Optimal clustering in Bayesian Capital Asset Pricing Model

We focus on robust Bayesian estimation of the systematic risk of an asset in presence of outlying points. We assume that the returns follow independent normal distributions with a product partition structure on the parameters of interest. A Bayesian decision theoretical approach is used to identify the partition that best separates standard and atypical data points. We apply a nonsmooth optimization algorithm to minimize the expected value of a given loss function. The methodology is illustrated with reference to the IPSA stock market index and the MIBTEL one.