The QIS team at BNP Paribas Global Markets introduces its new research paper where they have used techniques from information geometry in order to extend a popular approach to portfolio construction known as risk budgeting.
Risk budgeting has become ubiquitous in modern finance, and the team’s work establishes a link between this approach and other commonly-used ways to construct risk-parity portfolios. Their contribution is twofold:
First – to the best of their knowledge – the paper is the first of its kind to apply techniques from information theory and geometry to risk parity. In this approach, investors can adjust their risk-budgeting portfolio in order to get closer to the minimum-risk portfolio or to any reference allocation. A closed-form formula determines the contribution of each asset to the risk of the portfolio. This conclusion shall be particularly relevant for all investors who use risk parity for their portfolio. The research provides numerical evidence on the benefit of using alpha risk-parity.
Second, the authors use statistical divergences in order to control the divergence between two portfolio allocations. Approaches that rely on entropy functions implicitly assume that the reference portfolio is equally weighted. Shannon’s cross entropy has been used in order to consider any reference portfolio. In the framework of divergence functions, it is easier to combine a general reference portfolio with a general entropic index.