Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)

Eric Kwame Austro Gozah; Eric Neebo Wiah; Albert Buabeng; Paul Yaw Addai Yeboah

doi:doi:10.11648/j.ajmcm.20200503.11

| Peer-Reviewed

Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)

Eric Kwame Austro Gozah, Eric Neebo Wiah, Albert Buabeng, Paul Yaw Addai Yeboah

Published in American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)

Received: 10 June 2020 Accepted: 23 June 2020 Published: 6 July 2020

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

The study was conducted to identify the performing stocks as well as examine the portfolio optimization with associated Value at Risk (VaR) for some selected stocks on the Ghana Stock Exchange (GSE). A historical data of 15 companies categorized into Financial Stock Index (FSI) and Composite Index (CI) from 2000 to 2017 were obtained from Bank of Ghana (BoG), Ghana Stock Exchange (GSE) and Gold Coast Security (GCS). From the study, ETI, HFC, SIC, TOTAL, FML, UNIL and GOIL stocks were identified to be over performing on the Ghana Stock Exchange. Also, CAL, EBG, ALW, AYRTN, GOIL were identified as aggressive stocks; GCB, SCB, TOTAL, GGBL as defensive stocks; and ETI, HFC, SIC, FML, PZC, UNIL as inversely moving towards the market return. The optimal portfolio asset allocation, for the minimum VaR portfolio showed a marginal diversification in other stocks in the cases of FSI, but greater portion was invested in HFC. However, in the case of CI displayed no indication of diversification in the portfolio as 67.30% of investors invested in AYRTN and only 32.70% in the remaining securities. The study then proceeded to find the optimal portfolio with risk-free asset for both indexes. It was recommended that further study should extend the approaches used by considering Conditional Value at Risk (CVaR) as the VaR measure does not give any information about potential losses in the worst cases.

Published in	American Journal of Mathematical and Computer Modelling (Volume 5, Issue 3)
DOI	10.11648/j.ajmcm.20200503.11
Page(s)	61-69
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), 2020. Published by Science Publishing Group

Keywords

Stock, Financial Stock Index, Composite Index, VaR, Portfolio, Optimization

References

[1]	Anon. (2004), “Output, the Stock Market and Interest Rates”, Databank Brokerage Ltd., 9 pp.
[2]	Das, S., Markowitz, H., Scheid, J. and Statman, M. (2010), “Portfolio optimization with mental accounts”, Journal of Financial and Quantitative Analysis, Vol. 45, No. 2, pp. 311-334.
[3]	Degutis, A., & Novickytė, L. (2014), “The efficient market hypothesis: a critical review of literature and methodology”, Ekonomika, Vol. 93, No. 2, pp. 7-23.
[4]	Engels, M. (2004), Portfolio Optimisation: Beyond Markowitz, Conceptual and Practical Insights Leiden University, Netherlands, pp. 45-53.
[5]	Fabozzi, F. J. and Francis, J. C. (1979), “Mutual fund systematic risk for bull and bear markets: an empirical examination”, The Journal of Finance, Vol. 34, No. 5, pp. 1243-1250.
[6]	Frimpong, J. M. and Oteng-Abayie E. F. (2007), “Market Returns and weak-form efficiency: The case of the Ghana Stock Exchange”, Journal of Economics and Finance, Vol. 4, No. 3, pp. 88-96.
[7]	Jarque, C. M. and Bera, A. K. (1987), “A test for normality of observations and regression residuals”, International Statistical Review, Vol. 55, pp. 163-172.
[8]	Karadag, D. T. (2008), “Portfolio Risk Calculation and Stochastic Portfolio Optimisation by a Copula Based Approach”, Working Paper, Economics WPA, Bagazici University, 102 pp.
[9]	Konno, H. and Yamazaki, H. (1991), “Mean-absolute deviation portfolio optimization model and its applications to Tokyo stock market”, Management science, Vol. 37, No. 5, pp. 519-531.
[10]	Magnus, F. J., Fosu, E. and Oteng-Abayie, J. (2006), “Modelling and Forecasting Volatility of Returns on Ghana Stock Exchange Using Garch Models”, Am. Journal of Applied Science, Vol. 3, No. 10, pp. 2042-2048.
[11]	Markowitz, H. M. (1952), “Portfolio Selection”, The Journal of Finance, Vol. 7, No. 1, pp. 77-91.
[12]	Mensah, M., Awunyo-Vitor, E. and El Wilson, S. (2012), “Challenges and Prospects of the Ghana Stock Exchange”, Developing Country Studies, Vol 2, No. 10, pp. 226-250.
[13]	Perold, A. F. (1984), “Large-scale portfolio optimization”, Management science, Vol. 30, No. 10, pp. 1143-1160.
[14]	Quismorio, A. B. (2010), “The tail distribution of the Philippines stock price index”, Up College of Business Administration, Discussion Papers, DP No. 1003, pp. 87-95.
[15]	Sharpe, W. (1966), “Mutual Fund Performance”, The Journal of Business, Vol. 39, No. 1, pp. 119-138.
[16]	Wiah, E. N., Odoi, B. and Antwi, K. O. (2018), “Asset Portfolio Optimisation of Some Selected Equities Using Geometric Mean and Semi Variance”, Ghana Journal of Technology, Vol. 2, No. 2, pp. 24–33.

