A new class of Shariah-compliant portfolio optimization model: diversification analysis

Doong Toong Lim; Khang Wen Goh; Lam Hong Lee; Doong Toong Lim; Khang Wen Goh; Lam Hong Lee

doi:10.3934/math.20231066

AIMS Mathematics

2023, Volume 8, Issue 9: 20933-20965. doi: 10.3934/math.20231066

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Research article

A new class of Shariah-compliant portfolio optimization model: diversification analysis

1.
Faculty of Computing and Engineering, Quest International University, Perak, Malaysia
2.
Faculty of Data Science and Information Technology, INTI International University, Nilai, Malaysia

Received: 12 April 2023 Revised: 07 June 2023 Accepted: 07 June 2023 Published: 30 June 2023
MSC : 90C90, 91G10, 91G70

This study proposes a novel Shariah-compliant portfolio optimization model tested on the daily historical return of 154 Shariah-compliant securities reported by the Shariah Advisory Council of Securities Commission Malaysia from 2011 to 2020. The mathematical model employs an annual rebalancing strategy subject to a Conditional Value-at-Risk (CVaR) constraint while considering practical and Islamic trading concerns, including transaction costs, holding limits, and zakat payment. To validate the model, the optimal portfolios are compared against an Islamic benchmark index, a market index, and portfolios generated by the mean-variance model, as well as a forecast accuracy test by the Mean Absolute Percentage Error and Mean Absolute Arctangent Percentage Error. Furthermore, this study examines the inter-stock relationship within the generated portfolios using correlation and Granger causality tests to identify the diversification performance. Results show an outperformance of the model in offering portfolios with higher risk-adjusted returns under a comparably short computational time and an indication of generally well-diversified portfolios by the weak correlations between securities. The study further noted that the model is adept at risk management in addition to higher forecast accuracy during financial crises by showing remarkably fewer causal relationships during bear markets in 2011, 2014, and 2020. The findings of an inversed relationship between portfolio risk and the number of causalities between securities offer new insights into the effect of dynamic relationships between securities on portfolio diversification. In conclusion, the proposed model carries higher moral and social values than the conventional models while portraying high potential in enhancing the efficiency of asset allocation, contributing to economic diversification and the scarce literature on Islamic portfolio optimization modelling. The study also supports the substantially increasing demand for Shariah-compliant strategies following globalization and the changing demographic of the real financial world with growing priorities of social and sustainability values.
- portfolio optimization,
- Shariah-compliant portfolio,
- Islamic finance,
- diversification,
- causality,
- economic diversification
Citation: Doong Toong Lim, Khang Wen Goh, Lam Hong Lee. A new class of Shariah-compliant portfolio optimization model: diversification analysis[J]. AIMS Mathematics, 2023, 8(9): 20933-20965. doi: 10.3934/math.20231066

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Abstract

This study proposes a novel Shariah-compliant portfolio optimization model tested on the daily historical return of 154 Shariah-compliant securities reported by the Shariah Advisory Council of Securities Commission Malaysia from 2011 to 2020. The mathematical model employs an annual rebalancing strategy subject to a Conditional Value-at-Risk (CVaR) constraint while considering practical and Islamic trading concerns, including transaction costs, holding limits, and zakat payment. To validate the model, the optimal portfolios are compared against an Islamic benchmark index, a market index, and portfolios generated by the mean-variance model, as well as a forecast accuracy test by the Mean Absolute Percentage Error and Mean Absolute Arctangent Percentage Error. Furthermore, this study examines the inter-stock relationship within the generated portfolios using correlation and Granger causality tests to identify the diversification performance. Results show an outperformance of the model in offering portfolios with higher risk-adjusted returns under a comparably short computational time and an indication of generally well-diversified portfolios by the weak correlations between securities. The study further noted that the model is adept at risk management in addition to higher forecast accuracy during financial crises by showing remarkably fewer causal relationships during bear markets in 2011, 2014, and 2020. The findings of an inversed relationship between portfolio risk and the number of causalities between securities offer new insights into the effect of dynamic relationships between securities on portfolio diversification. In conclusion, the proposed model carries higher moral and social values than the conventional models while portraying high potential in enhancing the efficiency of asset allocation, contributing to economic diversification and the scarce literature on Islamic portfolio optimization modelling. The study also supports the substantially increasing demand for Shariah-compliant strategies following globalization and the changing demographic of the real financial world with growing priorities of social and sustainability values.

