Insights into Robust Portfolio Optimization: Decomposing Robust Portfolios into Mean-Variance and Risk-Based Portfolios

30 Pages Posted: 9 Sep 2015

See all articles by Romain Perchet

Romain Perchet

BNP Paribas Asset Management

Lu Xiao

BNP Paribas Investment Partners

Raul Leote de Carvalho

BNP Paribas Asset Management

Thomas Heckel

BNP Paribas Asset Management

Date Written: September 7, 2015

Abstract

For a number of different formulations of robust portfolio optimization, quadratic and absolute, we show that a) in the limit of low uncertainty in estimated asset mean returns the robust portfolio converges towards the mean-variance portfolio obtained with the same inputs; and b) in the limit of high uncertainty the robust portfolio converges towards a risk-based portfolio, which is a function of how the uncertainty in estimated asset mean returns is defined. We give examples in which the robust portfolio converges toward the minimum variance, the inverse variance, the equal-risk budget and the equally weighted portfolio in the limit of sufficiently large uncertainty in asset mean returns. At intermediate levels of uncertainty we find that a weighted average of the mean-variance portfolio and the respective limiting risk-based portfolio offer a good representation of the robust portfolio, in particular in the case of the quadratic formulation. The results remain valid even in the presence of portfolio constraints, in which case the limiting portfolios are the corresponding constrained mean-variance and constrained risk-based portfolios. We believe our results are important in particular for risk-based investors who wish to take into account expected returns to gently tilt away from their current allocations, e.g. risk parity or minimum variance.

Keywords: portfolio optimization, portfolio construction, robust optimization, risk-based portfolios, minimum variance, risk parity, equal-risk budget, equally-weighted, mean-variance, Markowitz

JEL Classification: G11, C61

Suggested Citation

Perchet, Romain and Xiao, Lu and Carvalho, Raul Leote de and Heckel, Thomas, Insights into Robust Portfolio Optimization: Decomposing Robust Portfolios into Mean-Variance and Risk-Based Portfolios (September 7, 2015). Available at SSRN: https://ssrn.com/abstract=2657976 or http://dx.doi.org/10.2139/ssrn.2657976

Romain Perchet

BNP Paribas Asset Management ( email )

14 rue Bergere
Paris, 75009
France

Lu Xiao

BNP Paribas Investment Partners ( email )

14 rue bergère
Paris, 75009
France

Raul Leote de Carvalho (Contact Author)

BNP Paribas Asset Management ( email )

14 rue Bergere
Paris, 75009
France
0033158972183 (Phone)

Thomas Heckel

BNP Paribas Asset Management ( email )

Paris
France

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