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The statistics of time varying cross-sectional information coefficients

Author

Listed:
  • Zhuanxin Ding

    (AlphaFocus Investment Research, LLC)

  • Yixiao Sun

    (University of California)

Abstract

The information coefficient (IC), defined as the correlation coefficient between a stock return and its factor exposures predictor variables, is one of the most commonly used statistics in quantitative financial analysis. In this paper, we establish consistency and asymptotic normality of the time series average of cross-sectional sample ICs when the true underlying ICs between the risk-adjusted residual return and the standardized factor exposures are time varying. We use those results to show that the time series average of the cross-sectional sample ICs divided by its sample standard deviation converges to the ex ante expected portfolio information ratio (IR) as derived in Ding and Martin (2017). A simulation study based on a true factor model shows that the finite sample results are strikingly close to what the theory suggests. We also conduct empirical simulations using actual stock returns and quantitative factor exposures, and we find that the logarithm of the estimated IR can be explained very well by a function of the IC mean, the IC standard deviation, and the sample size in exactly the same way as predicted by our theory built on a linear factor model with time varying ICs.

Suggested Citation

  • 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.
    • Handle: RePEc:pal:assmgt:v:24:y:2023:i:1:d:10.1057_s41260-022-00295-9
    DOI: 10.1057/s41260-022-00295-9
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    References listed on IDEAS

    as
    1. Yixiao Sun, 2013. "A heteroskedasticity and autocorrelation robust F test using an orthonormal series variance estimator," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 1-26, February.
    2. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    3. Ding, Zhuanxin & Martin, R. Douglas, 2017. "The fundamental law of active management: Redux," Journal of Empirical Finance, Elsevier, vol. 43(C), pages 91-114.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Information coefficient (IC); Asymptotic distribution; Information ratio (IR); Factor model; The fundamental law of active management (FLAM);
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables
    • C5 - Mathematical and Quantitative Methods - - Econometric Modeling

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