NMOF (version 2.10-0)

minCVaR: Minimum Conditional-Value-at-Risk (CVaR) Portfolios

Description

Compute minimum-CVaR portfolios, subject to lower and upper bounds on weights.

Usage

minCVaR(R, q = 0.1, wmin = 0, wmax = 1,
        min.return = NULL, m = NULL,
        method = "Rglpk",
        groups = NULL, groups.wmin = NULL, groups.wmax = NULL,
        Rglpk.control = list())

Value

a numeric vector (the portfolio weights); attached is an attribute whose name matches the method name

Arguments

R

the scenario matrix: a numeric (real) matrix

q

the Value-at-Risk level: a number between 0 and 0.5

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.

m

vector of expected returns. Only used if min.return is specified.

min.return

minimal required return. If m is not specified, the column means of R are used.

method

character. Currently, only "Rglpk" is supported.

groups

a list of group definitions

groups.wmin

a numeric vector

groups.wmax

a numeric vector

Rglpk.control

a list: settings passed to Rglpk_solve_LP

Author

Enrico Schumann

Details

Compute the minimum CVaR portfolio for a given scenario set. The default method uses the formulation as a Linear Programme, as described in Rockafellar/Uryasev (2000).

The function uses Rglpk_solve_LP from package Rglpk.

References

Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. tools:::Rd_expr_doi("10.1016/C2017-0-01621-X")

Rockafellar, R. T. and Uryasev, S. (2000). Optimization of Conditional Value-at-Risk. Journal of Risk. 2 (3), 21--41.

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

Schumann, E. (2020) Minimising Conditional Value-at-Risk (CVaR). https://enricoschumann.net/notes/minimising-conditional-var.html

See Also

minvar

Examples

if (requireNamespace("Rglpk")) {

  ns <- 5000  ## number of scenarios
  na <- 20    ## nunber of assets
  R <- randomReturns(na, ns, sd = 0.01, rho = 0.5)

  res <- minCVaR(R, 0.25)
  c(res)  ## portfolio weights
}