Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange

Abonongo John; Anuwoje Ida Logubayom; Ackora-Prah J.

doi:doi:10.11648/j.ijafrm.20170201.14

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Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange

Abonongo John, Anuwoje Ida Logubayom, Ackora-Prah J.

Published in International Journal of Accounting, Finance and Risk Management (Volume 2, Issue 1)

Received: 11 September 2016 Accepted: 25 November 2016 Published: 13 February 2017

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Abstract

Analyzing risk has been a principal concern of actuarial and insurance professionals which plays a fundamental role in the theory of portfolio selection where the prime objective is to find a portfolio that maximizes expected return while reducing risk. Portfolio optimization has been applied to asset management and in building strategic asset allocation. The purpose of this paper is to construct optimal and efficient portfolios using the matrix approach. This paper used secondary data on 13 stocks (ETI, GCB, GOIL, TOTAL, FML, GGBL, CLYD, EGL, PZC, UNIL, TLW, AGA and BOPP) from the Ghana Stock Exchange (GSE) database comprising the monthly closing prices from the period 02/01/2004 to 16/01/2015. The results revealed that, all the portfolios were optimal and that portfolios 1, 2, 4, 5, 6, 9, 10, 11 and 12 with expected return 2.523, 2.593, 2.827, 3.642, 2.405, 2.812, 5.229, 3.559 and 5.928 respectively were efficient portfolios whereas portfolios 3, 7 and 8 with expected return 0.377, 0.699 and 0.152 respectively were inefficient portfolios with reference to the expected return of the global minimum variance portfolio (2.360). GGBL was seen as the stock with the highest allocation of wealth in most of the portfolios. Six out of the 12 portfolios had CLYD exhibiting the least asset allocation.

Published in	International Journal of Accounting, Finance and Risk Management (Volume 2, Issue 1)
DOI	10.11648/j.ijafrm.20170201.14
Page(s)	21-30
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

Portfolio Optimization, Efficient Frontier, Mean-Variance, Matrix Approach

References

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[2]	Ceria, S. and Stubbs, R. A (2006). Incorporating estimation errors into portfolio selection: Robust portfolio construction. Journal of Asset Management 7(2): 109-127.
[3]	Costa, O. L. V. and Paiva, A. C (2002). Robust Portfolio Selection Using Linear-matrix Inequality. Journal of Economic Dynamics and Control 26: 889-909.
[4]	Drake, P. P and Fabozzi, F. J (2010). The Basics of Finance: An Introduction to Financial Markets, Business Finance and Portfolio Management. John Wiley and Sons, New Jersy.
[5]	Frantz, P. and Payne, R. (2009). Corporate finance. Chapter 2. London: University of London Press.
[6]	Cornuejols, G. and Tutuncu, R.(2007): Optimization methods in Finance. Cambridge University Press, Cambridge.
[7]	Goldfarb, D. and Lyenga, r G. (2003): Robust portfolio selection problems. Math. Opr. Res. 28:1-38.
[8]	Jagannathan, R. and Ma, T. (2003). “Risk Reduction in Large Portfolios: Why Imposing the Wrong Constraints Helps”. Journal of Finance 58: 1651-1684.
[9]	Manuel Tarrazo (2013). Portfolio Optimization with Correlation Matrix: How, Why, and Why Not. Journal of Finance and Investment Analysis 2 (3): 17-34
[10]	Markowitz, H. M (1952). Portfolio Selection. Journal of finance 7: 77-91
[11]	Markowitz, H. M (1959). Portfolio selection Efficient Diversification of Investments, Wiley, New York.
[12]	Merton, R. C. (1980). On Estimation of Expected Return on the Market: “An Exploratory Investigation”. Journal of Financial Economics 8: 323-361.
[13]	Mulvey, J. and Erkan H. G (2003). Decentralized Risk Management for Global P/C Insurance Companies. Working paper. In: Applications of stochastic programming. Eds:Wallace S. W., Ziemba W. T. MPS-SLAM Series on optimization, Philadephia, PA, 503-530.
[14]	Myles E. M (2013). A Simplified Perspective ofthe Markowitz Portfolio Theory. Global Journal of Business Research 7 (1): 59-70
[15]	Schneeweis, T., Crowder, G., Kazemi, H., (2010). The new science of asset allocation. Risk management in a multi-asset world. Hoboken, NJ: Wiley & Sons.
[16]	Tutuncu, R. H. and Koeing M.: Robust asset allocation. Annal of Operations Research 132: 157-187.

