fig51 <- function(post=F)
{
 if(post)
  {#ps.options (colors=ps.colors.rgb[c("blue", "magenta", "cyan",
   #"green", "MediumBlue", "red", "black", "yellow", "blue"),])
    postscript("Fig51.ps", width=4.4, height=2.5, horizontal=F,
        pointsize=8)
  }
 else {if(dev.cur()==1) par(ask=T)}

 par(mfrow = c(1,2), mar=c(5,5,3,1)+0.1)
 par(mex=0.5,csi=0.11)

mreturn <- c(5, 20, 50)/100           #excessive return
vol     <- c(12, 40, 110)/100          #volatility
corr    <- matrix(c(1, 0.7, 0.4, 0.7, 1, 0.5, 0.4, 0.5, 1),byrow=T,
    ncol=3)                       #correlation 
cova   <- diag(vol) %*% corr %*% diag(vol) #covariance matrix
alpha <- solve(cova, mreturn)    #optional portifolio allocation
P <-  sum(mreturn*alpha)       #Sharpe ratio
sigma <- seq(0,5, 0.01)
mu <- 1.05 + sqrt(P)*sigma
plot(sigma^2, mu, xlab="variance", ylab="mean", type="l", ylim=c(0,4)) 
title("Mean-variance efficient frontier", "(a)")
plot(sigma, mu, xlab="SD", ylab="mean", type="l", ylim=c(0,4)) 
title("Mean-SD efficient frontier", "(b)")

 if(post) dev.off()
}