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The fundamental law of active management: Redux

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  • Ding, Zhuanxin
  • Martin, R. Douglas

Abstract

We develop a fundamental law of active management based on cross-section factor models for residual returns where the latter have unconditional mean zero and the factor exposures have zero mean and unit variance. Under our model framework the factor returns are cross-sectional information coefficients ICt that vary randomly over time with constant mean and variance. The fundamental law holds for portfolio managers who use conditional expectation of the residual returns and the associated conditional covariance matrix as inputs to active quadratic utility portfolio optimization. The fundamental law formula shows that the optimal portfolio's information ratio (IR) is positively related to the mean of ICt and the number of assets N in the portfolio selection universe, inversely related to the volatility of ICt, and is an absolute upper bound on IR as N tends to infinity. Support for our choice of factor model and our fundamental law is provided by an empirical study showing that significantly higher IR values are obtained using our choice of factor model as compared with IR values using an industry standard factor model.

Suggested Citation

  • Ding, Zhuanxin & Martin, R. Douglas, 2017. "The fundamental law of active management: Redux," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 91-114.
    • Handle: RePEc:eee:empfin:v:43:y:2017:i:c:p:91-114
    DOI: 10.1016/j.jempfin.2017.05.005
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    Cited by:

    1. Zhuanxin Ding & Yixiao Sun, 2023. "The statistics of time varying cross-sectional information coefficients," Journal of Asset Management, Palgrave Macmillan, vol. 24(1), pages 1-15, February.
    2. Prat, Georges & Uctum, Remzi, 2021. "Term structure of interest rates: Modelling the risk premium using a two horizons framework," Journal of Economic Behavior & Organization, Elsevier, vol. 182(C), pages 421-436.
    3. Zhuanxin Ding & R. Douglas Martin & Chaojun Yang, 2020. "Portfolio turnover when IC is time-varying," Journal of Asset Management, Palgrave Macmillan, vol. 21(7), pages 609-622, December.
    4. Winkler, Julian, 2023. "Managing fundamentals versus preferences: Re-balancing portfolios and stock returns," MPRA Paper 119149, University Library of Munich, Germany.
    5. Yuqin Sun & Yungao Wu & Gejirifu De, 2023. "A Novel Black-Litterman Model with Time-Varying Covariance for Optimal Asset Allocation of Pension Funds," Mathematics, MDPI, vol. 11(6), pages 1-21, March.
    6. Yijian Chuan & Lan Wu, 2019. "Centralizing-Unitizing Standardized High-Dimensional Directional Statistics and Its Applications in Finance," Papers 1912.10709, arXiv.org, revised Aug 2020.
    7. Feng Zhang & Xi Wang & Honggao Cao, 2021. "Turnover-Adjusted Information Ratio," Papers 2105.10306, arXiv.org.
    8. Feng Zhang & Ruite Guo & Honggao Cao, 2020. "Information Coefficient as a Performance Measure of Stock Selection Models," Papers 2010.08601, arXiv.org.

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