Large-Scale Portfolio Optimization
Large-Scale Portfolio Optimization
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DOI：
10.1287/mnsc.30.10.1143
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发表时间：
1984-10
影响因子：
5.4
通讯作者：
André F. Perold
中科院分区：
文献类型：
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作者：
André F. Perold
本文提出了一种求解大规模均值-方差投资组合优化问题的实用算法。重点是开发一个有效的计算方法适用于广泛的投资组合模型所采用的投资界。这些与“通常的”二次规划的区别在于：i.使用因子和情景收益模型所产生的协方差矩阵的形式，ii.包括交易限制和成本。第三个方面是问题是否应该在风险-回报权衡参数λ中参数化地解决问题，或者单独解决λ的几个离散值。我们展示了如何通过引入一些额外的变量和约束的协方差矩阵的“稀疏化”，并通过将交易成本计划作为一个基本上非线性的不可微函数来处理，可以使参数算法非常有效。然后，我们将展示如何将这两种看似无关的方法结合起来，以产生良好的近似解时，最小交易规模的限制“购买或出售至少一定数量，或根本没有”。结合起来，这些方法使得在CPU时间和存储是限制因素的计算机上不可能的规模上的问题的参数解成为可能。
This paper describes a practical algorithm for large-scale mean-variance portfolio optimization. The emphasis is on developing an efficient computational approach applicable to the broad range of portfolio models employed by the investment community. What distinguishes these from the "usual" quadratic program is i the form of the covariance matrix arising from the use of factor and scenario models of return, and ii the inclusion of transactions limits and costs. A third aspect is the question of whether the problem should be solved parametrically in the risk-reward trade off parameter, λ, or separately for several discrete values of λ. We show how the parametric algorithm can be made extremely efficient by "sparsifying" the covariance matrix with the introduction of a few additional variables and constraints, and by treating the transaction cost schedule as an essentially nonlinear nondifferentiable function. Then we show how these two seemingly unrelated approaches can be combined to yield good approximate solutions when minimum trading size restrictions "buy or sell at least a certain amount, or not at all" are added. In combination, these approaches make possible the parametric solution of problems on a scale not heretofore possible on computers where CPU time and storage are the constraining factors.