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针对传统统计套利模型缺乏度量风险指标和没有给出最优的持有周期的缺陷,本文构建了基于ROC曲线的统计套利模型,首先是检验资产组合是否服从均值回复过程,若服从,则可以实施统计套利;其次是用AUC指标度量统计套利的风险,根据AUC指标和期望收益进行资产权重配置和确定持有周期,根据YI指标确定组合的均衡点,最后是实施统计套利策略。通过数值模拟分析,表明ROC曲线能够检验资产组合是否满足均值回复过程,进而结合A股市场进行实证分析,在不考虑交易成本的情况下和市场允许卖空的情况下,基于ROC曲线的统计套利模型能够获得相对稳定的收益。
In view of the lack of measurement risk index and the failure to give the optimal holding cycle in traditional statistical arbitrage models, a statistical arbitrage model based on ROC curve is constructed in this paper. The first is to test whether the asset portfolio obeys the mean recovery process, Statistical arbitrage; followed by the AUC measure the risk of statistical arbitrage, asset allocation based on AUC indicators and expected return and determine the holding cycle, according to YI indicators to determine the equilibrium point of the portfolio, and finally the implementation of statistical arbitrage strategy. The numerical simulation shows that the ROC curve can test whether the asset portfolio meets the average recovery process and then makes an empirical analysis based on the A-share market. Statistical arbitrage based on the ROC curve can be done without considering the transaction costs and when the market is allowed to sell short. The model can get a relatively stable return.