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APA Style

Abonongo John, Anuwoje Ida Logubayom, Ackora-Prah J. (2017). Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. International Journal of Accounting, Finance and Risk Management, 2(1), 21-30. https://doi.org/10.11648/j.ijafrm.20170201.14

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ACS Style

Abonongo John; Anuwoje Ida Logubayom; Ackora-Prah J. Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. Int. J. Account. Finance Risk Manag. 2017, 2(1), 21-30. doi: 10.11648/j.ijafrm.20170201.14

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AMA Style

Abonongo John, Anuwoje Ida Logubayom, Ackora-Prah J. Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. Int J Account Finance Risk Manag. 2017;2(1):21-30. doi: 10.11648/j.ijafrm.20170201.14

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@article{10.11648/j.ijafrm.20170201.14,
  author = {Abonongo John and Anuwoje Ida Logubayom and Ackora-Prah J.},
  title = {Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange},
  journal = {International Journal of Accounting, Finance and Risk Management},
  volume = {2},
  number = {1},
  pages = {21-30},
  doi = {10.11648/j.ijafrm.20170201.14},
  url = {https://doi.org/10.11648/j.ijafrm.20170201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijafrm.20170201.14},
  abstract = {Analyzing risk has been a principal concern of actuarial and insurance professionals which plays a fundamental role in the theory of portfolio selection where the prime objective is to find a portfolio that maximizes expected return while reducing risk. Portfolio optimization has been applied to asset management and in building strategic asset allocation. The purpose of this paper is to construct optimal and efficient portfolios using the matrix approach. This paper used secondary data on 13 stocks (ETI, GCB, GOIL, TOTAL, FML, GGBL, CLYD, EGL, PZC, UNIL, TLW, AGA and BOPP) from the Ghana Stock Exchange (GSE) database comprising the monthly closing prices from the period 02/01/2004 to 16/01/2015. The results revealed that, all the portfolios were optimal and that portfolios 1, 2, 4, 5, 6, 9, 10, 11 and 12 with expected return 2.523, 2.593, 2.827, 3.642, 2.405, 2.812, 5.229, 3.559 and 5.928 respectively were efficient portfolios whereas portfolios 3, 7 and 8 with expected return 0.377, 0.699 and 0.152 respectively were inefficient portfolios with reference to the expected return of the global minimum variance portfolio (2.360). GGBL was seen as the stock with the highest allocation of wealth in most of the portfolios. Six out of the 12 portfolios had CLYD exhibiting the least asset allocation.},
 year = {2017}
}

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TY  - JOUR
T1  - Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange
AU  - Abonongo John
AU  - Anuwoje Ida Logubayom
AU  - Ackora-Prah J.
Y1  - 2017/02/13
PY  - 2017
N1  - https://doi.org/10.11648/j.ijafrm.20170201.14
DO  - 10.11648/j.ijafrm.20170201.14
T2  - International Journal of Accounting, Finance and Risk Management
JF  - International Journal of Accounting, Finance and Risk Management
JO  - International Journal of Accounting, Finance and Risk Management
SP  - 21
EP  - 30
PB  - Science Publishing Group
SN  - 2578-9376
UR  - https://doi.org/10.11648/j.ijafrm.20170201.14
AB  - Analyzing risk has been a principal concern of actuarial and insurance professionals which plays a fundamental role in the theory of portfolio selection where the prime objective is to find a portfolio that maximizes expected return while reducing risk. Portfolio optimization has been applied to asset management and in building strategic asset allocation. The purpose of this paper is to construct optimal and efficient portfolios using the matrix approach. This paper used secondary data on 13 stocks (ETI, GCB, GOIL, TOTAL, FML, GGBL, CLYD, EGL, PZC, UNIL, TLW, AGA and BOPP) from the Ghana Stock Exchange (GSE) database comprising the monthly closing prices from the period 02/01/2004 to 16/01/2015. The results revealed that, all the portfolios were optimal and that portfolios 1, 2, 4, 5, 6, 9, 10, 11 and 12 with expected return 2.523, 2.593, 2.827, 3.642, 2.405, 2.812, 5.229, 3.559 and 5.928 respectively were efficient portfolios whereas portfolios 3, 7 and 8 with expected return 0.377, 0.699 and 0.152 respectively were inefficient portfolios with reference to the expected return of the global minimum variance portfolio (2.360). GGBL was seen as the stock with the highest allocation of wealth in most of the portfolios. Six out of the 12 portfolios had CLYD exhibiting the least asset allocation.
VL  - 2
IS  - 1
ER  -

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Author Information

Abonongo John

College of Science, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana
Anuwoje Ida Logubayom

Faculty of Mathematical Sciences, Department of Statistics, University for Development Studies, Navrongo, Ghana
Ackora-Prah J.

