efficient.portfolio: Compute minimum variance portfolio subject to target return

In IntroCompFinR: Introduction to Computational Finance in R

Description

Compute minimum variance portfolio subject to target return either allowing all assets to be sold short or not allowing any asset to be sold short. The returned object is of class portfolio.

Usage

efficient.portfolio(er, cov.mat, target.return, shorts = TRUE)

Arguments

er	N x 1 vector of expected returns
cov.mat	N x N return covariance matrix
target.return	scalar, target expected return
shorts	logical, if TRUE then short sales (negative portfolio weights) are allowed. If FALSE then no asset is allowed to be sold short.

Details

A mean-variance efficient portfolio x allowing short sales (negative weights) that achieves the target expected return μ_0 solves the optimization problem: min t(x)Σ x s.t. t(x)1=1 and t(x)μ=μ_0, for which there is an analytic solution using matrix algebra. If short sales are not allowed then the portfolio is computed numerically using the function solve.QP() from the quadprog package.

Value

call	captures function call
er	portfolio expected return
sd	portfolio standard deviation
weights	N x 1 vector of portfolio weights

Author(s)

Eric Zivot

Examples

# construct the data
asset.names = c("MSFT", "NORD", "SBUX")
er = c(0.0427, 0.0015, 0.0285)
names(er) = asset.names
covmat = matrix(c(0.0100, 0.0018, 0.0011,
                  0.0018, 0.0109, 0.0026,
                  0.0011, 0.0026, 0.0199),
                nrow=3, ncol=3)
r.free = 0.005
dimnames(covmat) = list(asset.names, asset.names)

# compute efficient portfolio subject to target return
target.return = er["MSFT"]
e.port.msft = efficient.portfolio(er, covmat, target.return)
e.port.msft
summary(e.port.msft, risk.free=r.free)
plot(e.port.msft, col="blue")

# compute efficient portfolio subject to target return with no short sales
target.return = er["MSFT"]
e.port.msft.ns = efficient.portfolio(er, covmat, target.return, shorts=FALSE)
e.port.msft.ns
summary(e.port.msft.ns, risk.free=r.free)
plot(e.port.msft.ns, col="blue")

IntroCompFinR documentation built on May 2, 2019, 4:46 p.m.