References

[1]	H. Derbel, T. Bouraoui, N. Dammak, Can Islamic finance constitute a solution to crisis?, International Journal of Economics and Finance, 3 (2011), 75–83. https://doi.org/10.5539/ijef.v3n3p75 doi: 10.5539/ijef.v3n3p75
[2]	R. N. Kayed, M. K. Hassan, The global financial crisis and Islamic finance, Thunderbird Int. Bus. Rev., 53 (2011), 551–564. https://doi.org/10.1002/tie.20434 doi: 10.1002/tie.20434
[3]	M. I. Tabash, R. S. Dhankar, The flow of Islamic finance and economic growth: an empirical evidence of Middle East, Journal of Finance and Accounting, 2 (2014), 11–19. https://doi.org/10.11648/j.jfa.20140201.12 doi: 10.11648/j.jfa.20140201.12
[4]	M. Abduh, Volatility of Malaysian conventional and Islamic indices: does financial crisis matter?, J. Islamic Account. Bus. Res., 11 (2020), 1–11. https://doi.org/10.1108/JIABR-07-2017-0103 doi: 10.1108/JIABR-07-2017-0103
[5]	M. M. Butt, E. C. de-Run, A. U-Din, D. Mutum, Religious symbolism in Islamic financial service advertisements, J. Islamic Mark., 9 (2018), 384–401. https://doi.org/10.1108/JIMA-03-2017-0034 doi: 10.1108/JIMA-03-2017-0034
[6]	D. Ashraf, M. S. Rizwan, G. Ahmad, Islamic equity investments and the COVID-19 pandemic, Pac.-Basin Financ. J., 73 (2022), 101765. https://doi.org/10.1016/j.pacfin.2022.101765 doi: 10.1016/j.pacfin.2022.101765
[7]	Journal of the Malaysian Judiciary July 2020, Judicial Appointments Commission, Level 5, Palace of Justice, Precinct 3, 62506 Putrajaya, Malaysia, 2020. Available from: https://www.jac.gov.my/spk/images/stories/4_penerbitan/journal_malaysian_judiciary/julai2020.pdf.
[8]	D. T. Lim, K. W. Goh, Y. W. Sim, A review on portfolio optimization models for Islamic finance, AIMS Mathematics, 8 (2023), 10329–10356. https://doi.org/10.3934/math.2023523 doi: 10.3934/math.2023523
[9]	Z. Iqbal, A. Mirakhor, An introduction to Islamic finance: theory and practice, John Wiley & Sons, 2011. https://doi.org/10.1002/9781118390474
[10]	M. R. Embong, R. Taha, M. N. M. Nor, Role of zakat to eradicate poverty in Malaysia, Jurnal Pengurusan, 39 (2013), 141–150. https://doi.org/10.17576/pengurusan-2013-39-13 doi: 10.17576/pengurusan-2013-39-13
[11]	M. A. Uddin, A. U. F. Ahmad, Conventional futures: derivatives in Islamic law of contract, Int. J. Law Manag., 62 (2020), 315–337. https://doi.org/10.1108/IJLMA-10-2017-0242 doi: 10.1108/IJLMA-10-2017-0242
[12]	M. Ayub, Derivatives and Islamic finance, Working Paper, State Bank of Pakistan Karachi, 2003. Available from: https://www.sbp.org.pk/departments/ibd/derivatives_islamic.pdf.
[13]	M. I. Hodžić, Z. D. Sijerčić, T. Names, All-weather financial portfolio optimization with Islamic constraints and risk minimization, In: Critical issues and challenges in Islamic economics and finance development, Cham: Palgrave Macmillan, 2017,115–136. https://doi.org/10.1007/978-3-319-45029-2_6
[14]	J. C. Adams, P. Ahmed, The performance of faith-based funds, J. Invest., 22 (2013), 83–92. https://doi.org/10.3905/joi.2013.22.4.083 doi: 10.3905/joi.2013.22.4.083
[15]	J. A. Sandwick, P. Collazzo, Modern portfolio theory with sharia: a comparative analysis, J. Asset Manag., 22 (2021), 30–42. https://doi.org/10.1057/s41260-020-00187-w doi: 10.1057/s41260-020-00187-w
[16]	S. Braiek, R. Bedoui, L. Belkacem, Islamic portfolio optimization under systemic risk: Vine Copula‐CoVaR based model, Int. J. Fin. Econ., 27 (2022), 1321–1339. https://doi.org/10.1002/ijfe.2217 doi: 10.1002/ijfe.2217
