IDEAS home Printed from https://ideas.repec.org/a/eee/empfin/v72y2023icp251-275.html
   My bibliography  Save this article

Uncertainty in the Black–Litterman model: Empirical estimation of the equilibrium

Author

Listed:
  • Fuhrer, Adrian
  • Hock, Thorsten

Abstract

The Black–Litterman model is a widely used and well established application of the Bayesian framework to asset allocation problems. It is, however, difficult to calibrate, as it requires the specification of abstract uncertainty parameters. We propose a new, more flexible model that allows the empirical estimation of the equilibrium, alleviating the need for parametrization. In an empirical application, we illustrate the sensitivity of the classical Black–Litterman model to the choice of the uncertainty parameter. We then demonstrate that the flexible model successfully exploits information in the cross-section of index constituents’ returns to find an optimal trade-off in calibration of the uncertainty.

Suggested Citation

  • Fuhrer, Adrian & Hock, Thorsten, 2023. "Uncertainty in the Black–Litterman model: Empirical estimation of the equilibrium," Journal of Empirical Finance, Elsevier, vol. 72(C), pages 251-275.
    • Handle: RePEc:eee:empfin:v:72:y:2023:i:c:p:251-275
    DOI: 10.1016/j.jempfin.2023.03.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0927539823000312
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jempfin.2023.03.009?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. Michael C. Jensen, 1968. "The Performance Of Mutual Funds In The Period 1945–1964," Journal of Finance, American Finance Association, vol. 23(2), pages 389-416, May.
    2. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    3. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    4. Best, Michael J & Grauer, Robert R, 1991. "On the Sensitivity of Mean-Variance-Efficient Portfolios to Changes in Asset Means: Some Analytical and Computational Results," The Review of Financial Studies, Society for Financial Studies, vol. 4(2), pages 315-342.
    5. Ledoit, Oliver & Wolf, Michael, 2008. "Robust performance hypothesis testing with the Sharpe ratio," Journal of Empirical Finance, Elsevier, vol. 15(5), pages 850-859, December.
    6. 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.
    7. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    8. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    9. Rosella Giacometti & Marida Bertocchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2007. "Stable distributions in the Black-Litterman approach to asset allocation," Quantitative Finance, Taylor & Francis Journals, vol. 7(4), pages 423-433.
    10. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    11. Eugene F. Fama & Kenneth R. French, 2004. "The Capital Asset Pricing Model: Theory and Evidence," Journal of Economic Perspectives, American Economic Association, vol. 18(3), pages 25-46, Summer.
    12. Sharpe, William F., 1974. "Imputing Expected Security Returns from Portfolio Composition," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 9(3), pages 463-472, June.
    13. Robert F. Phillips, 2003. "Estimation of a Stratified Error-Components Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 501-521, May.
    14. Baltagi, Badi H & Griffin, James M, 1988. "A Generalized Error Component Model with Heteroscedastic Disturbances," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 29(4), pages 745-753, November.
    15. Jegadeesh, Narasimhan & Noh, Joonki & Pukthuanthong, Kuntara & Roll, Richard & Wang, Junbo, 2019. "Empirical tests of asset pricing models with individual assets: Resolving the errors-in-variables bias in risk premium estimation," Journal of Financial Economics, Elsevier, vol. 133(2), pages 273-298.
    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. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(1), pages 3-38, March.
    2. 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).
    3. Fracasso, Laís Martins & Müller, Fernanda Maria & Ramos, Henrique Pinto & Righi, Marcelo Brutti, 2023. "Is there a risk premium? Evidence from thirteen measures," The Quarterly Review of Economics and Finance, Elsevier, vol. 92(C), pages 182-199.
