We propose novel randomized geometric tools to detect low-volatility anomalies in stock markets; a principal problem in financial economics. Our modeling of the (detection) problem results in sampling and estimating the (relative) volume of geodesically non-convex and non-connected spherical patches that arise by intersecting a non-standard simplex with a sphere. To sample, we introduce two novel Markov Chain Monte Carlo (MCMC) algorithms that exploit the geometry of the problem and employ state-of-the-art continuous geometric random walks (such as Billiard walk and Hit-and-Run) adapted on spherical patches. To our knowledge, this is the first geometric formulation and MCMC-based analysis of the volatility puzzle in stock markets. We have implemented our algorithms in C++ (along with an R interface) and we illustrate the power of our approach by performing extensive experiments on real data. Our analyses provide accurate detection and new insights into the distribution of portfolios' performance characteristics. Moreover, we use our tools to show that classical methods for low-volatility anomaly detection in finance form bad proxies that could lead to misleading or inaccurate results.
翻译:我们提出了新颖的随机几何工具,以探测股票市场中的低波动异常现象;这是金融经济学的一个主要问题。我们的(探测)问题模型在抽样和估计(相对的)数量中导致对股票市场波动拼图进行的第一个几何配方和基于MCMC的分析。我们在C++(与R界面一起)应用了我们的算法,我们通过对真实数据进行广泛的实验来说明我们的方法的力量。我们的分析提供了准确的检测和对投资组合性能特征分布的新的洞察力。此外,我们利用我们的工具展示了低挥发性金融风险的典型方法或错误金融风险分析结果。