maxSharpe: Maximum-Sharpe-Ratio/Tangency Portfolio

In NMOF: Numerical Methods and Optimization in Finance

Maximum-Sharpe-Ratio/Tangency Portfolio

Description

Compute maximum Sharpe-ratio portfolios, subject to lower and upper bounds on weights.

Usage

maxSharpe(m, var, min.return,
          wmin = -Inf, wmax = Inf, method = "qp",
          groups = NULL, groups.wmin = NULL, groups.wmax = NULL)

Arguments

m	vector of expected (excess) returns.
var	the covariance matrix: a numeric (real), symmetric matrix
min.return	minimumm required return. This is a technical parameter, used only for QP.
wmin	numeric: a lower bound on weights. May also be a vector that holds specific bounds for each asset.
wmax	numeric: an upper bound on weights. May also be a vector that holds specific bounds for each asset.
method	character. Currently, only "qp" is supported.
groups	a list of group definitions
groups.wmin	a numeric vector
groups.wmax	a numeric vector

Details

The function uses solve.QP from package quadprog. Because of the algorithm that solve.QP uses, var has to be positive definit (i.e. must be of full rank).

Value

a numeric vector (the portfolio weights) with an attribute variance (the portfolio's variance)

Author(s)

Enrico Schumann

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/C2017-0-01621-X")}

Schumann, E. (2023) Financial Optimisation with R (NMOF Manual). http://enricoschumann.net/NMOF.htm#NMOFmanual

Schumann, E. (2012) Computing the global minimum-variance portfolio. http://enricoschumann.net/R/minvar.htm

See Also

minvar, mvPortfolio, mvFrontier

Examples

S <- var(R <- NMOF::randomReturns(3, 10, 0.03))
x <- solve(S, colMeans(R))
x/sum(x)
x <- coef(lm(rep(1, 10) ~ -1 + R))
unname(x/sum(x))

maxSharpe(m = colMeans(R), var = S)
maxSharpe(m = colMeans(R), var = S, wmin = 0, wmax = 1)

NMOF documentation built on Oct. 20, 2023, 9:07 a.m.