Smart Beta: Managing Diversification of Minimum Variance Portfolios

27 Pages Posted: 18 Apr 2015 Last revised: 20 Apr 2015

See all articles by Jean-Charles Richard

Jean-Charles Richard

Eisler Capital

Thierry Roncalli

Amundi Asset Management; University of Evry

Date Written: March 2015


In this article, we consider a new framework to understand risk-based portfolios (GMV, EW, ERC and MDP). This framework is similar to the constrained minimum variance model of Jurczenko et al. (2013), but with another definition of the diversification constraint. The corresponding optimization problem can then be solved using the CCD algorithm. This allows us to extend the results of Cazalet et al. (2014) and to better understand the trade-off relationships between volatility reduction, tracking error and risk diversification. In particular, we show that the smart beta portfolios differ because they implicitly target different levels of volatility reduction. We also develop new smart beta strategies by managing the level of volatility reduction and show that they present appealing properties compared with the traditional risk-based portfolios.

Keywords: Smart beta, risk-based allocation, minimum variance portfolio, GMV, EW, ERC, MDP, portfolio optimization, CCD algorithm

JEL Classification: C61, G11

Suggested Citation

Richard, Jean-Charles and Roncalli, Thierry, Smart Beta: Managing Diversification of Minimum Variance Portfolios (March 2015). Available at SSRN: or

Jean-Charles Richard

Eisler Capital ( email )

16 St. James's Street
London, SW1A1ER

Thierry Roncalli (Contact Author)

Amundi Asset Management ( email )

90 Boulevard Pasteur
Paris, 75015

University of Evry ( email )

Boulevard Francois Mitterrand
F-91025 Evry Cedex

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