tangency.portfolio: Compute tangency portfolio

In IntroCompFinR: Introduction to Computational Finance in R

Description

Compute tangency (maximum Sharpe ratio) portfolio. The portfolio can allow all assets to be shorted or not allow any assets to be shorted.

Usage

tangency.portfolio(er, cov.mat, risk.free, shorts = TRUE)

Arguments

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

Details

The tangency portfolio t is the portfolio of risky assets with the highest Sharpe's slope and solves the optimization problem: max (t(t)μ-r_f)/(t(t)Σ t^{1/2}) s.t. t(t)1=1 where r_f denotes the risk-free rate. If short sales are allowed then there is an analytic solution using matrix algebra. If short sales are not allowed then the maximum Sharpe ratio portfolio must be computed numerically.

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 tangency portfolio
tan.port <- tangency.portfolio(er, covmat, r.free)
tan.port
summary(tan.port, risk.free=r.free)
plot(tan.port, col="blue")

# compute tangency portfolio with no short sales
tan.port.ns <- tangency.portfolio(er, covmat, r.free, shorts=FALSE)
tan.port.ns
summary(tan.port.ns, risk.free=r.free)
plot(tan.port.ns, col="blue")

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