A coskewness shrinkage approach for estimating the skewness of linear combinations of random variables

Kris Boudt, Dries Cornilly*, Tim Verdonck

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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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 combination 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 proposed shrinkage coskewness estimators are useful in mean-variance-skewness efficient portfolio allocation of funds of hedge funds.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalJournal of Financial Econometrics
Issue number1
Early online date4 Oct 2018
Publication statusPublished - 2020

Bibliographical note

Funding Information:
This work was supported by the Research Foundation—Flanders [FWO research grant G023815N, PhD fellowship 1114117N to D.C.]; the Internal Funds KU Leuven (project C16/15/068); Google Summer of Code 2017; and the National Science Foundation of China [71771187 to K.B.].

Publisher Copyright:
© The Author(s) 2018. Published by Oxford University Press. All rights reserved.

Copyright 2021 Elsevier B.V., All rights reserved.


  • Coskewness
  • MSE
  • Multiple targets
  • Portfolio optimization
  • Shrinkage


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