IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v211y2011i3p533-555.html
   My bibliography  Save this article

Large deviations theorems for optimal investment problems with large portfolios

Author

Listed:
  • Chu, Ba
  • Knight, John
  • Satchell, Stephen

Abstract

The thrust of this paper is to develop a new theoretical framework, based on large deviations theory, for the problem of optimal asset allocation in large portfolios. This problem is, apart from being theoretically interesting, also of practical relevance; examples include, inter alia, hedge funds where optimal strategies involve a large number of assets. In particular, we also prove the upper bound of the shortfall probability (or the risk bound) for the case where there is a finite number of assets. In the two-assets scenario, the effects of two types of asymmetries (i.e., asymmetry in the portfolio return distribution and asymmetric dependence among assets) on optimal portfolios and risk bounds are investigated. We calibrate our method with international equity data. In sum, both a theoretical analysis of the method and an empirical application indicate the feasibility and the significance of our approach.

Suggested Citation

  • Chu, Ba & Knight, John & Satchell, Stephen, 2011. "Large deviations theorems for optimal investment problems with large portfolios," European Journal of Operational Research, Elsevier, vol. 211(3), pages 533-555, June.
    • Handle: RePEc:eee:ejores:v:211:y:2011:i:3:p:533-555
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(10)00871-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Suleyman Basak & Alex Shapiro & Lucie Teplá, 2006. "Risk Management with Benchmarking," Management Science, INFORMS, vol. 52(4), pages 542-557, April.
    2. Michael Stutzer, 2011. "Portfolio choice with endogenous utility: a large deviations approach," World Scientific Book Chapters, in: Leonard C MacLean & Edward O Thorp & William T Ziemba (ed.), THE KELLY CAPITAL GROWTH INVESTMENT CRITERION THEORY and PRACTICE, chapter 43, pages 619-640, World Scientific Publishing Co. Pte. Ltd..
    3. Kandel, Shmuel & Stambaugh, Robert F, 1996. "On the Predictability of Stock Returns: An Asset-Allocation Perspective," Journal of Finance, American Finance Association, vol. 51(2), pages 385-424, June.
    4. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 36(3), pages 335-346.
    5. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
    6. Gaivoronski, Alexei A. & Krylov, Sergiy & van der Wijst, Nico, 2005. "Optimal portfolio selection and dynamic benchmark tracking," European Journal of Operational Research, Elsevier, vol. 163(1), pages 115-131, May.
    7. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    8. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
    9. Bawa, Vijay S., 1978. "Safety-First, Stochastic Dominance, and Optimal Portfolio Choice," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 13(2), pages 255-271, June.
    10. J. L. Knight & S. E. Satchell & K. C. Tran, 1995. "Statistical modelling of asymmetric risk in asset returns," Applied Mathematical Finance, Taylor & Francis Journals, vol. 2(3), pages 155-172.
    11. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    12. Peter C. Fishburn, 1984. "Foundations of Risk Measurement. I. Risk As Probable Loss," Management Science, INFORMS, vol. 30(4), pages 396-406, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zura Kakushadze, 2014. "Mean-Reversion and Optimization," Papers 1408.2217, arXiv.org, revised Feb 2016.
    2. Djellout, Hacène & Guillin, Arnaud & Samoura, Yacouba, 2017. "Estimation of the realized (co-)volatility vector: Large deviations approach," Stochastic Processes and their Applications, Elsevier, vol. 127(9), pages 2926-2960.

    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. Penaranda, Francisco, 2007. "Portfolio choice beyond the traditional approach," LSE Research Online Documents on Economics 24481, London School of Economics and Political Science, LSE Library.
    2. Andrew Patton, 2002. "(IAM Series No 001) On the Out-Of-Sample Importance of Skewness and Asymetric Dependence for Asset Allocation," FMG Discussion Papers dp431, Financial Markets Group.
    3. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    4. Chung, Y. Peter & Hong, Hyun A. & Kim, S. Thomas, 2019. "What causes the asymmetric correlation in stock returns?," Journal of Empirical Finance, Elsevier, vol. 54(C), pages 190-212.
    5. José Afonso Faias & Juan Arismendi Zambrano, 2022. "Equity Risk Premium Predictability from Cross-Sectoral Downturns [International asset allocation with regime shifts]," The Review of Asset Pricing Studies, Society for Financial Studies, vol. 12(3), pages 808-842.
    6. Lee, Kuan-Hui & Yang, Cheol-Won, 2022. "The world price of tail risk," Pacific-Basin Finance Journal, Elsevier, vol. 71(C).
    7. Massimo Guidolin & Giovanna Nicodano, 2009. "Small caps in international equity portfolios: the effects of variance risk," Annals of Finance, Springer, vol. 5(1), pages 15-48, January.
    8. Campbell, Rachel A.J. & Forbes, Catherine S. & Koedijk, Kees G. & Kofman, Paul, 2008. "Increasing correlations or just fat tails?," Journal of Empirical Finance, Elsevier, vol. 15(2), pages 287-309, March.
    9. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2015. "US Monetary and Fiscal Policies - Conflict or Cooperation?," SIRE Discussion Papers 2015-78, Scottish Institute for Research in Economics (SIRE).
    10. Alcock, Jamie & Sinagl, Petra, 2022. "International determinants of asymmetric dependence in investment returns," Journal of International Money and Finance, Elsevier, vol. 122(C).
    11. Massimo Guidolin & Giovanna Nicodano, 2010. "Ex Post Portfolio Performance with Predictable Skewness and Kurtosis," Carlo Alberto Notebooks 191, Collegio Carlo Alberto.
    12. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    13. Alexander, Gordon J. & Baptista, Alexandre M., 2009. "Stress testing by financial intermediaries: Implications for portfolio selection and asset pricing," Journal of Financial Intermediation, Elsevier, vol. 18(1), pages 65-92, January.
    14. Cerrato, Mario & Crosby, John & Kim, Minjoo & Zhao, Yang, 2014. "Modeling Dependence Structure and Forecasting Portfolio Value-at-Risk with Dynamic Copulas," SIRE Discussion Papers 2015-25, Scottish Institute for Research in Economics (SIRE).
    15. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    16. Low, Rand Kwong Yew & Alcock, Jamie & Faff, Robert & Brailsford, Timothy, 2013. "Canonical vine copulas in the context of modern portfolio management: Are they worth it?," Journal of Banking & Finance, Elsevier, vol. 37(8), pages 3085-3099.
    17. Diego Ferreira & Andreza A. Palma, 2022. "On the subprime crisis and the Latin American financial markets: A regime switching skew‐normal approach," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(3), pages 3300-3314, July.
    18. Garcia, René & Tsafack, Georges, 2011. "Dependence structure and extreme comovements in international equity and bond markets," Journal of Banking & Finance, Elsevier, vol. 35(8), pages 1954-1970, August.
    19. Haim Levy, 2010. "The CAPM is Alive and Well: A Review and Synthesis," European Financial Management, European Financial Management Association, vol. 16(1), pages 43-71, January.
    20. Ruenzi, Stefan & Ungeheuer, Michael & Weigert, Florian, 2020. "Joint Extreme events in equity returns and liquidity and their cross-sectional pricing implications," Journal of Banking & Finance, Elsevier, vol. 115(C).

    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:eee:ejores:v:211:y:2011:i:3:p:533-555. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    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.