Supplementary Appendix to: A Coskewness Shrinkage Approach for Estimating the Skewness of Linear Combinations of Random Variables

Abstract

Full Paper is available at: https://ssrn.com/abstract=2839781

In the supplementary appendix to the paper Boudt, Cornilly, and Verdonck (2018) we discuss the impact of autocorrelation and a time-varying structure on the estima- tion of coskewness matrices and provide more explanation about structured estima- tion. We go into more detail about our approach of optimizing the targets and provide several examples of other coskewness matrices in the literature. In particular, we pro- vide guidance how to use the latent single-factor coskewness matrix of Simaan (1993) in a shrinkage setting and correct the estimators provided in Martellini and Ziemann (2010) to estimate C(Φ ,T) for their observed single-factor and constant correlation coskewness estimators. The simulation setting discussed in the main paper is explored into more detail and we study three additional data generating processes. Further- more, we provide details on the empirical application studied in the main paper and extend the empirical study of Martellini and Ziemann (2010). Finally, we introduce the R code, publicly available in the PerformanceAnalytics package of Peterson and Carl (2018), for all single- and multi-target shrinkage estimators.

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

JEL Classification: G110, C130