Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio

Phares Kaboneka; Wilson Mahera Charles; Silas Mirau

doi:doi:10.11648/j.acm.20140305.13

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Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio

Phares Kaboneka, Wilson Mahera Charles, Silas Mirau

Published in Applied and Computational Mathematics (Volume 3, Issue 5)

Received: 19 August 2014 Accepted: 30 August 2014 Published: 20 September 2014

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Abstract

Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier. Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.

Published in	Applied and Computational Mathematics (Volume 3, Issue 5)
DOI	10.11648/j.acm.20140305.13
Page(s)	205-216
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), 2014. Published by Science Publishing Group

Keywords

Stocks, Diversification, DSE, Frontier, Covariance Matrix, Expected Return, Portfolio

References

[1]	Gary C, and Uri G, (2010), portfolio choice and risk attitudes: an experiment, Economic Inquiry (ISSN 0095-2583), Vol. 48, No. 1, January 2010, 133 – 146
[2]	Robert J. Barro (1990), the review of financial studies, department of Economics, Harvard University, Littauer 120, Cambridge, MA 02138
[3]	Darrel, D. and singleton K, (2003) Credit Risk: Pricing Measurement and Management, Sci.Aging knowl.Environ 2003(44), or 23
[4]	Edwin J. Elton and Martin J. Gruber, "Modern portfolio theory, 1950 to date", Journal of Banking & Finance 21 (1997) 1743-1759
[5]	Markowitz, H. 1952, ‘Portfolio Selection,’ Journal of Finance, 7, 77-99. Efficient frontiers using estimated parameters. Ann. Operations
[6]	Sharpe,W, F, (1964) Capital asset prices: A theory of market equilibrium under conditions of risk." Journal of Finance 19 (3): 425-442.
[7]	Craig W. Hoden (2008), Excel modelling and Estimation in Investment (third Edition), Prentice Hall inc, upper saddle River. New Jersey 07458
[8]	Ziemba, W. T., (1993), the effect of errors in means, variances and covariance on optimal portfolio choice, J. Portfolio Management, (Winter) 6-11
[9]	Tobin, James. (1958a) Liquidity Preference as Behavior towards Risk. Review of Economic Studies 25 (2): 65–86
[10]	Broadie, M, (1993), Computing efficient frontiers using estimated parameters, Ann, Operations Research 45 (1): 21-58
[11]	Konno, H., (1988), Portfolio Optimization using LI Risk Function IHSS Report 88-9, Inst. of Human and Social Sciences, Tokyo Institute of Technology.
[12]	Puelz, A.V, (2002) A Stochastic Convergence Model for Portfolio Selection." Operations Research 50 (3): 462-476.
[13]	Konno, H, Yamazaki, H, (1991), Mean-Absolute Deviation Portfolio Optimization Model and Its Applications to Tokyo Stock Market." Management Science 37 (5): 519-531.
[14]	F. Mayanja, S. Mataramvura and W. Charles, (2011), "A Mathematical Approach to a Stocks Portfolio Selection: The Case of Uganda Securities Exchange (USE)," Journal of Mathematical Finance, Vol. 3 No. 4, 2013, pp. 487-501. doi: 10.4236/jmf.2013.34051.
[15]	Nitis Mukhopadyyay, (2000), Probability and Statistics Inference. University of Connecticut Storrs, Connecticut. Marcel Dekker, Inc.
[16]	Vern Sumnicht, (2008) Practical Applications of Post-Modern Portfolio Theory.
[17]	Loeper B. David, (2000) Modern Portfolio Reality (MPR).The Failures of Modern Portfolio Theory", Finance ware, Inc.

