On Entropy, Divergences and Portfolio Diversification

Hellinton Takada (Portfolio Manager, ITAU Asset Management)

Abstract: In terms asset allocation, there are some different approaches using entropy measures and divergences to ensure diversification. Actually, the concept of diversification has also slight variations depending on the context. For the risk-based methodologies first put into practice by the All Weather fund in 1996, the idea of diversification is related to the risk contribution of each available asset class or investment factor to the total portfolio risk. The maximum diversification or the risk parity allocation is achieved when the set of risk contributions is given by a uniform distribution. Meucci (2009, Managing diversification Risk 22 (5), 74–79) introduced the maximization of the Renyi entropy as part of a leverage constrained optimization problem to achieve such diversified risk contributions when dealing with uncorrelated investment factors. A generalization of the risk parity is the risk budgeting when there is a prior for the distribution of the risk contributions. Our contribution is the generalization of the existent optimization frameworks to be able to solve the risk budgeting problem. In addition, our framework does not possess any leverage constraint.