Yet another portfolio optimization question...
Im trying to maximize the return of a portfolio of four assets given the restrictions sum(P) = 1, MaxW <= 0.55 and MinW >= 0.05 using quadprog.
The average returns over the period are
avgR <- c(0.0008990382, 0.0002285502, 0.0001120934, 0.0001540948)
while the covariance matrix is
covM <- matrix(c(2.876044e-04, 6.758444e-05, 4.382673e-05, 1.167429e-04,
6.758444e-05, 2.331315e-04, 5.797771e-05, 1.087006e-04,
4.382673e-05, 5.797771e-05, 2.568974e-04, 8.544499e-05,
1.167429e-04, 1.087006e-04, 8.544499e-05, 2.085108e-03), ncol=4)
I have come this far
require(quadprog)
nAssets <- length(avgR)
Dmat <- 2 * covM
upperB <- 0.55
lowerB <- 0.05
ub <- rep(upperB, nAssets)
lb <- rep(lowerB, nAssets)
dvec <- avgR
Amat <- rbind(1, diag(nAssets), -diag(nAssets))
bvec <- c(1, lb, -ub)
solve <- solve.QP(Dmat = Dmat, dvec = dvec, Amat = t(Amat), bvec = bvec, meq = 1)
solve$solution
Which returns
0.55000000 0.33032755 0.06967245 0.05000000
as optimal allocation.
Using the same data in Excel I get another solution (with a higher return);
0.55 0.35 0.05 0.05
However, setting the upper bound to 0.65 both R and Excel return the same solution;
0.65 0.25 0.05 0.05
What am I missing?
