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.
Bibliographical noteFunding 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.].
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- Multiple targets
- Portfolio optimization