,
	header = TRUE, sep = "",
	as.is = TRUE,
	skip = 13, nrows=1020)
	#for simplicity use small mid large but series contains more granular also
	colnames(french_size)[3:5] <- c("Small30","Mid40","Large30")
	#get dates ready for xts index
	datestoformat <- french_size[,1]
	datestoformat <- paste(substr(datestoformat,1,4),
	substr(datestoformat,5,7),"01",sep="-")
	#get xts for analysis
	french_size_xts <- as.xts(french_size[,3:5],
	order.by=as.Date(datestoformat))
	mycolors = c("indianred3","slateblue4","darkolivegreen4")
	french_size_xts <- french_size_xts/100
	#jpeg#"size risk return.jpeg",height=6.5,width=6.5,res=96,units="in")
	chart.RiskReturnScatter(french_size_xts, main="Risk and Return by Size
	U. S. Stocks Since 1926",xlim=c(0,0.35),colorset=mycolors)
	mtext("Source: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french",
	side=1,line=2,cex=0.8,adj=0)
	#dev.off()
	#jpeg#"size correlation.jpeg",height=6.5,width=6.5,res=96,units="in")
	chart.Correlation(french_size_xts, main="Correlation by Size
	U. S. Stocks Since 1926")
	mtext("Source: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french",
	side=1,line=2,cex=0.8,adj=0)
	#dev.off()
	frontier <- portfolioFrontier(as.timeSeries(french_size_xts))
	pointsFrontier = frontierPoints(frontier, frontier = "both", auto=TRUE)
	targetRisk = getTargetRisk(frontier@portfolio)[,1]
	targetReturn = getTargetReturn(frontier@portfolio)[,1]
	ans = cbind(Risk = targetRisk, Return = targetReturn)
	colnames(ans) = c("targetRisk", "targetReturn")
	rownames(ans) = as.character(1:NROW(ans))
	#points(ans)
	#jpeg#"size frontier.jpeg",height=6.5,width=6.5,res=96,units="in")
	plot(ans,xlim=c(min(ans[,1]),max(ans[,1])+.025),ylim=c(0,0.016),type="l",lwd=2, xlab=NA,ylab=NA)
	#frontierPlot(frontier, pch=19,title=FALSE,xlim=c(min(ans[,1]),max(ans[,1])+.025),ylim=c(0,0.016),add=FALSE)
	#minvariancePoints(frontier,pch=19,col="red")
	#tangencyPoints(frontier,pch=19,col="blue")
	#tangencyLines(frontier,pch=19,col="blue")
	equalWeightsPoints(frontier,pch=15,col="grey")
	singleAssetPoints(frontier,pch=19,cex=1.5,col=mycolors)
	#twoAssetsLines(frontier,lty=3,col="grey")
	#sharpeRatioLines(frontier,col="orange",lwd=2)
	#legend("topleft",legend=colnames(french_size_xts),pch=19,col=mycolors,
	# cex=0.65)
	#label assets
	stats <- getStatistics(frontier)
	text(y=stats$mean,x=sqrt(diag(stats$Cov)),labels=names(stats$mean),pos=4,col=mycolors,cex=0.7)
	title(main="Efficient Frontier by Size since 1926",xlab="Risk(cov)",ylab="Monthly Return")
	mtext("Source: http://mba.tuck.dartmouth.edu/pages/faculty/ken.french",
	side=1,line=2,cex=0.8,adj=0)
	#dev.off()

view raw size risk return.r hosted with ❤ by GitHub