[17]	L. Charfeddine, A. Najah, F. Teulon, Socially responsible investing and Islamic funds: new perspectives for portfolio allocation, Res. Int. Bus. Financ., 36 (2016), 351–361. https://doi.org/10.1016/j.ribaf.2015.09.031 doi: 10.1016/j.ribaf.2015.09.031
[18]	OECD, How Islamic finance contributes to achieving the sustainable development goals, OECD Development Co-operation Policy Papers, Paris: OECD Publishing, 2020, 30. https://doi.org/10.1787/ac1480ca-en
[19]	A. J. Yesuf, D. Aassouli, Exploring synergies and performance evaluation between Islamic funds and socially responsible investment (SRIs) in light of the sustainable development goals (SDGs), Heliyon, 6 (2020), e04562. https://doi.org/10.1016/j.heliyon.2020.e04562 doi: 10.1016/j.heliyon.2020.e04562
[20]	R. Bauer, T. Ruof, P. Smeets, Get real! Individuals prefer more sustainable investments, Rev. Financ. Stud., 34 (2021), 3976–4043. https://doi.org/10.1093/rfs/hhab037 doi: 10.1093/rfs/hhab037
[21]	EY Americas, Why sustainable investing matters, 2020. Available from: https://www.ey.com/en_us/financial-services/why-sustainable-investing-matters.
[22]	H. Masri, A shariah-compliant portfolio selection model, J. Oper. Res. Soc., 69 (2018), 1568–1575. https://doi.org/10.1057/s41274-017-0223-6 doi: 10.1057/s41274-017-0223-6
[23]	E. Constantinou, A. Kazandjian, G. P. Kouretas, V. Tahmazian, Cointegration, causality and domestic portfolio diversification in the Cyprus stock exchange, EconPapers, Working Papers No 522.
[24]	U. Derigs, S. Marzban, New strategies and a new paradigm for Shariah-compliant portfolio optimization, J. Bank. Financ., 33 (2009), 1166–1176. https://doi.org/10.1016/j.jbankfin.2008.12.011 doi: 10.1016/j.jbankfin.2008.12.011
[25]	N. Bagheri, Deterministic goal programming approach for Islamic portfolio selection, Oper. Res., 21 (2021), 1447–1459. https://doi.org/10.1007/s12351-019-00517-w doi: 10.1007/s12351-019-00517-w
[26]	F. Black, Capital market equilibrium with restricted borrowing, The Journal of Business, 45 (1972), 444–455. doi: 10.1086/295472
[27]	A. A.-F. El-Ashker, The Islamic business enterprise, London: Croom Helm, 1987.
[28]	S. Hakim, M. Rashidian, Risk and return of Islamic stock market indexes, In: 9th Economic Research Forum Annual Conference in Sharjah, UAE, 2002, 26–28.
[29]	M. K. Hassan, A. N. F. Khan, T. Ngow, Is faith‐based investing rewarding? The case for Malaysian Islamic unit trust funds, J. Islamic Account. Bus. Res., 1 (2010), 148–171. https://doi.org/10.1108/17590811011086732 doi: 10.1108/17590811011086732
[30]	S. A. Hakim, Z. Hamid, A. K. Mydin Meera, Capital asset pricing model and pricing of Islamic financial instruments, Journal of King Abdulaziz University: Islamic Economics, 29 (2016), 1–19.
[31]	S. A. S. Hussin, N. Saring, Z. Zahid, N. A. Ramli, Performance of low volatility shariah equities in Malaysia, AIP Conference Proceedings, 1982 (2018), 020026. https://doi.org/10.1063/1.5045432 doi: 10.1063/1.5045432
[32]	A. Hoque, S. Rakhi, K. Hassan, T. Le, The performance of stock portfolios: evidence from analysing Malaysia case, and implication for open innovation, Journal of Open Innovation: Technology, Market, and Complexity, 6 (2020), 178. https://doi.org/10.3390/joitmc6040178 doi: 10.3390/joitmc6040178
