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Arbitrage, state prices and portfolio theory

In: Handbook of the Economics of Finance


  • Dybvig, Philip H.
  • Ross, Stephen A.


Neoclassical financial models provide the foundation for our understanding of finance. This chapter introduces the main ideas of neoclassical finance in a single-period context that avoids the technical difficulties of continuous-time models, but preserves the principal intuitions of the subject. The starting point of the analysis is the formulation of standard portfolio choice problems.A central conceptual result is the Fundamental Theorem of Asset Pricing, which asserts the equivalence of absence of arbitrage, the existence of a positive linear pricing rule, and the existence of an optimum for some agent who prefers more to less. A related conceptual result is the Pricing Rule Representation Theorem, which asserts that a positive linear pricing rule can be represented as using state prices, risk-neutral expectations, or a state-price density. Different equivalent representations are useful in different contexts.Many applied results can be derived from the first-order conditions of the portfolio choice problem. The first-order conditions say that marginal utility in each state is proportional to a consistent state-price density, where the constant of proportionality is determined by the budget constraint. If markets are complete, the implicit state-price density is uniquely determined by investment opportunities and must be the same as viewed by all agents, thus simplifying the choice problem. Solving first-order conditions for quantities gives us optimal portfolio choice, solving them for prices gives us asset pricing models, solving them for utilities gives us preferences, and solving them for probabilities gives us beliefs.We look at two popular asset pricing models, the CAPM and the APT, as well as complete-markets pricing. In the case of the CAPM, the first-order conditions link nicely to the traditional measures of portfolio performance.Further conceptual results include aggregation and mutual fund separation theory, both of which are useful for understanding equilibrium and asset pricing.

Suggested Citation

  • Dybvig, Philip H. & Ross, Stephen A., 2003. "Arbitrage, state prices and portfolio theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 10, pages 605-637, Elsevier.
  • Handle: RePEc:eee:finchp:2-10

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    Cited by:

    1. Kátay, Gábor & Péter, Harasztosi, 2017. "Currency Matching and Carry Trade by Non-Financial Corporations," Working Papers 2017-02, Joint Research Centre, European Commission.
    2. Stephen A. Ross, 2011. "The Recovery Theorem," NBER Working Papers 17323, National Bureau of Economic Research, Inc.
    3. Patrick Beissner, 2019. "Coherent-Price Systems and Uncertainty-Neutral Valuation," Risks, MDPI, vol. 7(3), pages 1-18, September.
    4. Alexander Zimper, 2017. "Rationalizable Information Equilibria," Working Papers 201745, University of Pretoria, Department of Economics.
    5. Satoshi Nakada & Shmuel Nitzan & Takashi Ui, 2022. "Robust Voting under Uncertainty," Working Papers on Central Bank Communication 038, University of Tokyo, Graduate School of Economics.
    6. NAKADA, Satoshi & NITZAN, Shmuel & UI, Takashi & 宇井, 貴志, 2017. "Robust Voting under Uncertainty," Discussion paper series HIAS-E-60, Hitotsubashi Institute for Advanced Study, Hitotsubashi University.
    7. repec:ebl:ecbull:v:30:y:2010:i:1:p:182-191 is not listed on IDEAS
    8. A Craig Burnside & Jeremy J Graveline, 2020. "On the Asset Market View of Exchange Rates," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 239-260.
    9. Krislert Samphantharak & Robert M. Townsend, 2018. "Risk and Return in Village Economies," American Economic Journal: Microeconomics, American Economic Association, vol. 10(1), pages 1-40, February.
    10. Panos Kouvelis & Rong Li, 2019. "Integrated Risk Management for Newsvendors with Value-at-Risk Constraints," Manufacturing & Service Operations Management, INFORMS, vol. 21(4), pages 816-832, October.
    11. Harasztosi, Péter & Kátay, Gábor, 2020. "Currency matching by non-financial corporations," Journal of Banking & Finance, Elsevier, vol. 113(C).
    12. Bong-Gyu Jang & Hyeng Keun Koo & Yuna Rhee, 2016. "Asset demands and consumption with longevity risk," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(3), pages 587-633, August.
    13. Tahir Choulli & Jun Deng & Junfeng Ma, 2015. "How non-arbitrage, viability and numéraire portfolio are related," Finance and Stochastics, Springer, vol. 19(4), pages 719-741, October.
    14. Jiang-Lun Wu & Wei Yang, 2013. "A Galerkin approximation scheme for the mean correction in a mean-reversion stochastic differential equation," Papers 1305.1868,
    15. Indrajit Mitra & Yu Xu, 2020. "Limited Household Risk Sharing: General Equilibrium Implications for the Term Structure of Interest Rates," FRB Atlanta Working Paper 2020-20, Federal Reserve Bank of Atlanta.
    16. Passadore, Juan & Xu, Yu, 2022. "Illiquidity in sovereign debt markets," Journal of International Economics, Elsevier, vol. 137(C).
    17. Tom Arnold & Richard Shockley, 2010. "Real Options Analysis and the Assumptions of Corporate Finance: A Non-Technical Review," Multinational Finance Journal, Multinational Finance Journal, vol. 14(1-2), pages 29-71, March-Jun.
    18. D. L. Wilcox & T. J. Gebbie, 2013. "On pricing kernels, information and risk," Papers 1310.4067,, revised Oct 2013.

    More about this item

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates


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