VaR and CVaR percentages in R - an UniWIBID example

# more: http://www.reakkt.com/2012/07/var-you-cannot-estimate-unknown.html

TxtNum <- function(txt,num,d=4) {

  return( paste(txt,format(num,digits=d)) )

}

VaR <- function(x,alpha) {

  n <- length(x)

  # 1% of the elements
  pct <- ceiling(n/100)

  x.sorted <- sort(x)

  # number of alpha coefficients
  alphaN <- length(alpha)

  var  <- sapply(alpha, function(d) quantile(x,d))

  cvar <- sapply(alpha*100, function(d) mean(head(x.sorted,d*pct)))

  list(VaR=var, CVaR=cvar, min=min(x))

}

PlotVaR <- function(x) {

  var.list <- VaR(x,c(0.05,0.01))

  plot(density(x),main="Unit Returns Density + VaR")

  mtext(paste(TxtNum("mean=",mean(x)),
              TxtNum("VaR 5%=",var.list$VaR[1]),
              TxtNum("VaR 1%=",var.list$VaR[2]),
              TxtNum("CVaR 5%=",var.list$CVaR[1]),
              TxtNum("CVaR 1%=",var.list$CVaR[2]),
              TxtNum("min=",var.list$min)),
        line=0.5,cex=0.8)

  abline(v=mean(x),col="Blue",lty="dotted")

  abline(v=quantile(x,0.05),col="Red",lty="dotted")
  abline(v=quantile(x,0.01),col="DarkRed",lty="dotted")

}

# UniWIBID data available at http://www.union-investment.pl/praktyczne/wycena/index_wycena.html
uniwibid.data <- read.csv("uniwibid.csv",header=TRUE,sep=";",dec=",")

uniwibid.date   <- rev(as.Date(uniwibid.data[,1]))
uniwibid.price  <- rev(as.numeric(as.character(uniwibid.data[,2])))
uniwibid.change <- log(uniwibid.price[-1]/uniwibid.price[-length(uniwibid.price)])

uniwibid <- cbind(uniwibid.date[-1],uniwibid.price[-1],uniwibid.change)
colnames(uniwibid) <- c("Date","Price","Change")

uniwibidN <- nrow(uniwibid)

shock.idx    <- which.min(uniwibid[,"Change"])
shock.change <- uniwibid[shock.idx,"Change"]

shock.retreat.idx <- tail(which(uniwibid[1:(shock.idx-1),"Price"]<=uniwibid[shock.idx,"Price"]),1)

as.Date(uniwibid[shock.idx,"Date"],origin="1970-01-01")
as.Date(uniwibid[shock.retreat.idx,"Date"],origin="1970-01-01")

Fn <- ecdf(uniwibid[1:(shock.idx-1),"Change"])
Fn(0) # return <= 0 probability

Fn <- ecdf(uniwibid[shock.idx:uniwibidN,"Change"])
Fn(0)

Fn <- ecdf(uniwibid[,"Change"])
Fn(0)

plot(uniwibid[1:(shock.idx-1),"Price"],type="l",main="UniWIBID Price",ylab="")
plot(uniwibid[shock.retreat.idx:uniwibidN,"Price"],type="l",main="UniWIBID Price",ylab="")

PlotVaR(uniwibid[1:(shock.idx-1),"Change"])

PlotVaR(uniwibid[shock.idx:uniwibidN,"Change"])

PlotVaR(uniwibid[shock.retreat.idx:uniwibidN,"Change"])

PlotVaR(uniwibid[,"Change"])