[33]	C.-F. Chen, S. Chiang, Portfolio diversification possibilities between the stock and housing markets in G7 countries: evidence from the time-varying Granger causality, Financ. Res. Lett., 49 (2022), 103124. https://doi.org/10.1016/j.frl.2022.103124 doi: 10.1016/j.frl.2022.103124
[34]	D. T. Lim, K. W. Goh, Y. W. Sim, K. Mokhtar, S. Thinagar, Estimation of stock market index volatility using the GARCH model: causality between stock indices, Asian Economic and Financial Review, 13 (2023), 162–179. https://doi.org/10.55493/5002.v13i3.4738 doi: 10.55493/5002.v13i3.4738
[35]	H. Markowitz, Portfolio selection, The Journal of Finance, 7 (1952), 77–91. https://doi.org/10.2307/2975974 doi: 10.2307/2975974
[36]	R. T. Rockafellar, S. Uryasev, Optimization of conditional value-at-risk, J. Risk, 2 (2000), 21–42. https://doi.org/10.21314/JOR.2000.038 doi: 10.21314/JOR.2000.038
[37]	S. T. Rachev, F. J. Fabozzi, S. V. Stoyanov, Advanced stochastic models, risk assessment, and portfolio optimization: the ideal risk, uncertainty, and performance measures, John Wiley & Sons, 2008.
[38]	M. M. Alam, C. S. Akbar, S. M. Shahriar, M. M. Elahi, The Islamic shariah principles for investment in stock market, Qual. Res. Financ. Mark., 9 (2017), 132–146. https://doi.org/10.1108/QRFM-09-2016-0029 doi: 10.1108/QRFM-09-2016-0029
[39]	Y. Tokat, N. W. Wicas, Portfolio rebalancing in theory and practice, J. Invest., 16 (2007), 52–59. https://doi.org/10.3905/joi.2007.686411 doi: 10.3905/joi.2007.686411
[40]	Z. Dai, H. Zhu, X. Zhang, Dynamic spillover effects and portfolio strategies between crude oil, gold and Chinese stock markets related to new energy vehicle, Energ. Econ., 109 (2022), 105959. https://doi.org/10.1016/j.eneco.2022.105959 doi: 10.1016/j.eneco.2022.105959
[41]	Bursa Malaysia, Transaction Costs, 2023. Available from: https://www.bursamalaysia.com/trade/trading_resources/equities/transaction_costs.
[42]	P. Bonami, M. A. Lejeune, An exact solution approach for portfolio optimization problems under stochastic and integer constraints, Oper. Res., 57 (2009), 650–670. https://doi.org/10.1287/opre.1080.0599 doi: 10.1287/opre.1080.0599
[43]	F. J. Fabozzi, P. N. Kolm, D. A. Pachamanova, S. M. Focardi, Robust portfolio optimization and management, John Wiley & Sons, 2007.
[44]	W. F. Sharpe, Mutual fund performance, The Journal of Business, 39 (1966), 119–138. doi: 10.1086/294846
[45]	J. L. Treynor, How to rate management of investment funds, Harvard Bus. Rev., 43 (1965), 63–75.
[46]	M. C. Jensen, The performance of mutual funds in the period 1945–1964, J. Financ., 23 (1968), 389–416. https://doi.org/10.2307/2325404 doi: 10.1111/j.1540-6261.1968.tb00815.x
[47]	C. D. Lewis, Industrial and business forecasting methods: a practical guide to exponential smoothing and curve fitting, London: Butterworths, 1982.
[48]	S. Makridakis, Accuracy measures: theoretical and practical concerns, Int. J. Forecasting, 9 (1993), 527–529. https://doi.org/10.1016/0169-2070(93)90079-3 doi: 10.1016/0169-2070(93)90079-3
[49]	S. Kim, H. Kim, A new metric of absolute percentage error for intermittent demand forecasts, Int. J. Forecasting, 32 (2016), 669–679. https://doi.org/10.1016/j.ijforecast.2015.12.003 doi: 10.1016/j.ijforecast.2015.12.003
[50]	C. W. J. Granger, Investigating causal relations by econometric models and cross-spectral methods, Econometrica, 37 (1969), 424–438. https://doi.org/10.2307/1912791 doi: 10.2307/1912791
