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# portOpt2.R -- version 2010-12-28
# mean--variance-efficient portfolio
require(quadprog)
# create random returns
na <- 20L # number of assets
ns <- 60L # number of observations
R <- array(rnorm(ns * na, mean = 0.005, sd = 0.015),
dim = c(ns, na))
m <- colMeans(R) # means
rd <- mean(m) # desired mean
wsup <- 0.1 # maximum holding size
winf <- 0.0 # minimum holding size
# set up matrices
Q <- 2 * cov(R)
A <- array( 1, dim = c(1L, na))
a <- 1
B <- array(m, dim = c(1L, na))
B <- rbind(B,-diag(na),diag(na))
b <- rbind(rd, array(-wsup, dim = c(na,1L)),
array( winf, dim = c(na,1L)))
result <- solve.QP(Dmat = Q,
dvec = rep(0,na),
Amat = t(rbind(A,B)),
bvec = rbind(a,b),
meq = 1L)
w <- result$solution
sum(w) # check budget constraint
w %*% m >= rd # check return constraint
summary(w) # check holding size constraint
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