市场摩擦条件下基于谱风险度量的投资组合优化模型
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摘要
设计并得到了对数型风险谱函数,构造了谱风险度量。在谱风险度量的基础上,分析并引入了实际股票市场中的市场摩擦、资产配置权重限制等约束条件,利用收益率总体分布的经验分布,建立了投资组合优化模型,并将模型转化为易求解且具有稳健性的非线性优化模型。实证分析表明,市场摩擦中交易费用条件的降低可以在保障收益不变的同时大幅度的降低投资组合风险。同时,所建立的投资组合优化模型也可以合理有效地进行投资组合配置。
This paper describes the design and formulation of a logarithmic risk spectrum,and the construction of the spectral risk measure(SRM).On the basis of SRM,we analyze and incorparate some actual conditions in real markets such as market friction and asset allocation proportion bounds.Then,we use the empirical distribution of the population distribution of the rate of return to obtain the portfolio optimization model.Finally we translate this to a non-linear optimization model which is easy to solve and has the required robustness.The empirical analysis shows that decreasing the transaction cost of market friction can substantially reduce the risk and ensure the required return rate.Furthermore,the model we have established can deal with the portfolio allocation rationally and effectively.
This paper describes the design and formulation of a logarithmic risk spectrum,and the construction of the spectral risk measure(SRM).On the basis of SRM,we analyze and incorparate some actual conditions in real markets such as market friction and asset allocation proportion bounds.Then,we use the empirical distribution of the population distribution of the rate of return to obtain the portfolio optimization model.Finally we translate this to a non-linear optimization model which is easy to solve and has the required robustness.The empirical analysis shows that decreasing the transaction cost of market friction can substantially reduce the risk and ensure the required return rate.Furthermore,the model we have established can deal with the portfolio allocation rationally and effectively.
引文
[1]马科维茨.哈利.M.资产组合选择和资本市场的均值-方差模型[M].上海:上海人民出版社,2006.Markowitz H M.Mean-variance analysis in portfoliochoice and capital markets[M].Shanghai:ShanghaiPeople's Publishing House,2006.(in Chinese)
[2]Szego G.Measure of risk[J].Journal of Banking andFinance,2002,26(7):1253-1272.
[3]Acerbi C,Tasche D.On the coherence of expected short-fall[J].Journal of Banking and Finance,2002,26(7):1487-1503.
[4]Acerbi C.Spectral measures of risk:a coherent represen-tation of subjective risk aversion[J].Journal of Bankingand Finance,2002,26(7):1505-1518.
[5]Chen Z P,Yang L.Nonlinearly weighted convex riskmeasure and its application[J].Journal of Banking andFinance,2011,35(7):1777-1793.
[6]Acerbi C,Simonetti P.Portfolio Optimization with Spec-tral Measures of Risk[EB/OL].[2002-03-27].http:∥ideas.repec.org/p/arx/papers/cond-mat-0203607.html.
[7]Acerbi C.Coherent Representations of Subjective Risk A-version[EB/OL].[2003-07-25].http://courses.es-sex.ac.uk/cf/cf968/Acerbi_wileybookchapter13.pdf.
[2]Szego G.Measure of risk[J].Journal of Banking andFinance,2002,26(7):1253-1272.
[3]Acerbi C,Tasche D.On the coherence of expected short-fall[J].Journal of Banking and Finance,2002,26(7):1487-1503.
[4]Acerbi C.Spectral measures of risk:a coherent represen-tation of subjective risk aversion[J].Journal of Bankingand Finance,2002,26(7):1505-1518.
[5]Chen Z P,Yang L.Nonlinearly weighted convex riskmeasure and its application[J].Journal of Banking andFinance,2011,35(7):1777-1793.
[6]Acerbi C,Simonetti P.Portfolio Optimization with Spec-tral Measures of Risk[EB/OL].[2002-03-27].http:∥ideas.repec.org/p/arx/papers/cond-mat-0203607.html.
[7]Acerbi C.Coherent Representations of Subjective Risk A-version[EB/OL].[2003-07-25].http://courses.es-sex.ac.uk/cf/cf968/Acerbi_wileybookchapter13.pdf.