An Application of The Markowitz’s Mean-Variance Framework in Constructing Optimal Portfolios using the Johannesburg Securities Exchange Tradeable Indices
Abstract
The aim of this study was to assess the feasibility of constructing optimal portfolios using the Johannesburg Securities Exchange (JSE) tradable sector indices. Three indices were employed, namely Financials, Industrials and Resources and these were benchmarked against the JSE All Share Index for the period January 2007 to December 2017. The period was split into three, namely before the 2007-2009 global financial crises, during the global financial crises and after the global financial crises. The Markowitz’s mean-variance optimisation framework was employed for the construction of global mean variance portfolios. The results of this study demonstrated that it was feasible to construct mean-variance efficient portfolios using the tradable sector indices from the JSE. It was also established that, on the other hand, global mean variance portfolios constructed in this study, outperformed the benchmark index in a bullish market in terms of the risk-return combinations. On the other hand, in bear markets, the global mean variance portfolios were observed to perform better than the benchmark index in terms of risk. Further, the results of the study showed that portfolios constructed from the three tradable indices yielded diversification benefits despite their positive correlation with each other. The results of the study corroborate the findings by other scholars that the mean-variance optimisation framework is effective in the construction of optimal portfolios using the Johannesburg Securities Exchange. The study also demonstrated that Markowitz’s mean-variance framework could be applied by investors faced with a plethora of investment constraints and choices to construct efficient portfolios utilising the JSE tradable sector indices in order to realise returns commensurate with their risk preferences.
References
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Brouwer, P. 2015. A model for the optimisation of an individual investor’s portfolio of exchange traded funds. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University.
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Chen, W.P., Chung, H., Ho, K.Y. & Hsu, T.L. 2010. Portfolio optimization models and mean–variance spanning tests. In Handbook of Quantitative Finance and Risk Management. Springer US. 165-184.
Clarke, R. G., De Silva, H., & Thorley, S. 2006. Minimum-variance portfolios in the US equity market. The Journal of Portfolio Management.33 (1):10-24.
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Du Plessis, C.D., 2014. Portfolio Optimisation for the Industrial Development Corporation (IDC). Unpublished doctoral dissertation. Johannesburg: University of the Witwatersrand.
Du Plessis, A.J. & Ward, M. 2009. A note on applying the Markowitz portfolio selection model as a passive investment strategy on the JSE. Investment Analysts Journal. (69): 39-45.
Engels, M. 2004. Portfolio optimization beyond Markowitz. Unpublished master’s thesis. Leiden: University of Leiden.
Fabozzi, F.J., Gupta, F. & Markowitz, H.M. 2002. The legacy of modern portfolio theory. The Journal of Investing, 11(3):7-22.
Fragkiskos, A., 2014. What is Portfolio Diversification? Alternative Investment Analyst Review. n.p.
Garaba, M., 2005. The current role of modern portfolio theory in asset management practice in South Africa. Unpublished doctoral dissertation. Grahamstown: Rhodes University.
Giri, L.K. 2016. Optimum portfolio construction using Markowitz model. Splint International Journal of Professionals, 3(12):83-94.
Grundy, K. & Malkiel, B. G. (1996). Reports of beta's death have been greatly exaggerated. The Journal of Portfolio Management, 22(3):36-44.
Gupta, R. & Basu, P.K. 2008. Portfolio optimisation in the Indian Stock Market industry sector analysis. Delhi Business Review, 9(1):21-30.
Haugen, R.A. & Baker, N.L. 1991. The Efficient Market Inefficiency of capitalization-weighted Stock Portfolios. Journal of Portfolio Management, 17(3):35-40.
Hübner, G. 2005. The generalized Treynor ratio. Review of Finance, 9(3):415-435.
Jiang, J. 2013. Application of modern portfolio theory in the case of Thai Equity Market. International Journal of Empirical Finance, 1(2):33-42.
Joshipura, M. & Joshipura, N. 2015. Risk anomaly: A review of literature. Asian Journal of Finance & Accounting, 7(2):138-151.
Lintner, J. 1965. The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1):13-37.
Lo, A.W., Mamaysky, H. & Wang, J. 2000. Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. The Journal of Finance, 55(4):1705-1765.
