Some general results on risk budgeting portfolios

Speaker: Prof. Pierpaolo Uberti, Department of Statistics and Quantitative Methods, University of Milano-Bicocca

Abstract:> Given a reference risk measure, risk budgeting defines a portfolio in which each asset contributes a predetermined amount to the total risk. We propose a novel approach—alternative to those proposed in the literature—for the computation of the risk budgeting portfolio. We define a Cauchy sequence within the simplex of R^n, whose limit corresponds to the risk budgeting portfolio. This construction allows for the straightforward implementation of an efficient algorithm, avoiding the need to solve auxiliary, equivalent optimization problems, which may be computationally challenging and difficult to interpret in a decision-theoretic context. From a theoretical point of view, starting from the Cauchy sequence, we define a function for which the risk budgeting portfolio is a fixed point. Therefore, sufficient conditions for the existence and uniqueness of the fixed point can be applied. Our methodology is developed for a general risk measure. The implementation is presented in detail for the standard deviation. We compare our algorithm with the standard optimization-based methods proposed in the literature. The computational efficiency of the proposed algorithm is also compared with standard approaches for different risk measures (standard deviation, value at risk, and expected shortfall).