Stochastic Arbitrage Opportunities: Set Estimation and Statistical Testing

Stelios Arvanitis () and Thierry Post
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Stelios Arvanitis: Department of Economics, Athens University of Economics and Business, 104 34 Athens, Greece
Thierry Post: Graduate School of Business, Nazarbayev University, Astana 010000, Kazakhstan

Mathematics, 2024, vol. 12, issue 4, 1-19

Abstract: We provide a formal statistical theory of consistent estimation of the set of all arbitrage portfolios that meet the description of being a stochastic arbitrage opportunity. Two empirical likelihood ratio tests are developed: one for the null that a given arbitrage portfolio is qualified, and another for the alternative that the portfolio is not qualified. Apart from considering generalized concepts and hypotheses based on multiple host portfolios, the statistical assumption framework is also more general than in earlier studies that focused on special cases with a single benchmark portfolio. Various extensions and generalizations of the theory are discussed. A Monte Carlo simulation study shows promising statistical size and power properties for testing the null, for representative data dimensions. The results of an empirical application illustrate the importance of selecting a proper blocking structure and moment estimation method.

Keywords: portfolio analysis; arbitrage portfolios; asset pricing; asymptotic statistics; empirical likelihood (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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