Managing the Risk Is Not Enough

Standard portfolio construction models are based on the implicit assumption that all information relevant to making investment choices is probabilizable. However, both empirical behaviors of market participants and the increased success of approaches like risk parity underly an implicit rejection of this paradigm. This rejection is caused by uncertainty about metrics from a probabilistic formalization, induced by the fundamental nature of financial dynamics. It is concretely expressed through research into a balanced distribution of sources of risk rather than the minimization of a risk measure, and by the mobilization of knowledge that escapes pure probabilistic logic. The present paper aims to extract the substance of these ways of considering uncertainty in order to reconcile the taking into account of the uncertainty about metrics from a probabilistic formalization, while preserving the advantages of the risk/return approach which is the basis of the modern portfolio theory. The thrust of the approach taken is that reducing uncertainty involves limiting the importance of financial bets as a function of the uncertainty associated with the premises on which they are based. In order to attribute a value to the uncertainty of the premises, the angle of analysis adopted here is the stability of risk factor relations on which the relevance of probabilistic metrics depends. Consequently, the first part focuses on the risk decomposition of a portfolio with respect to risk factors and analyze the impact of estimation errors of inputs related to risk factors on the risk measure. Based on this analysis, the second part of the paper defines a framework for the construction of a coherent uncertainty measure of a portfolio. The third part presents a model of portfolio construction including a coherent uncertainty measure of a portfolio: the Uncertainty-Risk-Return optimization. A general method to solve this non-convex program is then exposed. Finally, the properties of this new method of portfolio optimization incorporating the management of uncertainty are analyzed through concrete examples