Lombard, C.F. 2015. Decision-making under uncertainty: Markowitz optimisation as a passive strategy on the JSE. Unpublished doctoral dissertation. Potchefstroom: North-West University.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
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Markowitz, H.M. 1999. The early history of portfolio theory: 1600–1960. Financial Analysts Journal, 55(4):5-16.
Markowitz, H.M., Hebner, M.T. & Brunson, M.E., 2009. Does portfolio theory work during financial crises? Working paper n.p.
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Mbithi, J.A., Kisaka, S.E. & Kitur, E. 2015. Determining the optimal portfolio size on the Nairobi securities exchange. Research Journal of Finance and Accounting, 6(6):2222-2847.
Mossin, J. 1966. On a class of optimal stock depletion policies. Management Science, 13(1):120-130.
Oladele, O.S. & Bradfield, D. 2016. Low volatility sector-based portfolios: A South African case. ORiON, 32(1):55-78.
Olsen, T. 2014. A comparison of four different diversification strategies in the Norwegian market with portfolios consisting of stocks and bonds: A comparison of risk and return in portfolios of stocks and bonds in the Norwegian market based on equal weighting, 60/40, mean-variance, and risk parity. Unpublished master's thesis. Trondheim: Trondheim Business School.
Omisore, I., Yusuf, M. & Christopher, N. 2011. The modern portfolio theory as an investment decision tool. Journal of Accounting and Taxation, 4(2):19-28.
Paudel, R.B. & Koirala, S. 2006. Application of Markowitz and Sharpe Models in Nepalese Stock Market. Journal of Nepalese Business Studies, (3):18-35.
Popina, S. & Martyniuk, O. 2016. Some aspects of security portfolio optimization. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, (434 Quantitative Methods in Accounting and Finance), 434:159-165.
Ramanathan, K.V. & Jahnavi, K.N. 2014. Construction of optimal equity portfolio using the Sharpe index model with reference to banking and Information technology sectors In India from 2009-2013. International Journal of Business and Administration Research Review, 2(3):122-131.
Rocha, E.M.D.L. 2016. Security selection in post-modern portfolio theory: an application to the European stock market. Unpublished doctoral dissertation. Lisbon: Lisbon School of Economics and Management.
Roopanand, R. 2001. The mean variance efficiency on the JSE All Share Index (ALSI) and its implications for portfolio management. Unpublished master’s thesis. Durban: University of Natal.
Ross, S.A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(2):341-360.
Rutterford, J. and Sotiropoulos, D.P., 2016. Financial diversification before modern portfolio theory: UK financial advice documents in the late nineteenth and the beginning of the twentieth century. The European Journal of the History of Economic Thought, 23(6), pp.919-945.
Sharpe, W.F., 1963. A simplified model for portfolio analysis. Management science, 9(2), pp.277-293.
Sharpe, W.F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3):425-442.
Subrahmanyam, A. 2008. Behavioural finance: A review and synthesis. European Financial Management, 14(1):12-29.
Szczygielski, J.J. & Chipeta, C. 2015. Risk factors in returns of the South African stock market. Studies in Economics and Econometrics, 39(1):47-70.
Thirimanna, T.H.S.R., Tilakartane, C., Mahakalanda, I. & Pathirathne, L. 2013. Portfolio selection using cointegration and modern portfolio theory: An application to the Colombo Stock Exchange. Matematika, 29:195-202.
Treynor, J.L. 1961. “Market value, time, and risk.” Unpublished manuscript. “Rough Draft” dated 8/8/61: p95 – 209
Vukovic, A. & Bjerknes, L. 2017. Automated advice: A portfolio management perspective on robo-advisors. Unpublished masters dissertation. Trondheim: Norwegian University of Science and Technology.
Yahaya, A., Abubakar, A.H. & Garba, J. 2011. Statistical analysis on the advantages of portfolio diversification. International Journal of Pure and Applied Sciences and Technology 7(2):98-106.
Ahuja, A. 2015. Portfolio diversification in the Karachi Stock Exchange. Pakistan Journal of Engineering, Technology & Science, 1(1):37-44.
Ayodeji, O.A. & Ingram, L. 2015. Efficient portfolio optimisation using the conditional value at risk approach. Journal of Organisational Studies and Innovation, 2(2):39-65.
Baltes, N. & Dragoe, A.G.M. 2017. Rentability and risk in trading financial titles on the Romanian capital market. Theoretical and Applied Economics, 24. Special edition:57-64.