Cite This Article

Plain Text BibTeX RIS

APA Style

Eric Kwame Austro Gozah, Eric Neebo Wiah, Albert Buabeng, Paul Yaw Addai Yeboah. (2020). Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). American Journal of Mathematical and Computer Modelling, 5(3), 61-69. https://doi.org/10.11648/j.ajmcm.20200503.11

Copy | Download

ACS Style

Eric Kwame Austro Gozah; Eric Neebo Wiah; Albert Buabeng; Paul Yaw Addai Yeboah. Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). Am. J. Math. Comput. Model. 2020, 5(3), 61-69. doi: 10.11648/j.ajmcm.20200503.11

Copy | Download

AMA Style

Eric Kwame Austro Gozah, Eric Neebo Wiah, Albert Buabeng, Paul Yaw Addai Yeboah. Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). Am J Math Comput Model. 2020;5(3):61-69. doi: 10.11648/j.ajmcm.20200503.11

Copy | Download

@article{10.11648/j.ajmcm.20200503.11,
  author = {Eric Kwame Austro Gozah and Eric Neebo Wiah and Albert Buabeng and Paul Yaw Addai Yeboah},
  title = {Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {3},
  pages = {61-69},
  doi = {10.11648/j.ajmcm.20200503.11},
  url = {https://doi.org/10.11648/j.ajmcm.20200503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200503.11},
  abstract = {The study was conducted to identify the performing stocks as well as examine the portfolio optimization with associated Value at Risk (VaR) for some selected stocks on the Ghana Stock Exchange (GSE). A historical data of 15 companies categorized into Financial Stock Index (FSI) and Composite Index (CI) from 2000 to 2017 were obtained from Bank of Ghana (BoG), Ghana Stock Exchange (GSE) and Gold Coast Security (GCS). From the study, ETI, HFC, SIC, TOTAL, FML, UNIL and GOIL stocks were identified to be over performing on the Ghana Stock Exchange. Also, CAL, EBG, ALW, AYRTN, GOIL were identified as aggressive stocks; GCB, SCB, TOTAL, GGBL as defensive stocks; and ETI, HFC, SIC, FML, PZC, UNIL as inversely moving towards the market return. The optimal portfolio asset allocation, for the minimum VaR portfolio showed a marginal diversification in other stocks in the cases of FSI, but greater portion was invested in HFC. However, in the case of CI displayed no indication of diversification in the portfolio as 67.30% of investors invested in AYRTN and only 32.70% in the remaining securities. The study then proceeded to find the optimal portfolio with risk-free asset for both indexes. It was recommended that further study should extend the approaches used by considering Conditional Value at Risk (CVaR) as the VaR measure does not give any information about potential losses in the worst cases.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)
AU  - Eric Kwame Austro Gozah
AU  - Eric Neebo Wiah
AU  - Albert Buabeng
AU  - Paul Yaw Addai Yeboah
Y1  - 2020/07/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200503.11
DO  - 10.11648/j.ajmcm.20200503.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 61
EP  - 69
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200503.11
AB  - The study was conducted to identify the performing stocks as well as examine the portfolio optimization with associated Value at Risk (VaR) for some selected stocks on the Ghana Stock Exchange (GSE). A historical data of 15 companies categorized into Financial Stock Index (FSI) and Composite Index (CI) from 2000 to 2017 were obtained from Bank of Ghana (BoG), Ghana Stock Exchange (GSE) and Gold Coast Security (GCS). From the study, ETI, HFC, SIC, TOTAL, FML, UNIL and GOIL stocks were identified to be over performing on the Ghana Stock Exchange. Also, CAL, EBG, ALW, AYRTN, GOIL were identified as aggressive stocks; GCB, SCB, TOTAL, GGBL as defensive stocks; and ETI, HFC, SIC, FML, PZC, UNIL as inversely moving towards the market return. The optimal portfolio asset allocation, for the minimum VaR portfolio showed a marginal diversification in other stocks in the cases of FSI, but greater portion was invested in HFC. However, in the case of CI displayed no indication of diversification in the portfolio as 67.30% of investors invested in AYRTN and only 32.70% in the remaining securities. The study then proceeded to find the optimal portfolio with risk-free asset for both indexes. It was recommended that further study should extend the approaches used by considering Conditional Value at Risk (CVaR) as the VaR measure does not give any information about potential losses in the worst cases.
VL  - 5
IS  - 3
ER  -

Copy | Download

Author Information

Eric Kwame Austro Gozah

Mathematics Department, Dambai College of Education, Dambai, Ghana
Eric Neebo Wiah

Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana
Albert Buabeng

Department of Mathematical Sciences, Faculty of Engineering, University of Mines and Technology, Tarkwa, Ghana
Paul Yaw Addai Yeboah

