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The Black–Litterman model: a consistent estimation of the parameter tau

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  • Erindi Allaj

Abstract

In addition to giving a detailed description and explanation of the Black–Litterman (BL) model, this paper deals with estimation of the parameter tau. This parameter is the most mysterious one in the BL model, as the literature does not provide specific guidance on its calibration. Specifically, I develop an estimation procedure that yields a suitable and consistent estimate of tau, which results in a modification of the original BL model. The approach combines cross-section and time-series regressions, both commonly approach to estimate the capital asset pricing model. The novelty here consists in utilizing random intercepts when estimating the time-series regressions. In addition, a new definition of beta is derived. Within this framework, the parameter tau is obtained from the cross-sectional regression. The approach is able to capture the serial, cross, and cross-lag correlations of the excess returns. To illustrate the new framework, I provide an empirical application and show that it is easily applicable by portfolio managers. Copyright Swiss Society for Financial Market Research 2013

Suggested Citation

  • Erindi Allaj, 2013. "The Black–Litterman model: a consistent estimation of the parameter tau," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 27(2), pages 217-251, June.
    • Handle: RePEc:kap:fmktpm:v:27:y:2013:i:2:p:217-251
    DOI: 10.1007/s11408-013-0205-x
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    Cited by:

    1. Zura Kakushadze, 2014. "Mean-Reversion and Optimization," Papers 1408.2217, arXiv.org, revised Feb 2016.
    2. Randy O’Toole, 2017. "The Black–Litterman model: active risk targeting and the parameter tau," Journal of Asset Management, Palgrave Macmillan, vol. 18(7), pages 580-587, December.
    3. Frieder Meyer-Bullerdiek, 2021. "Out-of-sample performance of the Black-Litterman model," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 10(2), pages 1-2.
    4. Pyo, Sujin & Lee, Jaewook, 2018. "Exploiting the low-risk anomaly using machine learning to enhance the Black–Litterman framework: Evidence from South Korea," Pacific-Basin Finance Journal, Elsevier, vol. 51(C), pages 1-12.

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    More about this item

    Keywords

    Black–Litterman model; Market efficiency; Bayesian statistics; GLS estimation; Two-stage CAPM estimation; Mean–variance optimization; C11; C33; G11; G12;
    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
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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