demo/MeanDiversificationFrontier.R

In R-Finance/Meucci: Collection of functionality ported from the MATLAB code of Attilio Meucci.

# This script computes the mean-diversification efficient frontier
# see A. Meucci - "Managing Diversification", Risk Magazine, June 2009
# available at www.ssrn.com

# Code by A. Meucci. This version March 2009. 
# Last version available at MATLAB central as "Managing Diversification"

# inputs
# upload returns covariance and expectations

# define benchmark and portfolio weights
N = nrow( Mu )
w_0 = rep( 1, N ) / N

# define constraints
# long-short constraints...
Constr = list()
Constr$A = rbind( diag( N ), -diag( N ) )
Constr$b = rbind( as.matrix( rep( 1, N ) ), as.matrix( rep( 0.1, N ) ) )
Constr$Aeq = t( as.matrix( rep( 1 , N ) ) ) # budget constraint...
Constr$beq = as.matrix( 1 )

# mean-diversification analysis and frontier
EntropyFrontier = MeanTCEntropyFrontier( S , Mu , w_b , w_0 , Constr )

# mean-diversification of current allocation
m = t( Mu ) %*% ( w_0 - w_b )
s = sqrt( t( w_0 - w_b ) %*% S %*% ( w_0 - w_b ) )
GenPCResult = GenPCBasis( S , emptyMatrix )
v_tilde = G %*% ( w_0 - w_b )
TE_contr = ( v_tilde * v_tilde ) / s
R_2 = max( 10^(-10) , TE_contr/sum(TE_contr) )
Ne = exp( -t( R_2 ) %*% log( R_2 ) )