Generalized Stochastic Arbitrage Opportunities

Abstract

Concepts are introduced and applied for analyzing and selecting arbitrage portfolios in the face of uncertainty about initial positions and risk preferences. A stochastic arbitrage opportunity is defined as a zero-cost investment portfolio that enhances every feasible host portfolio for all admissible utility functions. The alternative to the existence of such investment opportunities is the existence of a solution to a dual system of asset pricing restrictions based on a class of stochastic discount factors. Feasible approaches to numerical optimization and statistical inference are discussed. Empirical results suggest that equity factor investing is appealing for all risk-averse stock investors with a wide range of initial position and sufficiently low transactions costs by mixing multiple factor portfolios with high after-cost appraisal ratios, low mutual correlation, and negative exposures to the relevant host portfolios. These findings weaken the case for risk-based explanations for the profitability of factor investing. This paper was accepted by Kay Giesecke, finance. Supplemental Material: The data files are available at https://doi.org/10.1287/mnsc.2023.4892 .