The Maximum Diversification Index

We propose a new method to assess the risk diversification potential of a given investment set, using only the information content of the covariance matrix of returns. Namely, we extend Rudin and Morgan's (2006) work to numerically solve for the "Maximum Diversification Index" by means of a genetic algorithm. Using stock returns data from the S&P-500 index, we show that the MDI can be efficiently implemented to delimit a large set of investable assets by eliminating those subjects that do not improve the diversification characteristics of the underlying portfolio pool. Indeed, a subset of the S&P-500 stocks obtained using the MDI procedure preserves the mean-variance properties of the initial dataset as shown by the ex-post efficient frontiers.