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A Threshold Model Approach To Estimating The Abnormal Stock Returns



    () (Department of Economics and Hong Kong Institute of Asia-Pacific Studies, The Chinese University of Hong Kong, Hong Kong;
    Department of International Economics and Trade, Nanjing University, China)


    (Department of Economics, The Chinese University of Hong Kong, Hong Kong)


    () (Department of Economics and Finance, City University of Hong Kong, Hong Kong)


The classical capital asset pricing model postulates a linear relationship between stock returns and stock risks. However, a number of subsequent empirical studies have revealed some anomalies in this relationship, especially for firms with small size and high book-to-market values. A possible explanation for the anomalies is the existence of threshold effects in the proxies of stock risks. However, conventional threshold models only allow for one threshold variable, which limits their applicability in this context. In this paper, we address this issue by applying the econometric technique developed by Bai et al. (2012). We estimate the joint threshold effects of firm size and book-to-market equity ratio on the stock returns using a sample of 5,271 US firms. The test results yield clear evidence for the existence of threshold effects in both firm features. We find that abnormal returns exist when the firm size falls below 52.04 million USD and the book-to-market ratio exceeds 0.4085.

Suggested Citation

  • Terence Tai-Leung Chong & Wing Hei Mak & Isabel Kit-Ming Yan, 2013. "A Threshold Model Approach To Estimating The Abnormal Stock Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 8(01), pages 1-17.
  • Handle: RePEc:wsi:afexxx:v:08:y:2013:i:01:n:s2010495213500012
    DOI: 10.1142/S2010495213500012

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    More about this item


    Multiple threshold variables; CAPM model; bootstrapping; C12; C22; C23; G11;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions


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