Tail diversification strategy. An application to MSCI World Sector Indeces

In the theory of asset allocation and in the practice of portfolio management the diversification strategy is generally thought of in terms of market capitalization and investment style, yet sector diversification is equally important. As demonstrated empirically in recent years, pursuing a growth investment style via internet stocks leads to substantially different portfolios-and results- than pursuing growth via healthcare stocks. In addition, the severe recent crisis induces to consider extreme values dependence, preferring in the selecting procedure assets with low dependence between negative extreme returns. In this point of view, this paper provides a way to compose a portfolio choosing MSCI (Morgan Stanley Capital International) sector weighted indeces, designed to measure the equity performance of Industry, by the analysis of multivariate lower tail dependence. The selection procedure is based on modelling marginal behaviour of each stock index returns via a GARCH type model and, after, using a copula function to join the margins into a multivariate distribution. In this paper a particular familiy of copula functions is proposed to model the multivariate distribution of MSCI stock index returns, a Family of Multivariate Biparametric (MB) Copulae, a multivariate extension of BB family (Joe, 1997). In particular, the MB1 and MB7 copula functions are selected, because they allow to estimate both tail dependence in a asymmetric way. Due to computational complexity of high-dimensional copulae, the selection of stock index returns in portfolio is sequentially executed. In the first, two assets are chosen, privileging those with the minimum lower tail dependence coefficient measured on the joint distribution. Then, the selection of a third asset in portfolio, given the previous couple, follows the same path, choosing the triple with the minimum trivariate lower tail dependence and so on to add the remaining assets. At each step, the joint multivariate distribution is obtained by one of the selected copula functions with the best performance to the data, which is measured by the application of Kolmogorov test.