R/mathGmv.R

In PCRA: Companion to Portfolio Construction and Risk Analysis

#' @title Global Minimum Variance Portfolio (GMV)
#' 
#' @description Computes the weights of a GMV portfolio, and its mean return
#' and volatility based on portfolio asset returns
#' 
#' @param returns Matrix or xts object of returns
#' @param digits Integer value of number of significant digits, default NULL
#' 
#' @return List of GMV portfolio weights, mean return and volatility
#' 
#' @examples
#' args(mathGmv)
#' @export
mathGmv <- function(returns, digits = NULL)
{
	V <- var(returns)
	one <- rep(1, nrow(V))
	z <- solve(V, one)		# Compute z = V.inv * 1
	cc <- t(one) %*% z		# Compute cc = 1.transpose * V.inv * 1
	cc <- as.numeric(cc)	# Convert 1-by-1 matrix to a scalar
	wtsGmv <- z/cc
	mu <- apply(returns, 2, mean)
	a <- t(mu) %*% z
	muGmv <- as.numeric(a/cc)
	volGmv <- 1/cc^0.5
	if(is.null(digits))
	{out = list(wts = wtsGmv,mu = muGmv, vol = volGmv)}
	else
	{out = list(WTS.GMV = wtsGmv, MU.GMV = muGmv, VOL.GMV = volGmv)
		out = lapply(out,round,digits=digits)}
	out
}