Approximations for the Value-at-Risk approach to risk-return analysis

An evergreen debate in Finance concerns the rules for making portfolio hedge decisions. A traditional tool proposed in the literature is the well-known standard deviation based Sharpe Ratio, which has been recently generalized in order to involve also other popular risk measures , such as VaR (Value-at-Risk) or CVaR (Conditional Value at Risk). This approach gives the correct choice of portfolio selection in a mean- world as long as is homogeneous of order 1. But, unfortunately, in important cases calculating the exact incremental Sharpe Ratio for ranking profitable portfolios turns out to be computationally too costly. Therefore, more easy-to-use rules for a rapid portfolio selection are needed. The research in this direction for VaR is the aim of the paper.