Arbitrage Pricing Theory

Bruce C. Dieffenbach ()
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Bruce C. Dieffenbach: Independent author

Chapter 66 in Conjugate Duality in Economic Analysis, 2026, pp 509-516 from Springer

Abstract: Abstract Ross puts forward the arbitrage pricing theory (Ross, S. A. (1976, December). The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13 (3), 341–360; Ross, S. A. (1977). Return, risk, and arbitrage. In I. Friend & J. L. Bicksler (Eds.), Risk and return in finance (pp. 189–218). Cambridge, MA: Ballinger). The idea is that a factor structure of asset returns leads naturally to a model of risk premia, because otherwise there would exist an opportunity for arbitrage. After summarizing the argument of Ross, we develop the idea via a moment space of portfolios, which captures the factor structure by introducing a basis. The moment space decomposes into orthogonal complements: a systematic-risk subspace and a no-systematic-risk subspace. Calculating the Sharpe ratio in each subspace obtains a formulation of the arbitrage pricing theory.

Date: 2026
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DOI: 10.1007/978-3-032-21396-9_66

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