R/mathWtsEfrontRisky.R

In PCRA: Companion to Portfolio Construction and Risk Analysis

#' @title Efficient Frontier Portfolio Weights Vectors
#' 
#' @description Uses time series of asset returns to compute the weights vectors
#' for a set of points along the efficient frontier that are defined by their
#' mean return values
#' 
#' @param returns A multivariate xts object of n asset returns 
#' @param mu.efront A vector of specified efficient frontier mean returns
#' @param digits Integer number of significant digits with default NULL
#'
#' @return
#' A matrix with first row containing the mean (MU) along the efficient
#' frontier, the second row containing the standard deviation, and the 
#' following n rows contain the n weight vectors along the efficient fronier
#' 
#' @examples
#' args(mathWtsEfrontRisky)
#' 
#' @export
mathWtsEfrontRisky <- function(returns, mu.efront, digits = NULL) 
{
  V <- var(returns)
  mu <- apply(returns, 2, mean)
  n.assets <- length(mu)
  one <- rep(1, n.assets)
  z1 <- solve(V, one)
  a <- as.numeric(t(mu) %*% z1)
  cc <- as.numeric(t(one) %*% z1)
  z2 <- solve(V, mu)
  b <- as.numeric(t(mu) %*% z2)
  d <- b * cc - a^2
  g1 <- as.matrix((b * z1 - a * z2)/d, ncol = 1)
  g2 <- as.matrix((cc * z2 - a * z1)/d, ncol = 1)
  n <- length(mu.efront)
  a1 <- matrix(rep(g1, n), ncol = n)
  a2 <- g2 %*% mu.efront
  wts.efront <- a1 + a2
  wts.efront <- as.data.frame(wts.efront)
  vol.efront <- (1/cc + (cc/d) * (mu.efront - a/cc)^2)^0.5
  out <- rbind(vol.efront, mu.efront, wts.efront)
  rowNames <- c("MU", "VOL", paste("W-", sep = "", names(returns)))
  row.names(out) <- rowNames
  names(out) <- paste("P", sep = "", 1:n)
  if (is.null(digits)) {
    out
  }
  else {
    out <- sapply(out, FUN = round, digits = digits)
    row.names(out) <- rowNames
    data.frame(out)
  }
}