divRatio {NMOF}

Diversification Ratio

Description

Compute the diversification ratio of a portfolio.

Usage

divRatio(w, var)

Arguments

w

numeric: a vector of weights

var

numeric matrix: the variance–covariance matrix

Details

The function provides an efficient implementation of the diversification ratio, suitable for optimisation.

Value

a numeric vector of length one

Author(s)

Enrico Schumann

References

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

Yves Choueifaty and Yves Coignard (2008) Toward Maximum Diversification. Journal of Portfolio Management 35(1), 40–51.

See Also

pm, drawdown

Examples

na  <- 10     ## number of assets
rho <- 0.5    ## correlation
v_min <- 0.2  ## minimum vol
v_max <- 0.4  ## maximum vol

## set up a covariance matrix S
C <- array(rho, dim = c(na,na))
diag(C) <- 1
vols <- seq(v_min, v_max, length.out = na)
S <- outer(vols, vols) * C

w <- rep(1/na, na)  ## weights
divRatio(w, S)