Bausys, M. 2009. The performance of minimum variance portfolios in the Baltic Equity Markets. Unpublished masters dissertation. Riga: Stockholm School of Economics
Bower, B. & Wentz, P. 2005. Portfolio optimization: MAD vs. Markowitz. Rose-Hulman Undergraduate. Mathematics Journal, 6(2,3):1-12.
Brouwer, P. 2015. A model for the optimisation of an individual investor’s portfolio of exchange traded funds. Unpublished doctoral dissertation. Stellenbosch: Stellenbosch University.
Brown, R., 2015. Analysis of investments & management of portfolios. 10th edition.
Cairns, P. 2016. How volatile is the JSE really? Moneyweb Retrieved from https://www.moneyweb.co.za/investing/volatile-jse-really/ [Accessed 21 October 2017].
Chen, W.P., Chung, H., Ho, K.Y. & Hsu, T.L. 2010. Portfolio optimization models and mean–variance spanning tests. In Handbook of Quantitative Finance and Risk Management. Springer US. 165-184.
Clarke, R. G., De Silva, H., & Thorley, S. 2006. Minimum-variance portfolios in the US equity market. The Journal of Portfolio Management.33 (1):10-24.
Contreras, O.E., Lizama, C. & Stein, R.A., 2016. The old ways are (sometimes) the best: The performance of simple mean-variance portfolio optimization in various markets. Investment Company Fact Book:1-25
Darko, S. 2012, Optimal portfolio using Markowitz. Unpublished master’s thesis. Ashanti: Kwame Nkrumah University of Science and Technology.
Du Plessis, C.D., 2014. Portfolio Optimisation for the Industrial Development Corporation (IDC). Unpublished doctoral dissertation. Johannesburg: University of the Witwatersrand.
Du Plessis, A.J. & Ward, M. 2009. A note on applying the Markowitz portfolio selection model as a passive investment strategy on the JSE. Investment Analysts Journal. (69): 39-45.
Engels, M. 2004. Portfolio optimization beyond Markowitz. Unpublished master’s thesis. Leiden: University of Leiden.
Fabozzi, F.J., Gupta, F. & Markowitz, H.M. 2002. The legacy of modern portfolio theory. The Journal of Investing, 11(3):7-22.
Fragkiskos, A., 2014. What is Portfolio Diversification? Alternative Investment Analyst Review. n.p.
Garaba, M., 2005. The current role of modern portfolio theory in asset management practice in South Africa. Unpublished doctoral dissertation. Grahamstown: Rhodes University.
Giri, L.K. 2016. Optimum portfolio construction using Markowitz model. Splint International Journal of Professionals, 3(12):83-94.
Grundy, K. & Malkiel, B. G. (1996). Reports of beta's death have been greatly exaggerated. The Journal of Portfolio Management, 22(3):36-44.
Gupta, R. & Basu, P.K. 2008. Portfolio optimisation in the Indian Stock Market industry sector analysis. Delhi Business Review, 9(1):21-30.
Haugen, R.A. & Baker, N.L. 1991. The Efficient Market Inefficiency of capitalization-weighted Stock Portfolios. Journal of Portfolio Management, 17(3):35-40.
Hübner, G. 2005. The generalized Treynor ratio. Review of Finance, 9(3):415-435.
Jiang, J. 2013. Application of modern portfolio theory in the case of Thai Equity Market. International Journal of Empirical Finance, 1(2):33-42.
Joshipura, M. & Joshipura, N. 2015. Risk anomaly: A review of literature. Asian Journal of Finance & Accounting, 7(2):138-151.
Lintner, J. 1965. The valuation of risky assets and the selection of risky investments in stock portfolios and capital budgets. Review of Economics and Statistics, 47(1):13-37.
Lo, A.W., Mamaysky, H. & Wang, J. 2000. Foundations of technical analysis: Computational algorithms, statistical inference, and empirical implementation. The Journal of Finance, 55(4):1705-1765.
Lombard, C.F. 2015. Decision-making under uncertainty: Markowitz optimisation as a passive strategy on the JSE. Unpublished doctoral dissertation. Potchefstroom: North-West University.
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77-91.
Markowitz, H. 1959. Portfolio Selection. Southern Economic Journal 32:263-74.
Markowitz, H.M. 1999. The early history of portfolio theory: 1600–1960. Financial Analysts Journal, 55(4):5-16.
