A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables

Journal of Financial Econometrics, Forthcoming

32 Pages Posted: 20 Sep 2016 Last revised: 15 Aug 2018

See all articles by Kris Boudt

Kris Boudt

Ghent University; Vrije Universiteit Brussel; Vrije Universiteit Amsterdam

Dries Cornilly

Vrije Universiteit Brussel (VUB); KU Leuven

Tim Verdonck

KU Leuven

Date Written: September 16, 2016

Abstract

Supplementary Appendix is available at: https://ssrn.com/abstract=2970015. Decision making in finance often requires an accurate estimate of the coskewness matrix to optimize the allocation to random variables with asymmetric distributions. The classical sample estimator of the coskewness matrix performs poorly for small sample sizes. A solution is to use shrinkage estimators, defined as the convex com- bination between the sample coskewness matrix and a target matrix. We propose unbiased consistent estimators for the MSE loss function and include the possibility of having multiple target matrices. In a portfolio application, we find that the pro- posed shrinkage coskewness estimators are useful in mean-variance-skewness efficient portfolio allocation of funds of hedge funds.

Keywords: Coskewness, MSE, multiple targets, portfolio optimisation, shrinkage

JEL Classification: C100, C130, G110

Suggested Citation

Boudt, Kris and Cornilly, Dries and Verdonck, Tim, A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables (September 16, 2016). Journal of Financial Econometrics, Forthcoming. Available at SSRN: https://ssrn.com/abstract=2839781 or http://dx.doi.org/10.2139/ssrn.2839781

Kris Boudt

Ghent University ( email )

Sint-Pietersplein 5
Gent, 9000
Belgium

Vrije Universiteit Brussel ( email )

Pleinlaan 2
http://www.vub.ac.be/
Brussels, 1050
Belgium

Vrije Universiteit Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Dries Cornilly (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brussels 1050
Belgium

KU Leuven

Celestijnenlaan 200B
Leuven, Vlaams-Brabant 3001
Belgium

Tim Verdonck

KU Leuven ( email )

Celestijnenlaan 200B
Leuven, 3001
Belgium

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