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Extensions of the VaR approach to portfolio selection with non-normal returns Tse, Wai

Abstract

The well-known mean-variance approach to portfolio selection problem proposed by Markowitz (1952) is often citicized for its use of variance as a measure of risk exposure. Recently, Value at Risk (VaR) has become a popular alternative for measuring risk in many firms. Using the idea of VaR, we formulated a chance constrained programming problem for portfolio selection. Untill recently, most real life applications rely on the normality distributional assumption of the asset returns which seems to be inconsistent with the empirical distributions. To relax this assumption, our study focused on the extensions of the VaR approach to portfolio selection to the class of Elliptically Contoured Distributed returns, and time-varying distributed returns. For the later case, we proposed a new solution via empirical distributions. Moreover, a profile map of returns versus risks was proposed so that, the optimal portfolio could be identified for various time-window sizes. The performance of various portfolios over different time periods were evaluated by means of off-sample cumulative returns and a new return-to-risk measure.

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