Markowitz, H.M., Hebner, M.T. & Brunson, M.E., 2009. Does portfolio theory work during financial crises? Working paper n.p.
Mbithi, J.A., 2014. Determining the optimal portfolio size on the Nairobi securities exchange. Unpublished MBA project. Nairobi: University of Nairobi.
Mbithi, J.A., Kisaka, S.E. & Kitur, E. 2015. Determining the optimal portfolio size on the Nairobi securities exchange. Research Journal of Finance and Accounting, 6(6):2222-2847.
Mossin, J. 1966. On a class of optimal stock depletion policies. Management Science, 13(1):120-130.
Oladele, O.S. & Bradfield, D. 2016. Low volatility sector-based portfolios: A South African case. ORiON, 32(1):55-78.
Olsen, T. 2014. A comparison of four different diversification strategies in the Norwegian market with portfolios consisting of stocks and bonds: A comparison of risk and return in portfolios of stocks and bonds in the Norwegian market based on equal weighting, 60/40, mean-variance, and risk parity. Unpublished master's thesis. Trondheim: Trondheim Business School.
Omisore, I., Yusuf, M. & Christopher, N. 2011. The modern portfolio theory as an investment decision tool. Journal of Accounting and Taxation, 4(2):19-28.
Paudel, R.B. & Koirala, S. 2006. Application of Markowitz and Sharpe Models in Nepalese Stock Market. Journal of Nepalese Business Studies, (3):18-35.
Popina, S. & Martyniuk, O. 2016. Some aspects of security portfolio optimization. Prace Naukowe Uniwersytetu Ekonomicznego we Wrocławiu, (434 Quantitative Methods in Accounting and Finance), 434:159-165.
Ramanathan, K.V. & Jahnavi, K.N. 2014. Construction of optimal equity portfolio using the Sharpe index model with reference to banking and Information technology sectors In India from 2009-2013. International Journal of Business and Administration Research Review, 2(3):122-131.
Rocha, E.M.D.L. 2016. Security selection in post-modern portfolio theory: an application to the European stock market. Unpublished doctoral dissertation. Lisbon: Lisbon School of Economics and Management.
Roopanand, R. 2001. The mean variance efficiency on the JSE All Share Index (ALSI) and its implications for portfolio management. Unpublished master’s thesis. Durban: University of Natal.
Ross, S.A. 1976. The arbitrage theory of capital asset pricing. Journal of Economic Theory, 13(2):341-360.
Rutterford, J. and Sotiropoulos, D.P., 2016. Financial diversification before modern portfolio theory: UK financial advice documents in the late nineteenth and the beginning of the twentieth century. The European Journal of the History of Economic Thought, 23(6), pp.919-945.
Sharpe, W.F., 1963. A simplified model for portfolio analysis. Management science, 9(2), pp.277-293.
Sharpe, W.F. 1964. Capital asset prices: A theory of market equilibrium under conditions of risk. The Journal of Finance, 19(3):425-442.
Subrahmanyam, A. 2008. Behavioural finance: A review and synthesis. European Financial Management, 14(1):12-29.
Szczygielski, J.J. & Chipeta, C. 2015. Risk factors in returns of the South African stock market. Studies in Economics and Econometrics, 39(1):47-70.
Thirimanna, T.H.S.R., Tilakartane, C., Mahakalanda, I. & Pathirathne, L. 2013. Portfolio selection using cointegration and modern portfolio theory: An application to the Colombo Stock Exchange. Matematika, 29:195-202.
Treynor, J.L. 1961. “Market value, time, and risk.” Unpublished manuscript. “Rough Draft” dated 8/8/61: p95 – 209
Vukovic, A. & Bjerknes, L. 2017. Automated advice: A portfolio management perspective on robo-advisors. Unpublished masters dissertation. Trondheim: Norwegian University of Science and Technology.
Yahaya, A., Abubakar, A.H. & Garba, J. 2011. Statistical analysis on the advantages of portfolio diversification. International Journal of Pure and Applied Sciences and Technology 7(2):98-106.
Published
2020-07-14
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Huni, S., & Sibindi, A. B. (2020). An Application of The Markowitz’s Mean-Variance Framework in Constructing Optimal Portfolios using the Johannesburg Securities Exchange Tradeable Indices: Array. The Journal of Accounting and Management, 10(2). Retrieved from https://dj.univ-danubius.ro/index.php/JAM/article/view/376
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