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The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model

Fangzhou Huang Orcid Logo, Jiao Song, Nick J. Taylor

Data Science in Finance and Economics, Volume: 1, Issue: 2, Pages: 141 - 164

Swansea University Author: Fangzhou Huang Orcid Logo

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DOI (Published version): 10.3934/dsfe.2021008

Abstract

With fast evolving econometric techniques being adopted in asset pricing, traditional linear asset pricing models have been criticized by their limited function on capturing the time-varying nature of data and risk, especially the absence of data smoothing is of concern. In this paper, the impact of...

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Published in: Data Science in Finance and Economics
ISSN: 2769-2140
Published: American Institute of Mathematical Sciences (AIMS) 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa57738
first_indexed 2021-08-31T13:27:36Z
last_indexed 2021-09-23T03:21:14Z
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spelling 2021-09-22T12:02:17.7420712 v2 57738 2021-08-31 The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model 056c3ea10b44f9eb5b15e965119478de 0000-0002-3789-8593 Fangzhou Huang Fangzhou Huang true false 2021-08-31 CBAE With fast evolving econometric techniques being adopted in asset pricing, traditional linear asset pricing models have been criticized by their limited function on capturing the time-varying nature of data and risk, especially the absence of data smoothing is of concern. In this paper, the impact of data smoothing is explored by applying two asset pricing models with non-linear feature: cubic piecewise polynomial function (CPPF) model and the Fourier Flexible Form (FFF) model are performed on US stock returns as an experiment. The traditional beta coefficient is treated asymmetrically as downside beta and upside beta in order to capture corresponding risk, and further, to explore the risk premia attached in a cross-sectional context. It is found that both models show better goodness of fit comparing to classic linear asset pricing model cross-sectionally. When appropriate knots and orders are determined by Akaike Information Criteria (AIC), the goodness of fit is further improved, and the model with both CPPF and FFF betas employed showed the best fit among other models. The findings fill the gap in literature, specifically on both investigating and pricing the time variation and asymmetric nature of systematic risk. The methods and models proposed in this paper embed advanced mathematical techniques of data smoothing and widen the options of asset pricing models. The application of proposed models is proven to superiorly provide high degree of explanatory power to capture and price time-varying risk in stock market. Journal Article Data Science in Finance and Economics 1 2 141 164 American Institute of Mathematical Sciences (AIMS) 2769-2140 asset pricing; cubic piecewise polynomial function; Fourier Flexible Form; downside beta; upside beta 30 8 2021 2021-08-30 10.3934/dsfe.2021008 COLLEGE NANME Management School COLLEGE CODE CBAE Swansea University 2021-09-22T12:02:17.7420712 2021-08-31T14:18:06.4608319 Faculty of Humanities and Social Sciences School of Management - Accounting and Finance Fangzhou Huang 0000-0002-3789-8593 1 Jiao Song 2 Nick J. Taylor 3 57738__20963__3c6ad168d7654f78b7d2656becf375d9.pdf 57738.pdf 2021-09-22T11:59:44.9105531 Output 635554 application/pdf Version of Record true © 2021 the Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License true eng http://creativecommons.org/licenses/by/4.0
title The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
spellingShingle The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
Fangzhou Huang
title_short The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
title_full The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
title_fullStr The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
title_full_unstemmed The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
title_sort The impact of time-varying risk on stock returns: an experiment of cubic piecewise polynomial function model and the Fourier Flexible Form model
author_id_str_mv 056c3ea10b44f9eb5b15e965119478de
author_id_fullname_str_mv 056c3ea10b44f9eb5b15e965119478de_***_Fangzhou Huang
author Fangzhou Huang
author2 Fangzhou Huang
Jiao Song
Nick J. Taylor
format Journal article
container_title Data Science in Finance and Economics
container_volume 1
container_issue 2
container_start_page 141
publishDate 2021
institution Swansea University
issn 2769-2140
doi_str_mv 10.3934/dsfe.2021008
publisher American Institute of Mathematical Sciences (AIMS)
college_str Faculty of Humanities and Social Sciences
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hierarchy_top_id facultyofhumanitiesandsocialsciences
hierarchy_top_title Faculty of Humanities and Social Sciences
hierarchy_parent_id facultyofhumanitiesandsocialsciences
hierarchy_parent_title Faculty of Humanities and Social Sciences
department_str School of Management - Accounting and Finance{{{_:::_}}}Faculty of Humanities and Social Sciences{{{_:::_}}}School of Management - Accounting and Finance
document_store_str 1
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description With fast evolving econometric techniques being adopted in asset pricing, traditional linear asset pricing models have been criticized by their limited function on capturing the time-varying nature of data and risk, especially the absence of data smoothing is of concern. In this paper, the impact of data smoothing is explored by applying two asset pricing models with non-linear feature: cubic piecewise polynomial function (CPPF) model and the Fourier Flexible Form (FFF) model are performed on US stock returns as an experiment. The traditional beta coefficient is treated asymmetrically as downside beta and upside beta in order to capture corresponding risk, and further, to explore the risk premia attached in a cross-sectional context. It is found that both models show better goodness of fit comparing to classic linear asset pricing model cross-sectionally. When appropriate knots and orders are determined by Akaike Information Criteria (AIC), the goodness of fit is further improved, and the model with both CPPF and FFF betas employed showed the best fit among other models. The findings fill the gap in literature, specifically on both investigating and pricing the time variation and asymmetric nature of systematic risk. The methods and models proposed in this paper embed advanced mathematical techniques of data smoothing and widen the options of asset pricing models. The application of proposed models is proven to superiorly provide high degree of explanatory power to capture and price time-varying risk in stock market.
published_date 2021-08-30T05:08:16Z
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