A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions

Ezekiel Oseni; Razak Olawale Olanrewaju

doi:doi:10.11648/j.ijfbr.20170303.12

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A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions

Ezekiel Oseni, Razak Olawale Olanrewaju

Published in International Journal of Finance and Banking Research (Volume 3, Issue 3)

Received: 10 April 2017 Accepted: 14 April 2017 Published: 16 June 2017

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Abstract

This study describes the approach for estimating the beta-risk of the Capital Asset Price Model (CAPM) when the normality (Gaussian) assumption of both the error term and the excess return on an asset holds, and also when their normality assumption is violated or failed due to outliers or excessive skewness and excessive kurtosis. The student-t distribution was used as an alternative distribution to capture these anomalies. The monthly All-share Index (ASI) of 12 crucial Market Portfolios / Sectors derived from Nigeria Stock Exchange (NSE) were subjected to both the Gaussian error innovation and Student-t error innovation in this study. However, it was noted that estimates of portfolios’ beta-risk and its standard error for Gaussian and student-t were approximately the same when the sector follows a normal distribution while the standard errors of portfolio beta-risk estimates will be smaller under student-t innovation than that of Gaussian innovation when the sector does not follow normal distribution due to these anomalies. Furthermore, it was discovered that building & construction, manufacturing, quarry & mining, communication, transportation, education and utilities sectors have been having lower volatility, that is, in boosting the economy over the last 15 years.

Published in	International Journal of Finance and Banking Research (Volume 3, Issue 3)
DOI	10.11648/j.ijfbr.20170303.12
Page(s)	44-52
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Beta-Risk, Capm, Expected Returns, Gaussian Innovation, Student-T Innovation, Systematic Risk

References

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APA Style

Ezekiel Oseni, Razak Olawale Olanrewaju. (2017). A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. International Journal of Finance and Banking Research, 3(3), 44-52. https://doi.org/10.11648/j.ijfbr.20170303.12

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ACS Style

Ezekiel Oseni; Razak Olawale Olanrewaju. A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. Int. J. Finance Bank. Res. 2017, 3(3), 44-52. doi: 10.11648/j.ijfbr.20170303.12

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AMA Style

Ezekiel Oseni, Razak Olawale Olanrewaju. A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. Int J Finance Bank Res. 2017;3(3):44-52. doi: 10.11648/j.ijfbr.20170303.12

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@article{10.11648/j.ijfbr.20170303.12,
  author = {Ezekiel Oseni and Razak Olawale Olanrewaju},
  title = {A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions},
  journal = {International Journal of Finance and Banking Research},
  volume = {3},
  number = {3},
  pages = {44-52},
  doi = {10.11648/j.ijfbr.20170303.12},
  url = {https://doi.org/10.11648/j.ijfbr.20170303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfbr.20170303.12},
  abstract = {This study describes the approach for estimating the beta-risk of the Capital Asset Price Model (CAPM) when the normality (Gaussian) assumption of both the error term and the excess return on an asset holds, and also when their normality assumption is violated or failed due to outliers or excessive skewness and excessive kurtosis. The student-t distribution was used as an alternative distribution to capture these anomalies. The monthly All-share Index (ASI) of 12 crucial Market Portfolios / Sectors derived from Nigeria Stock Exchange (NSE) were subjected to both the Gaussian error innovation and Student-t error innovation in this study. However, it was noted that estimates of portfolios’ beta-risk and its standard error for Gaussian and student-t were approximately the same when the sector follows a normal distribution while the standard errors of portfolio beta-risk estimates will be smaller under student-t innovation than that of Gaussian innovation when the sector does not follow normal distribution due to these anomalies. Furthermore, it was discovered that building & construction, manufacturing, quarry & mining, communication, transportation, education and utilities sectors have been having lower volatility, that is, in boosting the economy over the last 15 years.},
 year = {2017}
}

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TY  - JOUR
T1  - A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions
AU  - Ezekiel Oseni
AU  - Razak Olawale Olanrewaju
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfbr.20170303.12
DO  - 10.11648/j.ijfbr.20170303.12
T2  - International Journal of Finance and Banking Research
JF  - International Journal of Finance and Banking Research
JO  - International Journal of Finance and Banking Research
SP  - 44
EP  - 52
PB  - Science Publishing Group
SN  - 2472-2278
UR  - https://doi.org/10.11648/j.ijfbr.20170303.12
AB  - This study describes the approach for estimating the beta-risk of the Capital Asset Price Model (CAPM) when the normality (Gaussian) assumption of both the error term and the excess return on an asset holds, and also when their normality assumption is violated or failed due to outliers or excessive skewness and excessive kurtosis. The student-t distribution was used as an alternative distribution to capture these anomalies. The monthly All-share Index (ASI) of 12 crucial Market Portfolios / Sectors derived from Nigeria Stock Exchange (NSE) were subjected to both the Gaussian error innovation and Student-t error innovation in this study. However, it was noted that estimates of portfolios’ beta-risk and its standard error for Gaussian and student-t were approximately the same when the sector follows a normal distribution while the standard errors of portfolio beta-risk estimates will be smaller under student-t innovation than that of Gaussian innovation when the sector does not follow normal distribution due to these anomalies. Furthermore, it was discovered that building & construction, manufacturing, quarry & mining, communication, transportation, education and utilities sectors have been having lower volatility, that is, in boosting the economy over the last 15 years.
VL  - 3
IS  - 3
ER  -

