efficient.frontier: Compute efficient frontier of risky assets
In IntroCompFinR: Introduction to Computational Finance in R

Description Usage Arguments Details Value Author(s) Examples

The function constructs the set of mean-variance efficient portfolios that either allow all assets to be sold short or not allow any asset to be sold short. The returned object is of class Markowitz for which there are print, summary and plot methods.

1 2	efficient.frontier(er, cov.mat, nport = 20, alpha.min = -0.5, alpha.max = 1.5, shorts = TRUE)

`er`	N x 1 vector of expected returns
`cov.mat`	N x N return covariance matrix
`nport`	scalar, number of efficient portfolios to compute
`alpha.min`	minimum value of alpha, default is -.5
`alpha.max`	maximum value of alpha, default is 1.5
`shorts`	logical, if TRUE then short sales (negative portfolio weights) are allowed. If FALSE then no asset is allowed to be sold short

If short sales are allowed (negative weights) then the set of efficient portfolios of risky assets can be computed as a convex combination of any two efficient portfolios. It is convenient to use the global minimum variance portfolio as one portfolio and an efficient portfolio with target expected return equal to the maximum expected return of the assets under consideration as the other portfolio. Call these portfolios m and x, respectively. Then for any number alpha, another efficient portfolio can be computed as z=α m+(1-α)x. If short sales are not allowed, then the set of efficient portfolios is computed by repeated calls to the function efficient.portfolio(), with shorts=FALSE, for a grid of target expected returns starting at the expected return of the global minimum variance portfolio (not allowing short sales) and ending at the expected return equal to the maximum expected return of the assets under consideration.

`call`	captures function call
`er`	nport x 1 vector of expected returns of efficient porfolios
`sd`	nport x 1 vector of standard deviations of efficient portfolios
`weights`	nport x N matrix of weights of efficient portfolios

Eric Zivot

# 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)

# tangency portfolio
tan.port <- tangency.portfolio(er, covmat, r.free)
# compute global minimum variance portfolio
gmin.port = globalMin.portfolio(er, covmat)

# compute portfolio frontier
ef <- efficient.frontier(er, covmat, alpha.min=-2,
                         alpha.max=1.5, nport=20)
attributes(ef)

plot(ef)
plot(ef, plot.assets=TRUE, col="blue", pch=16)
points(gmin.port$sd, gmin.port$er, col="green", pch=16, cex=2)
points(tan.port$sd, tan.port$er, col="red", pch=16, cex=2)
text(gmin.port$sd, gmin.port$er, labels="GLOBAL MIN", pos=2)
text(tan.port$sd, tan.port$er, labels="TANGENCY", pos=2)
sr.tan = (tan.port$er - r.free)/tan.port$sd
abline(a=r.free, b=sr.tan, col="green", lwd=2)