Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors

18 Pages Posted: 11 Aug 2013 Last revised: 11 Nov 2015

See all articles by Attilio Meucci

Attilio Meucci

ARPM - Advanced Risk and Portfolio Management

Alberto Santangelo


Romain Deguest


Date Written: November 10, 2015


We measure the contributions to risk of a set of factors, strategies, or investments, based on "Minimum-Torsion Bets", namely a set of uncorrelated factors, optimized to closely track the factors used to allocate the portfolio. We then introduce a novel definition of contributions to risk, which generalizes the "marginal contributions to risk", traditionally used in banks for risk budgeting and in asset management to build risk parity strategies.

The Minimum-Torsion Bets allow us to also introduce a natural diversification score, the Effective Number of Minimum-Torsion Bets, which we use to measure and manage diversification.

We discuss the advantages of the Minimum-Torsion Bets over the traditional approach to diversification based on marginal contributions to risk. We present two case studies, a security-based investment in the stocks of the S&P 500, and a factor-based investment in the five Fama-French factors.

Keywords: Effective Number of Bets, PCA, Diversification Distribution, Marginal Risk Contributions, Procrustes Problem

JEL Classification: C1, G11

Suggested Citation

Meucci, Attilio and Santangelo, Alberto and Deguest, Romain, Risk Budgeting and Diversification Based on Optimized Uncorrelated Factors (November 10, 2015). Available at SSRN: https://ssrn.com/abstract=2276632 or http://dx.doi.org/10.2139/ssrn.2276632

Attilio Meucci (Contact Author)

ARPM - Advanced Risk and Portfolio Management ( email )

HOME PAGE: http://www.arpm.co/

Alberto Santangelo

FinScience ( email )


Romain Deguest

Fundvisory ( email )

112 rue la Boetie
Paris, 75008

HOME PAGE: http://www.fundvisory.com/

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