College of Science, Department of Mathematics, Kwame Nkrumah University of Science and Technology, Kumasi, Ghana

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APA Style

Abonongo John, Anuwoje Ida Logubayom, Ackora-Prah J. (2017). Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. International Journal of Accounting, Finance and Risk Management, 2(1), 21-30. https://doi.org/10.11648/j.ijafrm.20170201.14

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ACS Style

Abonongo John; Anuwoje Ida Logubayom; Ackora-Prah J. Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. Int. J. Account. Finance Risk Manag. 2017, 2(1), 21-30. doi: 10.11648/j.ijafrm.20170201.14

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AMA Style

Abonongo John, Anuwoje Ida Logubayom, Ackora-Prah J. Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange. Int J Account Finance Risk Manag. 2017;2(1):21-30. doi: 10.11648/j.ijafrm.20170201.14

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@article{10.11648/j.ijafrm.20170201.14,
  author = {Abonongo John and Anuwoje Ida Logubayom and Ackora-Prah J.},
  title = {Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange},
  journal = {International Journal of Accounting, Finance and Risk Management},
  volume = {2},
  number = {1},
  pages = {21-30},
  doi = {10.11648/j.ijafrm.20170201.14},
  url = {https://doi.org/10.11648/j.ijafrm.20170201.14},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijafrm.20170201.14},
  abstract = {Analyzing risk has been a principal concern of actuarial and insurance professionals which plays a fundamental role in the theory of portfolio selection where the prime objective is to find a portfolio that maximizes expected return while reducing risk. Portfolio optimization has been applied to asset management and in building strategic asset allocation. The purpose of this paper is to construct optimal and efficient portfolios using the matrix approach. This paper used secondary data on 13 stocks (ETI, GCB, GOIL, TOTAL, FML, GGBL, CLYD, EGL, PZC, UNIL, TLW, AGA and BOPP) from the Ghana Stock Exchange (GSE) database comprising the monthly closing prices from the period 02/01/2004 to 16/01/2015. The results revealed that, all the portfolios were optimal and that portfolios 1, 2, 4, 5, 6, 9, 10, 11 and 12 with expected return 2.523, 2.593, 2.827, 3.642, 2.405, 2.812, 5.229, 3.559 and 5.928 respectively were efficient portfolios whereas portfolios 3, 7 and 8 with expected return 0.377, 0.699 and 0.152 respectively were inefficient portfolios with reference to the expected return of the global minimum variance portfolio (2.360). GGBL was seen as the stock with the highest allocation of wealth in most of the portfolios. Six out of the 12 portfolios had CLYD exhibiting the least asset allocation.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Portfolio Optimization Using Matrix Approach: A Case of Some Stocks on the Ghana Stock Exchange
AU  - Abonongo John
AU  - Anuwoje Ida Logubayom
AU  - Ackora-Prah J.
Y1  - 2017/02/13
PY  - 2017
N1  - https://doi.org/10.11648/j.ijafrm.20170201.14
DO  - 10.11648/j.ijafrm.20170201.14
T2  - International Journal of Accounting, Finance and Risk Management
JF  - International Journal of Accounting, Finance and Risk Management
JO  - International Journal of Accounting, Finance and Risk Management
SP  - 21
EP  - 30
PB  - Science Publishing Group
SN  - 2578-9376
UR  - https://doi.org/10.11648/j.ijafrm.20170201.14
AB  - Analyzing risk has been a principal concern of actuarial and insurance professionals which plays a fundamental role in the theory of portfolio selection where the prime objective is to find a portfolio that maximizes expected return while reducing risk. Portfolio optimization has been applied to asset management and in building strategic asset allocation. The purpose of this paper is to construct optimal and efficient portfolios using the matrix approach. This paper used secondary data on 13 stocks (ETI, GCB, GOIL, TOTAL, FML, GGBL, CLYD, EGL, PZC, UNIL, TLW, AGA and BOPP) from the Ghana Stock Exchange (GSE) database comprising the monthly closing prices from the period 02/01/2004 to 16/01/2015. The results revealed that, all the portfolios were optimal and that portfolios 1, 2, 4, 5, 6, 9, 10, 11 and 12 with expected return 2.523, 2.593, 2.827, 3.642, 2.405, 2.812, 5.229, 3.559 and 5.928 respectively were efficient portfolios whereas portfolios 3, 7 and 8 with expected return 0.377, 0.699 and 0.152 respectively were inefficient portfolios with reference to the expected return of the global minimum variance portfolio (2.360). GGBL was seen as the stock with the highest allocation of wealth in most of the portfolios. Six out of the 12 portfolios had CLYD exhibiting the least asset allocation.
VL  - 2
IS  - 1
ER  -

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