It is useful to know that portfolio optimization is totally integrated in various R packages that we will discuss later. However, it's better to walk before we run; so let's start with a simple self-made R function that we would also itemize line by line as follows:
minvariance <- function(assets, mu = 0.005) {
return <- log(tail(assets, -1) / head(assets, -1))
Q <- rbind(cov(return), rep(1, ncol(assets)),
colMeans(return))
Q <- cbind(Q, rbind(t(tail(Q, 2)), matrix(0, 2, 2)))
b <- c(rep(0, ncol(assets)), 1, mu)
solve(Q, b)
}This is a direct implementation of the algorithm that we discussed in the Theorem (Lagrange) section.
For demonstration purposes, we have fetched some IT stock prices from a Quandl superset (http://www.quandl.com/USER_1KR/1KT), which is a public service providing an easy access to a large amount of quant data. Although the URL points to a downloadable comma-separated values (CSV...