Diversification Ratio
Compute the diversification ratio of a portfolio.
divRatio(w, var)
w |
numeric: a vector of weights |
var |
numeric matrix: the variance–covariance matrix |
The function provides an efficient implementation of the diversification ratio, suitable for optimisation.
a numeric vector of length one
Enrico Schumann
Gilli, M., Maringer, D. and Schumann, E. (2019) Numerical Methods and Optimization in Finance. 2nd edition. Elsevier. https://www.elsevier.com/books/numerical-methods-and-optimization-in-finance/gilli/978-0-12-815065-8
Yves Choueifaty and Yves Coignard (2008) Toward Maximum Diversification. Journal of Portfolio Management 35(1), 40–51.
pm, drawdown
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)
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