Visually Comparing Return Distributions

Here is a spot of code to create a series of small multiples for comparing return distributions. You may have spotted this in a presentation I posted about earlier, but I’ve been using it here and there and am finally satisfied that it is a generally useful view, so I functionalized it.

require(PerformanceAnalytics)
data(edhec)
page.Distributions(edhec[,c("Convertible Arbitrage", "Equity Market Neutral","Fixed Income Arbitrage", "Event Driven", "CTA Global", "Global Macro", "Long/Short Equity")])

When visually comparing distributions, there are a few characteristics to get right across the graphs. For example, each histogram’s bin sizes should match and the min and the max of each chart should line up.

I prefer all three views together. The histogram is a more typical view of the distribution, improved when overplotted with a normal distribution and with the zero bin marked, both being important references. The QQ plot is more important, again improved with confidence bands for a normal distribution.

This is just a first cut. There’s no reason that the normal distribution has to be the reference for these charts, but I’ll have to do some more parameterization. There is also a balance between the number of rows in the device and readability. Maybe I’ll insert some “pagination” like charts.BarVaR uses… What else?

This is checked into PApages on r-forge right now, in /sandbox as page.Distributions.R. I’m contemplating including it in PerformanceAnalytics, but I’m interested in your feedback before I do. Here’s the code:

# Histogram, QQPlot and ECDF plots aligned by scale for comparison
page.Distributions <- function (R, ...) {
  require(PerformanceAnalytics)
  op <- par(no.readonly = TRUE)
  # c(bottom, left, top, right)
  par(oma = c(5,0,2,1), mar=c(0,0,0,3))
  layout(matrix(1:(4*NCOL(R)), ncol=4, byrow=TRUE), widths=rep(c(.6,1,1,1),NCOL(R)))
  # layout.show(n=21)
  chart.mins=min(R, na.rm=TRUE)
  chart.maxs=max(R, na.rm=TRUE)
  row.names = sapply(colnames(R), function(x) paste(strwrap(x,10), collapse = "\n"), USE.NAMES=FALSE)
  for(i in 1:NCOL(R)){
    if(i==NCOL(R)){
      plot.new()
      text(x=1, y=0.5, adj=c(1,0.5), labels=row.names[i], cex=1.1)
      chart.Histogram(R[,i], main="", xlim=c(chart.mins, chart.maxs), 
                      breaks=seq(round(chart.mins, digits=2)-0.01, round(chart.maxs, digits=2)+0.01, by=0.01), 
                      show.outliers=TRUE, methods=c("add.normal"), colorset = 
                        c("black", "#00008F", "#005AFF", "#23FFDC", "#ECFF13", "#FF4A00", "#800000"))
      abline(v=0, col="darkgray", lty=2)
      chart.QQPlot(R[,i], main="", pch=20, envelope=0.95, col=c(1,"#005AFF"), ylim=c(chart.mins, chart.maxs))
      abline(v=0, col="darkgray", lty=2)
      chart.ECDF(R[,i], main="", xlim=c(chart.mins, chart.maxs), lwd=2)
      abline(v=0, col="darkgray", lty=2)
    }
    else{
      plot.new()
      text(x=1, y=0.5, adj=c(1,0.5), labels=row.names[i], cex=1.1)
      chart.Histogram(R[,i], main="", xlim=c(chart.mins, chart.maxs), 
                      breaks=seq(round(chart.mins, digits=2)-0.01, round(chart.maxs, digits=2)+0.01, by=0.01), 
                      xaxis=FALSE, yaxis=FALSE, show.outliers=TRUE, methods=c("add.normal"), colorset = 
                        c("black", "#00008F", "#005AFF", "#23FFDC", "#ECFF13", "#FF4A00", "#800000"))
      abline(v=0, col="darkgray", lty=2)
      chart.QQPlot(R[,i], main="", xaxis=FALSE, yaxis=FALSE, pch=20, envelope=0.95, col=c(1,"#005AFF"), ylim=c(chart.mins, chart.maxs))
      abline(v=0, col="darkgray", lty=2)
      chart.ECDF(R[,i], main="", xlim=c(chart.mins, chart.maxs), xaxis=FALSE, yaxis=FALSE, lwd=2)
      abline(v=0, col="darkgray", lty=2)
    }
  }
  par(op)
}