[51]	V. Alexeev, M. Dungey, Equity portfolio diversification with high frequency data, Quant. Financ., 15 (2015), 1205–1215. https://doi.org/10.1080/14697688.2014.973898 doi: 10.1080/14697688.2014.973898
[52]	J. L. Evans, S. H. Archer, Diversification and the reduction of dispersion: an empirical analysis, The Journal of Finance, 23 (1968), 761–767. https://doi.org/10.2307/2325905 doi: 10.2307/2325905
[53]	H. C. Jimbo, I. S. Ngongo, N. G. Andjiga, T. Suzuki, C. A. Onana, Portfolio optimization under cardinality constraints: a comparative study, Open Journal of Statistics, 7 (2017), 731–742. https://doi.org/10.4236/ojs.2017.74051 doi: 10.4236/ojs.2017.74051
[54]	A. D. Sanford, Granger causality in volatility between Australian equity and debt markets: a Bayesian analysis, Corporate Ownership & Control, 9 (2011), 587–596. https://doi.org/10.22495/cocv9i1c6art2 doi: 10.22495/cocv9i1c6art2
[55]	A. Bausch, F. Pils, Product diversification strategy and financial performance: meta-analytic evidence on causality and construct multidimensionality, Rev. Manag. Sci., 3 (2009), 157–190. https://doi.org/10.1007/s11846-009-0027-4 doi: 10.1007/s11846-009-0027-4
[56]	D. Hodson, The eurozone in 2011, J. Common Mark. Stud., 50 (2012), 178–194. https://doi.org/10.1111/j.1468-5965.2012.02270.x doi: 10.1111/j.1468-5965.2012.02270.x
[57]	N. B. Nizar, N. Z. Bahrudin, N. C. Yahya, S. N. M. Rashid, F. K. Tehubijuluw, Does US stock market affect Malaysia stock market during Covid-19 pandemic?, Journal of Entrepreneurship, Business and Economics, 10 (2022), 124–143.
[58]	S. H. Kang, G. S. Uddin, V. Troster, S.-M. Yoon, Directional spillover effects between ASEAN and world stock markets, J. Multinat. Financ. Manag., 52–53 (2019), 100592. https://doi.org/10.1016/j.mulfin.2019.100592 doi: 10.1016/j.mulfin.2019.100592
[59]	W. Bank, What triggered the oil price plunge of 2014-2016 and why it failed to deliver an economic impetus in eight charts, 2018. Available from: https://blogs.worldbank.org/developmenttalk/what-triggered-oil-price-plunge-2014-2016-and-why-it-failed-deliver-economic-impetus-eight-charts.
[60]	A. Ghorbel, M. Abdelhedi, Y. Boujelbene, Assessing the impact of crude oil price and investor sentiment on Islamic indices: Subprime crisis, J. Afr. Bus., 15 (2014), 13–24. https://doi.org/10.1080/15228916.2014.881222 doi: 10.1080/15228916.2014.881222
[61]	P. He, Y. Sun, Y. Zhang, T. Li, COVID-19's impact on stock prices across different sectors—An event study based on the Chinese stock market, Emerg. Mark. Financ. Tr., 56 (2020), 2198–2212. https://doi.org/10.1080/1540496X.2020.1785865 doi: 10.1080/1540496X.2020.1785865
[62]	A. A. Rahman, N. Z. M. Sidek, F. H. Tafri, Macroeconomic determinants of Malaysian stock market, African Journal of Business Management, 3 (2009), 95–106.
[63]	F. Z. Thang, Impact of interest rate and exchange rate on the stock market index in Malaysia: a cointegration analysis, Master's thesis, Universiti Sains, Penang, Malaysia, 2009.
[64]	H. T. Wong, Real exchange rate returns and real stock price returns in the stock market of Malaysia, Singap. Econ. Rev., 64 (2019), 1319–1349. https://doi.org/10.1142/S0217590816500387 doi: 10.1142/S0217590816500387

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