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Abstract
We consider a one-period portfolio optimization problem under model uncertainty. For this purpose, we introduce a measure of model risk. We derive analytical results for this measure of model risk in the mean-variance problem assuming we have observations drawn from a normal variance mixture model. This model allows for heavy tails, tail dependence and leptokurtosis of marginals. The results show that mean-variance optimization is seriously compromised by model uncertainty, in particular, for non-Gaussian data and small sample sizes. To mitigate these shortcomings, we propose a method to adjust the sample covariance matrix in order to reduce model risk.
Highlights
Traditional portfolio optimization techniques rely on the true model parameters being known
This optimization problem has a unique solution w∗ ∈ Rn given by w∗ =
In this paper we introduce a measure of model risk in a more general portfolio optimization context than mean-variance or risk minimization
Summary
Traditional portfolio optimization techniques rely on the true model parameters being known. In the framework of [25] the opportunity cost is evaluated and used to study the effects of model uncertainty on the portfolio optimization This approach is fundamentally different from the one we follow in this paper. From the analytical results derived in Kan and Zhou [21], it follows that the uncertainty in the covariance matrix has a large impact on the optimal portfolio when the number of assets is large compared to the sample size. We derive in Theorem 5 a rule which reduces the effects of model uncertainty under the assumption of known eigenvectors
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