Portfolio Rho-Presentativity

25 Pages Posted: 10 Sep 2017 Last revised: 15 Dec 2017

Date Written: December 14, 2017

Abstract

Given an investment universe, we consider the vector ρ(w) of correlations of all assets to a portfolio with weights w. This vector offers a representation equivalent to w and leads to the notion of ρ-presentative portfolio, that has a positive correlation, or exposure, to all assets. This class encompasses well-known portfolios, and comes as a complement to the notion of representative portfolio, that has positive amounts invested in all assets (e.g. the market-cap index).

We then introduce the concept of maximally ρ-presentative portfolios, that maximize under no particular constraint an aggregate exposure f(ρ(w)) to all assets, as measured by a symmetric, increasing and concave real-valued function f. We provide a basic characterization of these portfolios that is independent of f, show that they are long-only, form a union of polytopes and are quite rare. However, these portfolios offer a unifying framework for many well-known and possibly constrained long-only portfolios.

We also establish a correspondence between some classic long-only portfolio optimization problems constrained to have maximum weights and unconstrained problems whose objective involves ρ(w). This extends the analytical results obtained in Jagannathan and Ma (2003) by characterizing explicitly the impact on the objective of these constraints often used by practitioners. Finally, we propose several theoretical and numerical applications that illustrate our results.

Keywords: Portfolio Construction, Correlation Optimization, Portfolio Constraints, Representative Portfolios, Portfolio Diversification, Most Diversified Portfolio, Minimum Variance Portfolio, Equal Risk Contribution Portfolio

JEL Classification: G11, C61

Suggested Citation

Froidure, Tristan and Jalalzai, Khalid and Choueifaty, Yves, Portfolio Rho-Presentativity (December 14, 2017). Available at SSRN: https://ssrn.com/abstract=2971867 or http://dx.doi.org/10.2139/ssrn.2971867

Tristan Froidure (Contact Author)

TOBAM ( email )

49 avenue des Champs-Elysées
Paris, 75008
France

Khalid Jalalzai

TOBAM ( email )

No Address Available

Yves Choueifaty

TOBAM ( email )

49 avenue des Champs Elysées
Paris, 75008
France

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