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Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints

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  • Tong, Jun
  • Hu, Jiaqiao
  • Hu, Jianqiang

Abstract

The mean-variance capital asset pricing model (CAPM) is a useful mathematical tool for studying a variety of financial problems. In contrast to existing work in the literature, which has primarily focused on deriving analytical solutions under restrictive assumptions, we propose a numerical algorithm for efficiently computing the set of equilibrium prices of a CAPM model with heterogeneous investors and arbitrary margin requirements. We present the mathematical formulation of the CAPM model, derive structural properties of the portfolio selection and excess demand functions, and establish the asymptotic convergence of the proposed algorithm under mild conditions. To illustrate the utility of the algorithm, we perform sensitivity analysis on a simple example to study the impact of marginal requirements and interest rates on the resulting equilibrium prices. Numerical studies are also carried out to compare the performance of the algorithm with that of two other popular methods, namely, the fixed point method and the brand-and-bound algorithm.

Suggested Citation

  • Tong, Jun & Hu, Jiaqiao & Hu, Jianqiang, 2017. "Computing equilibrium prices for a capital asset pricing model with heterogeneous beliefs and margin-requirement constraints," European Journal of Operational Research, Elsevier, vol. 256(1), pages 24-34.
    • Handle: RePEc:eee:ejores:v:256:y:2017:i:1:p:24-34
    DOI: 10.1016/j.ejor.2016.07.010
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    1. Carl Chiarella & Roberto Dieci & Xue-Zhong He & Kai Li, 2013. "An evolutionary CAPM under heterogeneous beliefs," Annals of Finance, Springer, vol. 9(2), pages 185-215, May.
    2. Lintner, John, 1969. "The Aggregation of Investor's Diverse Judgments and Preferences in Purely Competitive Security Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 4(4), pages 347-400, December.
    3. Jing Hu & John Mitchell & Jong-Shi Pang & Bin Yu, 2012. "On linear programs with linear complementarity constraints," Journal of Global Optimization, Springer, vol. 53(1), pages 29-51, May.
    4. Lam, Kin & Yu, P.L.H. & Lee, P.H., 2010. "A margin scheme that advises on when to change required margin," European Journal of Operational Research, Elsevier, vol. 207(1), pages 524-530, November.
    5. Levy, Moshe, 2007. "Conditions for a CAPM equilibrium with positive prices," Journal of Economic Theory, Elsevier, vol. 137(1), pages 404-415, November.
    6. Nicolae Gârleanu & Lasse Heje Pedersen, 2011. "Margin-based Asset Pricing and Deviations from the Law of One Price," The Review of Financial Studies, Society for Financial Studies, vol. 24(6), pages 1980-2022.
    7. Shi, Lei, 2016. "Consumption-based CAPM with belief heterogeneity," Journal of Economic Dynamics and Control, Elsevier, vol. 65(C), pages 30-46.
    8. Haim Levy, 2006. "Capital Asset Prices with Heterogeneous Beliefs," The Journal of Business, University of Chicago Press, vol. 79(3), pages 1317-1354, May.
    9. Anufriev, Mikhail & Tuinstra, Jan, 2013. "The impact of short-selling constraints on financial market stability in a heterogeneous agents model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1523-1543.
    10. Alejandro Jofré & R. Terry Rockafellar & Roger J-B. Wets, 2007. "Variational Inequalities and Economic Equilibrium," Mathematics of Operations Research, INFORMS, vol. 32(1), pages 32-50, February.
    11. Jarrow, Robert A, 1980. "Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices," Journal of Finance, American Finance Association, vol. 35(5), pages 1105-1113, December.
    12. Nielsen, Lars Tyge, 1992. "Positive Prices in CAPM," Journal of Finance, American Finance Association, vol. 47(2), pages 791-808, June.
    13. Rahul Garg & Sanjiv Kapoor, 2006. "Auction Algorithms for Market Equilibrium," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 714-729, November.
    14. Eaves, B. Curtis & Schmedders, Karl, 1999. "General equilibrium models and homotopy methods," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1249-1279, September.
    15. Fama, Eugene F. & French, Kenneth R., 2007. "Disagreement, tastes, and asset prices," Journal of Financial Economics, Elsevier, vol. 83(3), pages 667-689, March.
    16. Mehdi Ghiyasvand & James B. Orlin, 2012. "A Simple Approximation Algorithm for Computing Arrow-Debreu Prices," Operations Research, INFORMS, vol. 60(5), pages 1245-1248, October.
    17. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    18. N. D. Yen, 1995. "Lipschitz Continuity of Solutions of Variational Inequalities with a Parametric Polyhedral Constraint," Mathematics of Operations Research, INFORMS, vol. 20(3), pages 695-708, August.
    19. Ning Sun & Zaifu Yang, 2003. "Existence of Equilibrium and Zero-Beta Pricing Formula in the Capital Asset Pricing Model with Heterogeneous Beliefs," Annals of Economics and Finance, Society for AEF, vol. 4(1), pages 51-71, May.
    20. Levy, Haim, 1978. "Equilibrium in an Imperfect Market: A Constraint on the Number of Securities in the Portfolio," American Economic Review, American Economic Association, vol. 68(4), pages 643-658, September.
    21. Oleg Rytchkov, 2014. "Asset Pricing with Dynamic Margin Constraints," Journal of Finance, American Finance Association, vol. 69(1), pages 405-452, February.
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    Cited by:

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