PORTFOLIO RHO-PRESENTATIVITY

Tristan Froidure (), Khalid Jalalzai () and Yves Choueifaty ()
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Tristan Froidure: TOBAM, 49-53 Avenue des Champs-Élysées, 75008 Paris, France
Khalid Jalalzai: TOBAM, 49-53 Avenue des Champs-Élysées, 75008 Paris, France
Yves Choueifaty: TOBAM, 49-53 Avenue des Champs-Élysées, 75008 Paris, France

International Journal of Theoretical and Applied Finance (IJTAF), 2019, vol. 22, issue 07, 1-52

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 complements 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 some symmetric, increasing and concave real-valued function f. A basic characterization is established and it is shown that these portfolios are long-only, diversified and form a finite union of polytopes that satisfies a local regularity condition with respect to changes of the covariance matrix of the assets. Despite its small size, this set encompasses many well-known and possibly constrained long-only portfolios, bringing them together in a common framework. This also allowed us characterizing explicitly the impact of maximum weight constraints on the minimum variance portfolio. Finally, several theoretical and numerical applications illustrate our results.

Keywords: Portfolio construction; correlation optimization; constraints; representative portfolios; diversification; maximally rho-presentative portfolios; optimized portfolio stability; long-only eigenvalues (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1142/S0219024919500341

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