Value-at-Risk in Portfolio Optimization: Properties and Computational Approach ⁄

摘要: The Value-at-Risk (V@R) is an important and widely used measure of the extent to which a given portfolio subject risk inherent in flnancial markets. In this paper, we present method calculating gives smallest V@R among those, yield at least some specifled expected return. Using approach, complete mean-V@R e‐cient frontier may be calculated. based on approximating historic by smoothed (SV@R) fllters out local irregularities. Moreover, compare as other well known measures such Conditional (CV@R) standard deviation. It shown that resulting frontiers are quite difierent. An investor, who wants control his should not look portfolios lying than frontier, although calculation algorithmically more complex. We support these flndings presenting results large scale experiment with representative selection stock bond indices from developed emerging markets involved computation many thousands V@R-optimal portfolios.