    4. Fernando Rubio, 2005. "Eficiencia De Mercado, Administracion De Carteras De Fondos Y Behavioural Finance," Finance 0503028, University Library of Munich, Germany, revised 23 Jul 2005.
    5. Choi, Paul Moon Sub & Choi, Joung Hwa, 2018. "Is individual trading priced in stocks?," Journal of International Money and Finance, Elsevier, vol. 85(C), pages 76-92.
    6. Jan A. Kempkes & Francesco Suprano & Andreas Wömpener, 2023. "An empirical evaluation of dynamic approaches for estimating firms’ expected cost of equity capital," The Financial Review, Eastern Finance Association, vol. 58(4), pages 859-886, November.
    7. Michael Ungeheuer & Martin Weber, 2021. "The Perception of Dependence, Investment Decisions, and Stock Prices," Journal of Finance, American Finance Association, vol. 76(2), pages 797-844, April.
    8. Hao Jiang & Marno Verbeek & Yu Wang, 2014. "Information Content When Mutual Funds Deviate from Benchmarks," Management Science, INFORMS, vol. 60(8), pages 2038-2053, August.
    9. Ladislav Kristoufek & Paulo Ferreira, 2018. "Capital asset pricing model in Portugal: Evidence from fractal regressions," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 17(3), pages 173-183, November.
    10. Linnenluecke, Martina K. & Chen, Xiaoyan & Ling, Xin & Smith, Tom & Zhu, Yushu, 2017. "Research in finance: A review of influential publications and a research agenda," Pacific-Basin Finance Journal, Elsevier, vol. 43(C), pages 188-199.
    11. Sebastian Lobe & Christian Walkshäusl, 2016. "Vice versus virtue investing around the world," Review of Managerial Science, Springer, vol. 10(2), pages 303-344, March.
    12. Attiya Yasmeen Javid, 2000. "Alternative Capital Asset Pricing Models: A Review of Theory and Evidence," PIDE Research Report 2000:3, Pakistan Institute of Development Economics.
    13. 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.
    14. Shahzad, Syed Jawad Hussain & Zakaria, Muhammad & Raza, Naveed, 2014. "Sensitivity Analysis of CAPM Estimates: Data Frequency and Time Frame," MPRA Paper 60110, University Library of Munich, Germany.
    15. Yan, Lei & Garcia, Philip, 2017. "Portfolio investment: Are commodities useful?," Journal of Commodity Markets, Elsevier, vol. 8(C), pages 43-55.
    16. Jan Bastin, 2015. "Volatility Effect: An Application on the German Stock Market [Efekt nízkého rizika: Aplikace na německý akciový trh]," Český finanční a účetní časopis, Prague University of Economics and Business, vol. 2015(1), pages 36-54.
    17. Qianwei Ying & Tahir Yousaf & Qurat ul Ain & Yasmeen Akhtar & Muhammad Shahid Rasheed, 2019. "Stock Investment and Excess Returns: A Critical Review in the Light of the Efficient Market Hypothesis," JRFM, MDPI, vol. 12(2), pages 1-22, June.
    18. Hanauer, Matthias X. & Lauterbach, Jochim G., 2019. "The cross-section of emerging market stock returns," Emerging Markets Review, Elsevier, vol. 38(C), pages 265-286.
    19. Morten Balling & Ernest Gnan, 2013. "The development of financial markets and financial theory: 50 years of interaction," SUERF 50th Anniversary Volume Chapters, in: Morten Balling & Ernest Gnan (ed.), 50 Years of Money and Finance: Lessons and Challenges, chapter 5, pages 157-194, SUERF - The European Money and Finance Forum.
    20. Ayub, Usman & Shah, Syed Zulfiqar Ali & Abbas, Qaisar, 2015. "Robust analysis for downside risk in portfolio management for a volatile stock market," Economic Modelling, Elsevier, vol. 44(C), pages 86-96.

    More about this item

    Keywords

    Asset allocation; Bayesian; Black–Litterman model; Error components models; Model uncertainty; Portfolio choice;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • D84 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Expectations; Speculations
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading

    Statistics

    Access and download statistics

    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:empfin:v:72:y:2023:i:c:p:251-275. 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/jempfin .

    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.