绝对离差证券组合投资模型及其模拟退火算法

Portfolio choice model based on mean absolute deviation and it's simulated annealing algorithm

马柯维兹均值—方差模型使用收益率的方差度量证券的风险 ,但是实际分布呈尖顶胖尾状 ,使得方差可能不存在 .作为度量风险的标准 ,绝对离差比方差更为合适 .用绝对离差刻画了风险 ,提出基于绝对离差的证券组合投资模型 ,并用模拟退火算法求解 .为了比较在两种风险标准下两种模型的优劣 ,首次定义了风险弹性 .实证分析表明 ,在不同收益率水平下 ,风险弹性的绝对值都大于 1 .说明绝对离差模型比均值 -方差模型无论在理论上还是在实际效果上都要更好 .实证分析还表明 。

Markowitz's mean variance model describes the risk of asset by variance, but variance may not exist because of fat tailedness of asset returns. As a measure of risk, mean absolute deviation is better than variance in a sense. In this paper,a portfolio choice model is proposed based on mean absolute deviation. The solution of the model is obtained by a simulated annealing algorithm. In order to compare the new models with Markowitz one,a risk elasticity is defined. The empirical result shows that the absolute values of risk elasticity are more than 1 under various returns and it also indicates that the proposed model based on mean absolute deviation is better than mean variance model based on variance both in theory and in practice. Two fund separation is found in mean absolute deviation portfolio choice model.