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Author Information

Ezekiel Oseni

Department of Banking and Finance, Faculty of Business Administration, University of Lagos, Lagos, Nigeria
Razak Olawale Olanrewaju

Department of Statistics, Faculty of Science, University of Ibadan, Ibadan, Nigeria

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APA Style

Ezekiel Oseni, Razak Olawale Olanrewaju. (2017). A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. International Journal of Finance and Banking Research, 3(3), 44-52. https://doi.org/10.11648/j.ijfbr.20170303.12

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ACS Style

Ezekiel Oseni; Razak Olawale Olanrewaju. A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. Int. J. Finance Bank. Res. 2017, 3(3), 44-52. doi: 10.11648/j.ijfbr.20170303.12

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AMA Style

Ezekiel Oseni, Razak Olawale Olanrewaju. A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions. Int J Finance Bank Res. 2017;3(3):44-52. doi: 10.11648/j.ijfbr.20170303.12

Copy | Download

@article{10.11648/j.ijfbr.20170303.12,
  author = {Ezekiel Oseni and Razak Olawale Olanrewaju},
  title = {A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions},
  journal = {International Journal of Finance and Banking Research},
  volume = {3},
  number = {3},
  pages = {44-52},
  doi = {10.11648/j.ijfbr.20170303.12},
  url = {https://doi.org/10.11648/j.ijfbr.20170303.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijfbr.20170303.12},
  abstract = {This study describes the approach for estimating the beta-risk of the Capital Asset Price Model (CAPM) when the normality (Gaussian) assumption of both the error term and the excess return on an asset holds, and also when their normality assumption is violated or failed due to outliers or excessive skewness and excessive kurtosis. The student-t distribution was used as an alternative distribution to capture these anomalies. The monthly All-share Index (ASI) of 12 crucial Market Portfolios / Sectors derived from Nigeria Stock Exchange (NSE) were subjected to both the Gaussian error innovation and Student-t error innovation in this study. However, it was noted that estimates of portfolios’ beta-risk and its standard error for Gaussian and student-t were approximately the same when the sector follows a normal distribution while the standard errors of portfolio beta-risk estimates will be smaller under student-t innovation than that of Gaussian innovation when the sector does not follow normal distribution due to these anomalies. Furthermore, it was discovered that building & construction, manufacturing, quarry & mining, communication, transportation, education and utilities sectors have been having lower volatility, that is, in boosting the economy over the last 15 years.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - A Capital Asset Pricing Model’s (CAPM’s) Beta Estimation in the Presence of Normality and Non-normality Assumptions
AU  - Ezekiel Oseni
AU  - Razak Olawale Olanrewaju
Y1  - 2017/06/16
PY  - 2017
N1  - https://doi.org/10.11648/j.ijfbr.20170303.12
DO  - 10.11648/j.ijfbr.20170303.12
T2  - International Journal of Finance and Banking Research
JF  - International Journal of Finance and Banking Research
JO  - International Journal of Finance and Banking Research
SP  - 44
EP  - 52
PB  - Science Publishing Group
SN  - 2472-2278
UR  - https://doi.org/10.11648/j.ijfbr.20170303.12
AB  - This study describes the approach for estimating the beta-risk of the Capital Asset Price Model (CAPM) when the normality (Gaussian) assumption of both the error term and the excess return on an asset holds, and also when their normality assumption is violated or failed due to outliers or excessive skewness and excessive kurtosis. The student-t distribution was used as an alternative distribution to capture these anomalies. The monthly All-share Index (ASI) of 12 crucial Market Portfolios / Sectors derived from Nigeria Stock Exchange (NSE) were subjected to both the Gaussian error innovation and Student-t error innovation in this study. However, it was noted that estimates of portfolios’ beta-risk and its standard error for Gaussian and student-t were approximately the same when the sector follows a normal distribution while the standard errors of portfolio beta-risk estimates will be smaller under student-t innovation than that of Gaussian innovation when the sector does not follow normal distribution due to these anomalies. Furthermore, it was discovered that building & construction, manufacturing, quarry & mining, communication, transportation, education and utilities sectors have been having lower volatility, that is, in boosting the economy over the last 15 years.
VL  - 3
IS  - 3
ER  -

Copy | Download