minCVaR function

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

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

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())

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

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.

Returns

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

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

Author(s)

Enrico Schumann

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
}