IDEAS home Printed from https://ideas.repec.org/a/wsi/apjorx/v34y2017i05ns0217595917500257.html
   My bibliography  Save this article

A Computational Algorithm for Equilibrium Asset Pricing Under Heterogeneous Information and Short-Sale Constraints

Author

Listed:
  • Jun Tong

    (School of Management, Shanghai University, Shanghai 200444, P. R. China)

  • Jian-Qiang Hu

    (Department of Management Science, Fudan University, Shanghai 200433, P. R. China)

  • Jiaqiao Hu

    (Department of Applied Mathematics and Statistics, State University of New York, Stony Brook, NY 11794, USA)

Abstract

We propose an efficient algorithm for computing the equilibrium of a capital asset pricing model with heterogeneous investors and short-sale constraints. We show that the equilibrium prices of the risky assets in the model are proportional to the Lagrangian multipliers of an equivalent dual formulation of the problem. Based on this observation, we derive sufficient conditions to guarantee the existence and uniqueness of equilibrium and prove the convergence of the algorithm. Numerical examples are also provided to illustrate the algorithm.

Suggested Citation

  • Jun Tong & Jian-Qiang Hu & Jiaqiao Hu, 2017. "A Computational Algorithm for Equilibrium Asset Pricing Under Heterogeneous Information and Short-Sale Constraints," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 34(05), pages 1-16, October.
    • Handle: RePEc:wsi:apjorx:v:34:y:2017:i:05:n:s0217595917500257
    DOI: 10.1142/S0217595917500257
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0217595917500257
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0217595917500257?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hens, Thorsten & Laitenberger, Jorg & Loffler, Andreas, 2002. "Two remarks on the uniqueness of equilibria in the CAPM," Journal of Mathematical Economics, Elsevier, vol. 37(2), pages 123-132, April.
    2. E. Eisenberg, 1961. "Aggregation of Utility Functions," Management Science, INFORMS, vol. 7(4), pages 337-350, July.
    3. Harrison Hong & Jeremy C. Stein, 2003. "Differences of Opinion, Short-Sales Constraints, and Market Crashes," The Review of Financial Studies, Society for Financial Studies, vol. 16(2), pages 487-525.
    4. 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.
    5. Allingham, Michael, 1991. "Existence Theorems in the Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 59(4), pages 1169-1174, July.
    6. Ginsburgh, Victor & Waelbroeck, Jean, 1979. "A Note on the Simultaneous Stability of Tatonnement Processes for Computing Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 20(2), pages 367-380, June.
    7. Nielsen, Lars Tyge, 1988. "Uniqueness of Equilibrium in the Classical Capital Asset Pricing Model," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 23(3), pages 329-336, September.
    8. Nielsen, Lars Tyge, 1990. "Existence of equilibrium in CAPM," Journal of Economic Theory, Elsevier, vol. 52(1), pages 223-231, October.
    9. H. Uzawa, 1960. "Walras' Tâtonnement in the Theory of Exchange," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 27(3), pages 182-194.
    10. 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.
    11. Fama, Eugene F. & French, Kenneth R., 2007. "Disagreement, tastes, and asset prices," Journal of Financial Economics, Elsevier, vol. 83(3), pages 667-689, March.
    12. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    13. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, September.
    14. Diamond, Douglas W. & Verrecchia, Robert E., 1987. "Constraints on short-selling and asset price adjustment to private information," Journal of Financial Economics, Elsevier, vol. 18(2), pages 277-311, June.
    15. 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.
    16. Lars Tyge Nielsen, 1989. "Asset Market Equilibrium with Short-Selling," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 56(3), pages 467-473.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rockafellar, R. Tyrrell & Uryasev, Stan & Zabarankin, M., 2007. "Equilibrium with investors using a diversity of deviation measures," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3251-3268, November.
    2. Ma, Chenghu & Hu, Jianqiang & Xu, Yifan, 2018. "Margins on short sales and equilibrium price indeterminacy," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 79-92.
    3. Jan Wenzelburger, 2010. "The two-fund separation theorem revisited," Annals of Finance, Springer, vol. 6(2), pages 221-239, March.
    4. 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.
    5. Wenzelburger, Jan, 2008. "A Note on the Two-fund Separation Theorem," MPRA Paper 11014, University Library of Munich, Germany, revised 31 Sep 2008.
    6. Thomas J. Brennan & Andrew W. Lo, 2010. "Impossible Frontiers," Management Science, INFORMS, vol. 56(6), pages 905-923, June.
    7. Fatma Lajeri-Chaherli, 2016. "On The Concavity And Quasiconcavity Properties Of ( Σ , Μ ) Utility Functions," Bulletin of Economic Research, Wiley Blackwell, vol. 68(3), pages 287-296, April.
    8. Wang, Tiandu & Ma, Chenghu & Sun, Qian, 2017. "The interaction between security lending market and security trading market," Pacific-Basin Finance Journal, Elsevier, vol. 46(PB), pages 309-322.
    9. Christoph Czichowsky & Martin Herdegen & David Martins, 2024. "Existence and uniqueness of quadratic and linear mean-variance equilibria in general semimartingale markets," Papers 2408.03134, arXiv.org.
    10. 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.
    11. Bottazzi, Jean-Marc & Hens, Thorsten & Loffler, Andreas, 1998. "Market Demand Functions in the Capital Asset Pricing Model," Journal of Economic Theory, Elsevier, vol. 79(2), pages 192-206, April.
    12. Lajeri-Chaherli, Fatma, 2003. "Partial derivatives, comparative risk behavior and concavity of utility functions," Mathematical Social Sciences, Elsevier, vol. 46(1), pages 81-99, August.
    13. Koch-Medina, Pablo & Wenzelburger, Jan, 2018. "Equilibria in the CAPM with non-tradeable endowments," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 93-107.
    14. Dana, Rose-Anne, 1999. "Existence, uniqueness and determinacy of equilibrium in C.A.P.M. with a riskless asset," Journal of Mathematical Economics, Elsevier, vol. 32(2), pages 167-175, October.
    15. Chen, Yong & Da, Zhi & Huang, Dayong, 2022. "Short selling efficiency," Journal of Financial Economics, Elsevier, vol. 145(2), pages 387-408.
    16. Chen, Joseph & Hong, Harrison & Stein, Jeremy C., 2002. "Breadth of ownership and stock returns," Journal of Financial Economics, Elsevier, vol. 66(2-3), pages 171-205.
    17. Jank, Stephan & Roling, Christoph & Smajlbegovic, Esad, 2021. "Flying under the radar: The effects of short-sale disclosure rules on investor behavior and stock prices," Journal of Financial Economics, Elsevier, vol. 139(1), pages 209-233.
    18. D. Won & G. Hahn & N. Yannelis, 2008. "Capital market equilibrium without riskless assets: heterogeneous expectations," Annals of Finance, Springer, vol. 4(2), pages 183-195, March.
    19. Stephen L. Lenkey, 2021. "Informed Trading with a Short-Sale Prohibition," Management Science, INFORMS, vol. 67(3), pages 1803-1824, March.
    20. Smimou, K. & Bector, C.R. & Jacoby, G., 2008. "Portfolio selection subject to experts' judgments," International Review of Financial Analysis, Elsevier, vol. 17(5), pages 1036-1054, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:apjorx:v:34:y:2017:i:05:n:s0217595917500257. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/apjor/apjor.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.