Selecting skilled mutual funds through the multiple testing framework has received increasing attention from finance researchers and statisticians. The intercept $\alpha$ of Carhart four-factor model is commonly used to measure the true performance of mutual funds, and positive $\alpha$'s are considered as skilled. We observe that the standardized OLS estimates of $\alpha$'s across the funds possess strong dependence and nonnormality structures, indicating that the conventional multiple testing methods are inadequate for selecting the skilled funds. We start from a decision theoretic perspective, and propose an optimal testing procedure to minimize a combination of false discovery rate and false non-discovery rate. Our proposed testing procedure is constructed based on the probability of each fund not being skilled conditional on the information across all of the funds in our study. To model the distribution of the information used for the testing procedure, we consider a mixture model under dependence and propose a new method called ``approximate empirical Bayes" to fit the parameters. Empirical studies show that our selected skilled funds have superior long-term and short-term performance, e.g., our selection strongly outperforms the S\&P 500 index during the same period.
翻译:通过多种测试框架选择技术共同基金的做法日益受到金融研究人员和统计学家的注意。卡哈特四要素模型的拦截美元/阿尔法元通常用于衡量共同基金的真实性能,正美元/阿尔法元被认为是熟练的。我们观察到,各基金之间标准化的OSLS估计数具有很强的依赖性和不常态性结构,表明常规的多重测试方法不足以选择技术基金。我们从决策理论角度出发,提出最佳测试程序,以尽量减少假发现率和假不披露率的结合。我们提议的测试程序是根据每个基金不以我们研究中所有基金的信息为条件的熟练可能性来构建的。为测试程序所用信息的分布建模,我们认为,一种依赖性的混合模型,并提出一种称为“接近经验的海湾”的新方法,以适应参数。“经验论”研究表明,我们选定的技术基金在同一时期具有较高的长期和短期性能,例如,我们选择的SQQP500指数的高度超度。