The reduced-rank beta in linear stochastic discount factor models |
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| Affiliation: | 1. Jindal Global Business School, OP Jindal Global University, Sonipat, Haryana, India;2. Indian Institute of Management Kashipur, Kundeshwari, Kashipur, District- Udham Singh Nagar, Uttarakhand-244713, India;3. Amrita School of Business, Coimbatore, Amrita Vishwa Vidyapeetham, India.;1. School of International Economics, China Foreign Affairs University, 24 Zhanlan Road, Xicheng District, Beijing 100037, China;2. School of Accounting, Guangdong University of Foreign Studies;3. Research Center for Accounting and Economic Development of Guangdong-Hong Kong-Macao Greater Bay Area, Guangdong University of Foreign Studies, 2 Baiyun Avenue, Baiyun District, Guangzhou 510420, China |
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| Abstract: | In a linear stochastic discount factor model, failure of the full-rank conditions affects the standard statistical inference of coefficients. We propose a novel risk measurement, the reduced-rank beta, which is the risk sensitivity to the effective part of factors for the full-rank covariance matrix. Our reduced-rank beta is a generalisation of the standard beta when the full-rank condition is not satisfied. By considering the Fama–French five-factor (FF5) model for the US equity market, the failure of the full-rank condition is found to affect beta estimates. We demonstrate the reduced-rank beta has important empirical implications for model reductions and anomaly explanations. |
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| Keywords: | Reduced-rank beta Stochastic discount factor Rank condition Spurious factor Asset pricing anomaly |
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