PySDTest: a Python/Stata Package for Stochastic Dominance Tests

TL;DR

PySDTest is a versatile Python/Stata package that enables advanced stochastic dominance testing with multiple methods and hypotheses, demonstrated through an empirical comparison of Bitcoin and S&P 500 returns.

Contribution

The paper introduces PySDTest, a comprehensive package for stochastic dominance testing that integrates various methods and extensions not previously available in a single tool.

Findings

S&P 500 second-order stochastically dominates Bitcoin.

The package supports flexible resampling and test statistic options.

Practical guidance for using the testing procedures is provided.

Abstract

We introduce PySDTest, a Python/Stata package for statistical tests of stochastic dominance. PySDTest implements various testing procedures such as Barrett and Donald (2003), Linton et al. (2005), Linton et al. (2010), and Donald and Hsu (2016), along with their extensions. Users can flexibly combine several resampling methods and test statistics, including the numerical delta method (D\"umbgen, 1993; Hong and Li, 2018; Fang and Santos, 2019). The package allows for testing advanced hypotheses on stochastic dominance relations, such as stochastic maximality among multiple prospects. We first provide an overview of the concepts of stochastic dominance and testing methods. Then, we offer practical guidance for using the package and the Stata command pysdtest. We apply PySDTest to investigate the portfolio choice problem between the daily returns of Bitcoin and the S&P 500 index as an empirical illustration. Our findings indicate that the S&P 500 index returns second-order stochastically dominate the Bitcoin returns.