Head, University Relations Office, University of Mines and Technology, Tarkwa, Ghana

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Eric Kwame Austro Gozah, Eric Neebo Wiah, Albert Buabeng, Paul Yaw Addai Yeboah. (2020). Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). American Journal of Mathematical and Computer Modelling, 5(3), 61-69. https://doi.org/10.11648/j.ajmcm.20200503.11

Copy | Download

ACS Style

Eric Kwame Austro Gozah; Eric Neebo Wiah; Albert Buabeng; Paul Yaw Addai Yeboah. Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). Am. J. Math. Comput. Model. 2020, 5(3), 61-69. doi: 10.11648/j.ajmcm.20200503.11

Copy | Download

AMA Style

Eric Kwame Austro Gozah, Eric Neebo Wiah, Albert Buabeng, Paul Yaw Addai Yeboah. Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR). Am J Math Comput Model. 2020;5(3):61-69. doi: 10.11648/j.ajmcm.20200503.11

Copy | Download

@article{10.11648/j.ajmcm.20200503.11,
  author = {Eric Kwame Austro Gozah and Eric Neebo Wiah and Albert Buabeng and Paul Yaw Addai Yeboah},
  title = {Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)},
  journal = {American Journal of Mathematical and Computer Modelling},
  volume = {5},
  number = {3},
  pages = {61-69},
  doi = {10.11648/j.ajmcm.20200503.11},
  url = {https://doi.org/10.11648/j.ajmcm.20200503.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20200503.11},
  abstract = {The study was conducted to identify the performing stocks as well as examine the portfolio optimization with associated Value at Risk (VaR) for some selected stocks on the Ghana Stock Exchange (GSE). A historical data of 15 companies categorized into Financial Stock Index (FSI) and Composite Index (CI) from 2000 to 2017 were obtained from Bank of Ghana (BoG), Ghana Stock Exchange (GSE) and Gold Coast Security (GCS). From the study, ETI, HFC, SIC, TOTAL, FML, UNIL and GOIL stocks were identified to be over performing on the Ghana Stock Exchange. Also, CAL, EBG, ALW, AYRTN, GOIL were identified as aggressive stocks; GCB, SCB, TOTAL, GGBL as defensive stocks; and ETI, HFC, SIC, FML, PZC, UNIL as inversely moving towards the market return. The optimal portfolio asset allocation, for the minimum VaR portfolio showed a marginal diversification in other stocks in the cases of FSI, but greater portion was invested in HFC. However, in the case of CI displayed no indication of diversification in the portfolio as 67.30% of investors invested in AYRTN and only 32.70% in the remaining securities. The study then proceeded to find the optimal portfolio with risk-free asset for both indexes. It was recommended that further study should extend the approaches used by considering Conditional Value at Risk (CVaR) as the VaR measure does not give any information about potential losses in the worst cases.},
 year = {2020}
}

Copy | Download

TY  - JOUR
T1  - Portfolio Optimization for Stock Market in Ghana Using Value-at-Risk (VaR)
AU  - Eric Kwame Austro Gozah
AU  - Eric Neebo Wiah
AU  - Albert Buabeng
AU  - Paul Yaw Addai Yeboah
Y1  - 2020/07/06
PY  - 2020
N1  - https://doi.org/10.11648/j.ajmcm.20200503.11
DO  - 10.11648/j.ajmcm.20200503.11
T2  - American Journal of Mathematical and Computer Modelling
JF  - American Journal of Mathematical and Computer Modelling
JO  - American Journal of Mathematical and Computer Modelling
SP  - 61
EP  - 69
PB  - Science Publishing Group
SN  - 2578-8280
UR  - https://doi.org/10.11648/j.ajmcm.20200503.11
AB  - The study was conducted to identify the performing stocks as well as examine the portfolio optimization with associated Value at Risk (VaR) for some selected stocks on the Ghana Stock Exchange (GSE). A historical data of 15 companies categorized into Financial Stock Index (FSI) and Composite Index (CI) from 2000 to 2017 were obtained from Bank of Ghana (BoG), Ghana Stock Exchange (GSE) and Gold Coast Security (GCS). From the study, ETI, HFC, SIC, TOTAL, FML, UNIL and GOIL stocks were identified to be over performing on the Ghana Stock Exchange. Also, CAL, EBG, ALW, AYRTN, GOIL were identified as aggressive stocks; GCB, SCB, TOTAL, GGBL as defensive stocks; and ETI, HFC, SIC, FML, PZC, UNIL as inversely moving towards the market return. The optimal portfolio asset allocation, for the minimum VaR portfolio showed a marginal diversification in other stocks in the cases of FSI, but greater portion was invested in HFC. However, in the case of CI displayed no indication of diversification in the portfolio as 67.30% of investors invested in AYRTN and only 32.70% in the remaining securities. The study then proceeded to find the optimal portfolio with risk-free asset for both indexes. It was recommended that further study should extend the approaches used by considering Conditional Value at Risk (CVaR) as the VaR measure does not give any information about potential losses in the worst cases.
VL  - 5
IS  - 3
ER  -

Copy | Download