Value-at-Risk in Portfolio Optimization: Properties and Computational Approach ⁄
Value-at-Risk in Portfolio Optimization: Properties and Computational Approach ⁄
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DOI：
10.21314/jor.2005.106
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发表时间：
2005-04
期刊：
影响因子：
0.7
通讯作者：
A. Gaivoronski;G. Pflug
中科院分区：
文献类型：
--
作者：
A. Gaivoronski;G. Pflug
风险价值 (VAR) 是衡量给定投资组合面临金融市场风险程度的重要且广泛使用的指标。在本文中，我们提出了一种计算投资组合的方法，该方法在至少产生一些指定预期回报的投资组合中给出最佳 VAR。该方法允许我们计算平均 VAR 有效边界。该方法基于平滑 VAR (SVAR) 对历史 VAR 的近似，过滤掉历史 VAR 函数的局部不规则行为。此外，我们将 VAR 作为一种风险度量与其他众所周知的风险度量进行比较，例如条件风险价值 (CVAR) 和标准差。我们表明，由此产生的有效边界是完全不同的。想要控制 VAR 的投资者不应该考虑位于 VAR 有效边界以外的投资组合，尽管该边界的计算在算法上比其他边界更复杂。我们通过展示大规模实验的结果来支持这一猜想，该实验选择了来自发达市场和新兴市场的代表性股票和债券指数，其中涉及数千个 VAR 最优投资组合的计算。
Value-at-Risk (VAR) is an important and widely used measure of the extent to which a given portfolio is subject to risk present in financial markets. In this paper, we present a method of calculating a portfolio that gives the optimal VAR among those which yield at least some specified expected return. This method allows us to calculate the mean-VAR-efficient frontier. The method is based on the approximation of historical VAR by smoothed VAR (SVAR), which filters out local irregular behavior of the historical VAR function. Moreover, we compare VAR as a risk measure to other well-known measures of risk, such as conditional value-at risk (CVAR) and the standard deviation. We show that the resulting efficient frontiers are quite different. An investor who wants to controls his or her VAR should not look at portfolios lying on other than the VAR efficient frontier, although the calculation of this frontier is algorithmically more complex than other frontiers. We support this conjecture by presenting the results of a large-scale experiment with a representative selection of stock and bond indices from developed and emerging markets that involved the computation of many thousand VAR-optimal portfolios.