Generalized Stochastic Arbitrage Opportunities
45 Pages Posted: 19 Apr 2021 Last revised: 3 Apr 2023
Date Written: April 17, 2021
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.
Keywords: Portfolio analysis; Arbitrage portfolios; Asset pricing; Incomplete markets; Factor investing
JEL Classification: C61, D81, G11
Suggested Citation: Suggested Citation