Second-Order Risk of Alternative Risk Parity Strategies

25 Pages Posted: 4 Feb 2019

See all articles by Simone Bernardi

Simone Bernardi

University of Zurich - Department of Banking and Finance

Markus Leippold

University of Zurich; Swiss Finance Institute

Harald Lohre

Robeco Quantitative Investments; Lancaster University Management School

Multiple version iconThere are 2 versions of this paper

Date Written: January 29, 2019


The concept of second-order risk operationalizes the estimation risk induced by model uncertainty in portfolio construction. We study its contribution to the realized volatility of recently developed alternative risk parity strategies that invest in an uncorrelated decomposition of the asset universe. For each strategy, we derive closed-form solutions for the second-order risk, subsequently illustrated in empirical analysis based on real market data. Our results suggest a relation between the contribution of second-order risk and the sensitivity of a portfolio to single eigenvectors of the covariance matrix of assets’ returns. Among the strategies considered, we find the principal risk parity strategy that invests equally in each eigenvector underlying the variance–covariance matrix to be immune to second-order risk. For the other strategies, second-order risk can be partially mitigated by means of statistical methods. In particular, we provide evidence for the eigenvalue adjustment being the most effective method for correcting the second-order risk bias.

Keywords: estimation risk, second-order risk, portfolio construction, risk parity, diversification

Suggested Citation

Bernardi, Simone and Leippold, Markus and Lohre, Harald, Second-Order Risk of Alternative Risk Parity Strategies (January 29, 2019). Journal of Risk, Forthcoming, Available at SSRN:

Simone Bernardi

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001

Markus Leippold (Contact Author)

University of Zurich ( email )

Rämistrasse 71
Zürich, CH-8006

Swiss Finance Institute ( email )

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4

Harald Lohre

Robeco Quantitative Investments ( email )

Weena 850
Rotterdam, 3011 AG

Lancaster University Management School

Lancaster LA1 4YX
United Kingdom


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