R/mathEfront.R

In PCRA: Companion to Portfolio Construction and Risk Analysis

#' @title Efficient Frontiers from Returns
#' 
#' @description Computes and plots the efficient frontier with and without 
#' risk-free asset, using a multivariate time series of returns to compute
#' the mean vector and covariance matrix
#' 
#' @param returns Multivariate xts object of portfolio returns
#' @param mu.max Numeric value, default NULL
#' @param sigma.max Numeric value, default NULL
#' @param rf Numeric value with default 0.003
#' @param rf.line Logical variable with default TRUE
#' @param stocks Logical variable with default TRUE
#' @param stock.names Logical variable with default TRUE
#' @param SRvalue Logical variable with default TRUE
#' @param npoints Integer number of efficient frontier points, default 100
#' @param digits Integer variable number of significant digits, default NULL
#' @param cexText Character expansion factor for text
#' @param cexPoints Expansion factor for points
#' 
#' @details When rf.line = TRUE, the linear efficient frontier is displayed,
#' and it is not displayed when rf.line = FALSE.
#' When values = TRUE, the Sharpe ratio and risk-free rate values are displayed
#' in the plot as SHARPE RATIO and RISK-FREE values.
#'
#' @return No value returned, instead a plot is displayed of the efficient frontier with
#' cash and risky assets, with risky assets only efficient frontier overlaid
#' @export
#'
#' @examples
#' args(mathEfront)
mathEfront <- function (returns, mu.max = NULL, sigma.max = NULL, 
                         rf = 0.003, rf.line = TRUE, stocks = TRUE, 
                         stock.names = TRUE, SRvalue = TRUE, npoints = 100, 
                         cexText = 0.8, cexPoints = 0.8, digits = NULL) 
{
  C <- var(returns)
  mu <- apply(returns, 2, mean)
  one <- rep(1, nrow(C))
  z <- solve(C, one)
  a <- as.numeric(t(mu) %*% z)
  cc <- as.numeric(t(one) %*% z)
  z <- solve(C, mu)
  b <- as.numeric(t(mu) %*% z)
  d <- b * cc - a^2
  mvp <- mathGmv(returns)
  tanp <- mathTport(returns, rf)
  sharpe <- (tanp$mu - rf)/tanp$vol
  mu.stocks <- apply(returns, 2, mean)
  sigma.stocks <- apply(returns, 2, var)^0.5
  if (missing(mu.max)) 
    mu.max <- 2 * max(mu.stocks)
  if (missing(sigma.max)) 
    sigma.max <- (1/cc + (cc/d) * (mu.max - a/cc)^2)^0.5
  sigma <- seq(1/(cc^0.5), sigma.max, length = npoints)
  mu <- a/cc + ((d * sigma^2)/cc - d/cc^2)^0.5
  mu[1] <- a/cc
  xlim <- range(0, sigma)
  ylim <- range(0, mu.max)
  x <- xlim[1] + 0.05 * (xlim[2] - xlim[1])
  y <- ylim[2] - 0.05 * (ylim[2] - ylim[1])
  plot(sigma, mu, xlim = xlim, ylim = ylim, type = "l", xaxs = "i",
       xlab = "Volatility", ylab = "Mean Return",  cex = 0.9)
  # title(main = "Efficient Frontier")
  lines(sigma, mu, lwd = 2)
  points(mvp$vol, mvp$mu, pch = 16, cex = cexPoints)
  text(mvp$vol, mvp$mu, "GMV", pos = 2, cex = 0.9)
  if (rf.line) {
    points(tanp$vol, tanp$mu, pch = 16)
    text(tanp$vol, tanp$mu, "T", pos = 2)
    abline(rf, (tanp$mu - rf)/tanp$vol, lwd = 1.0)
    if (SRvalue) {
      text(x, y, paste("SR = ", round(sharpe,2)), adj = 0, 
           cex = cexText)
      y <- ylim[2] - 0.13 * (ylim[2] - ylim[1])
      text(x, y, paste("RF = ", round(rf,4)), adj = 0, cex = cexText)
    }
  }
  if (stocks) {
    points(sigma.stocks, mu.stocks, pch = 19, cex = 0.7)
    if (stock.names) 
      text(sigma.stocks + 0.02 * xlim[2], mu.stocks, names(returns), 
           cex = cexText, adj = 0)
  }
}