Algorithms for loan evaluation
Altogether, the adjusted VaR has the desired properties to cope with nonnormal return distributions. Moreover, in conjunction with the correlation matrix of asset returns it allows to calculate the optimal portfolios with an algorithm similar to the quadratic programming algorithm used in the mean–variance framework. For the description of further transformations interested readers may refer to Mina and Ulmer (1999) and Li (2000).
Despite the obvious advantages of the VaR concept, investors should be careful when applying this approach for portfolio optimization. Although VaR fulfils our requirements with respect to reflecting downside risk, Artzner et al. (1997) have shown that it does not comply with one of the basic requirements of a satisfactory risk measure. In mathematical terms, it is not necessarily coherent, meaning that the condition of sub-additiveness is hurt. In other words, under certain circumstances the optimization problem has multiple local solutions. Convergence towards the one and only global optimum cannot be achieved with the usual Newton-style descent algorithms.
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