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Nearly unbiased estimation of sample skewness

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  • Li, Yifan

Abstract

In this paper we examine the finite sample bias of sample skewness estimator for financial returns. We show that the bias of conventional sample skewness comes from two sources: the covariance between past return and future volatility, known as the leverage effect, and the covariance between past volatility and future return, commonly referred to as the volatility feedback effect. We derive explicit expressions for this bias and propose a nearly unbiased skewness estimator under mild assumptions. Our simulation study shows that the proposed estimator leads to almost unbiased skewness estimates with a sightly elevated mean squared error, and can reduce the bias of the skewness coefficient estimates by 40%. In our empirical application, we find that bias-corrected average skewness can better predict future market returns comparing to the case without bias-correction. This leads to an improved performance of skewness-based portfolios in terms of Sharpe ratio, certainty equivalence and transaction cost.

Suggested Citation

  • Li, Yifan, 2020. "Nearly unbiased estimation of sample skewness," Economics Letters, Elsevier, vol. 192(C).
  • Handle: RePEc:eee:ecolet:v:192:y:2020:i:c:s0165176520301324
    DOI: 10.1016/j.econlet.2020.109174
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    Cited by:

    1. Annaert, Jan & De Ceuster, Marc & Van Cappellen, Jef, 2023. "Can average skewness really predict financial returns? The euro area case," Finance Research Letters, Elsevier, vol. 52(C).
    2. Yifan Li & Yao Rao, 2021. "A simple nearly unbiased estimator of cross‐covariances," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(2), pages 240-266, March.
    3. Carnero, M. Angeles & León, Angel & Ñíguez, Trino-Manuel, 2023. "Skewness in energy returns: estimation, testing and retain-->implications for tail risk," The Quarterly Review of Economics and Finance, Elsevier, vol. 90(C), pages 178-189.
    4. Annaert, Jan & De Ceuster, Marc & Van Doninck, Freek, 2022. "Decomposing the idiosyncratic volatility anomaly among euro area stocks," Finance Research Letters, Elsevier, vol. 47(PB).

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    More about this item

    Keywords

    Skewness; Bias; Return predictability;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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