Estimating Allocations for Value-at-Risk Portfolio Optimzation
24 Pages Posted: 25 Oct 2007
Date Written: August 28, 2007
Value-at-Risk, despite being adopted as the standard risk measure in finance, but suffers severe objections from a practical point of vue, due to a lack of convexity, and since it does not reward diversification (which is an essential feature in portfolio optimization). Furthermore, it is also known as having poor behavior in risk estimation (which has been justified to impose the use of parametric models, but which induces then model errors). The aim of this paper is to chose in favour or against the use of VaR but to add some more information to this discussion, especially from the estimation point of view. Here we propose a simple method not only to estimate the optimal allocation based on a Value-at-Risk minimization constraint, but also to derive - empirical - confidence intervals based on the fact that the underlying distribution is unkown, and can be estimated based on past observations.
Keywords: nonparametric estimation, optimal allocations, Value-at-Risk
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