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Phares Kaboneka, Wilson Mahera Charles, Silas Mirau. (2014). Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Applied and Computational Mathematics, 3(5), 205-216. https://doi.org/10.11648/j.acm.20140305.13

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Phares Kaboneka; Wilson Mahera Charles; Silas Mirau. Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Appl. Comput. Math. 2014, 3(5), 205-216. doi: 10.11648/j.acm.20140305.13

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AMA Style

Phares Kaboneka, Wilson Mahera Charles, Silas Mirau. Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Appl Comput Math. 2014;3(5):205-216. doi: 10.11648/j.acm.20140305.13

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@article{10.11648/j.acm.20140305.13,
  author = {Phares Kaboneka and Wilson Mahera Charles and Silas Mirau},
  title = {Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {205-216},
  doi = {10.11648/j.acm.20140305.13},
  url = {https://doi.org/10.11648/j.acm.20140305.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.13},
  abstract = {Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier.  Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.},
 year = {2014}
}

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TY  - JOUR
T1  - Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio
AU  - Phares Kaboneka
AU  - Wilson Mahera Charles
AU  - Silas Mirau
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.13
DO  - 10.11648/j.acm.20140305.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 205
EP  - 216
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.13
AB  - Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier.  Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.
VL  - 3
IS  - 5
ER  -

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Author Information

Phares Kaboneka

Department of Applied Mathematics and Computational Science and Engineering, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania
Wilson Mahera Charles

Department of Applied Mathematics and Computational Science and Engineering, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania
Silas Mirau

Department of Applied Mathematics and Computational Science and Engineering, Nelson Mandela African Institution of Science and Technology, Arusha, Tanzania

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Plain Text BibTeX RIS

APA Style

Phares Kaboneka, Wilson Mahera Charles, Silas Mirau. (2014). Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Applied and Computational Mathematics, 3(5), 205-216. https://doi.org/10.11648/j.acm.20140305.13

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ACS Style

Phares Kaboneka; Wilson Mahera Charles; Silas Mirau. Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Appl. Comput. Math. 2014, 3(5), 205-216. doi: 10.11648/j.acm.20140305.13

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AMA Style

Phares Kaboneka, Wilson Mahera Charles, Silas Mirau. Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio. Appl Comput Math. 2014;3(5):205-216. doi: 10.11648/j.acm.20140305.13

Copy | Download

@article{10.11648/j.acm.20140305.13,
  author = {Phares Kaboneka and Wilson Mahera Charles and Silas Mirau},
  title = {Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio},
  journal = {Applied and Computational Mathematics},
  volume = {3},
  number = {5},
  pages = {205-216},
  doi = {10.11648/j.acm.20140305.13},
  url = {https://doi.org/10.11648/j.acm.20140305.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140305.13},
  abstract = {Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier.  Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.},
 year = {2014}
}

Copy | Download

TY  - JOUR
T1  - Analysis of the Effects of Diversification for Dar Es Salaam Stock Exchange Optimal Portfolio
AU  - Phares Kaboneka
AU  - Wilson Mahera Charles
AU  - Silas Mirau
Y1  - 2014/09/20
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140305.13
DO  - 10.11648/j.acm.20140305.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 205
EP  - 216
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140305.13
AB  - Dar es Salaam stock exchange (DSE) market is among the stock markets dealing with financial securities transactions and it operates under the brokerage system. Different individuals have little knowledge on how these stock markets operate and many of them fear to invest in stock business because they don’t have the base line of their decision especially on the risk bearings. This paper is based solely on DSE stocks data for the period of past nine years and it tries to give out the nature of return of the stocks, the effects on restrictions at the DSE stock environment to the stock returns and also it explores the effect of diversification on return and on risk (standard deviation). The study uses the classical Markowitz Modern Portfolio Theory (MPT) model in its analysis with little modification so as to meet with the DSE environment. Data from DSE was analysed by using the excel solver and its macros like the solver add – in. After the analysis it is observed that restrictions have an effect on the stock risk and return, where it reduce risk and increases return because the unconstrained frontier is greater than the constrained frontier.  Moreover it is found that for the diversification to have a significant effect the stocks have to be nearly or perfectly negatively correlated.
VL  - 3
IS  - 5
ER  -

Copy | Download