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Incorporating alpha uncertainty into portfolio decisions: A Bayesian revisit of the Treynor–Black model

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  • Zhongzhi (Lawrence) He

    (Faculty of Business, Brock University)

Abstract

As in any alpha strategy, a manager confronts the estimation risk of alpha. The alpha uncertainty may result in unstable active portfolios whose weights are sensitive to small changes in the estimates of alpha. This paper develops an integrated Bayesian framework to account for alpha uncertainty. The solution is to shrink the sample estimates of alpha towards the equilibrium-implied value of zero, with the relative weight on the theoretical value determined by the level of overall active risk budget assigned by the manager. The classic Treynor–Black model is revisited within the Bayesian framework, and portfolio decisions are made through three stages that separately manage the active and passive components of the portfolio. The impact of different levels of active risk budget on each stage of portfolio decisions is empirically demonstrated, and the results characterise a full spectrum of optimal portfolios that range from a purely passive strategy to an extremely active one.

Suggested Citation

  • Zhongzhi (Lawrence) He, 2007. "Incorporating alpha uncertainty into portfolio decisions: A Bayesian revisit of the Treynor–Black model," Journal of Asset Management, Palgrave Macmillan, vol. 8(3), pages 161-175, September.
    • Handle: RePEc:pal:assmgt:v:8:y:2007:i:3:d:10.1057_palgrave.jam.2250071
    DOI: 10.1057/palgrave.jam.2250071
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    References listed on IDEAS

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    Cited by:

    1. John Birge & Luis Chavez-Bedoya, 2014. "Modeling manager confidence in forecasted excess returns under active portfolio management," Journal of Asset Management, Palgrave Macmillan, vol. 15(6), pages 353-365, December.
    2. Zhongzhi Lawrence He, 2018. "Comparing Asset Pricing Models: Distance-based Metrics and Bayesian Interpretations," Papers 1803.01389, arXiv.org.

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