Markowitz and Single Index Models for Optimal Portfolio Formation: Evidence from the SRI-KEHATI Index
DOI:
https://doi.org/10.54518/eir.4.1.2026.1402Keywords:
Markowitz Model, Paired T-test, Single Index Model, SRI-KEHATI IndexAbstract
The growing integration of ESG criteria into investment frameworks has elevated both stock screening and portfolio construction as critical determinants of sustainable investment outcomes. This study comprises the Markowitz Model and the Single Index Model (SIM) in constructing optimal portfolio from ten SRI-KEHATI Index constituent stocks over January 2021 to February 2026. Using 265 weekly return observations, Kolmogoroc-Smirnov normality tests confirmed distributional assumptions for both return and risk difference series, justifying the parametric paired-sample t-test. The Markowitz model produced a cross-sectoral portfolio comprising BBRI (32.43%), BMRI (32.58%), JSMR (33.53%), and DSNG (1.46%), while the SIM applying weekly risk-free rate of 0.09% and cut-off rate C*= 0.0002397, identified BMRI (30.52%), JSMR (27.12%), BBNI (25.99%), and DSNG (16.37%). Despite their compositional differences, the two models yielded no statistically significant difference in return or risk, although the SIM recorded a higher Sharpe ratio. The findings suggest that within an ESG-screened universe, optimisation methodology shapes portfolio structure without necessarily producing materially different performance outcomes, reinforcing the importance of evaluating both screening criteria and construction methodology as jointly consequential dimensions of sustainable portfolio design.
References
Avramov, D., Cheng, S., Lioui, A., & Tarelli, A. (2022). Sustainable investing with ESG rating uncertainty. Journal of Financial Economics, 145(2), 642–664. https://doi.org/10.1016/j.jfineco.2021.09.009
Best, M. J., & Grauer, R. R. (1991). On the sensitivity of mean-variance-efficient portfolios to changes in asset means: Some analytical and computational results. The Review of Financial Studies, 4(2), 315–342. https://doi.org/10.1093/rfs/4.2.315
Boyd, S., Johansson, K., Kahn, R., Schiele, P., & Schmelzer, T. (2024). Markowitz portfolio construction at seventy. The Journal of Portfolio Management, 50(8), 117–160. https://doi.org/10.3905/jpm.2024.50.8.117
Chibane, M., & Joubrel, M. (2024). The ESG-efficient frontier under ESG rating uncertainty. Finance Research Letters, 67, Article 105881. https://doi.org/10.1016/j.frl.2024.105881
DeMiguel, V., Garlappi, L., & Uppal, R. (2009). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? The Review of Financial Studies, 22(5), 1915–1953. https://doi.org/10.1093/rfs/hhm075
Elton, E. J., Gruber, M. J., & Padberg, M. W. (1977). Simple criteria for optimal portfolio selection with upper bounds. Operations Research, 25(6), 952–967. https://doi.org/10.1287/opre.25.6.952
Gunawan, A., Fajriyah, R., Bimakasa, M. A., & Untari, S. N. (2024). Analysis of portfolio formation on the LQ45 stocks index, using the Markowitz and single index models. BAREKENG: Journal of Mathematics and Its Applications, 18(4), 2363–2374. https://doi.org/10.30598/barekengvol18iss4pp2363-2374
Huang, H.-H., Chang, T.-H., & Wang, C.-P. (2024). Investment performance comparison among various portfolio selection strategies in Taiwan stock market. Asia Pacific Management Review, 29(2), 195–214. https://doi.org/10.1016/j.apmrv.2024.03.001
Investing.com. (2026). SRI-KEHATI Index (JKSRI) and IDX Composite (JKSE) historical data. Retrieved March 3, 2026, from https://www.investing.com
Kan, R., & Zhou, G. (2007). Optimal portfolio choice with parameter uncertainty. Journal of Financial and Quantitative Analysis, 42(3), 621–656. https://doi.org/10.1017/S0022109000004129
Keykhaei, R. (2016). Mean-variance portfolio optimization when each asset has individual uncertain exit-time. Pakistan Journal of Statistics and Operation Research, 12(4), 765–773. https://doi.org/10.18187/pjsor.v12i4.1251
Kolm, P. N., Tütüncü, R., & Fabozzi, F. J. (2014). 60 years of portfolio optimization: Practical challenges and current trends. European Journal of Operational Research, 234(2), 356–371. https://doi.org/10.1016/j.ejor.2013.10.060
Lorimer, D. A., van Schalkwyk, C. H., & Szczygielski, J. J. (2024). Portfolio optimisation using alternative risk measures. Finance Research Letters, 67, Article 105758. https://doi.org/10.1016/j.frl.2024.105758
Lyu, W., Cui, S., & Li, T. (2022). Markowitz and index models for optimizing investment portfolio study during COVID-19 pandemic. In Proceedings of the 13th International Conference on E-Education, E-Business, E-Management, and E-Learning (pp. 500–509). Association for Computing Machinery. https://doi.org/10.1145/3514262.3514338
Markowitz, H. (1952). Portfolio selection. The Journal of Finance, 7(1), 77–91. https://doi.org/10.1111/j.1540-6261.1952.tb01525.x
Müller, L., & Joubrel, M. (2025). A novel approach to sustainable mean-variance portfolio optimization: Accounting for ESG-related uncertainty. Finance Research Letters, 85, Article 108056. https://doi.org/10.1016/j.frl.2025.108056
Pal, R., Chaudhuri, T. D., & Mukhopadhyay, S. (2021). Portfolio formation and optimization with continuous realignment: A suggested method for choosing the best portfolio of stocks using variable length NSGA-II. Expert Systems with Applications, 186, Article 115732. https://doi.org/10.1016/j.eswa.2021.115732
Poddar, A., Bhattacharya, S., & Bhatt, R. R. (2024). Employing behavioural portfolio theory for sustainable investment: Examining drawdown risks and ESG factors. Investment Analysts Journal, 54(1), 110–138. https://doi.org/10.1080/10293523.2024.2375818
Sajadi, S. M. A., Fereydooni, A., Athari, S. A., & Farhadi, S. (2025). A sustainable portfolio construction model based on ESG and deep learning algorithms: Evidence from the U.S. market. Computational Economics. Advance online publication. https://doi.org/10.1007/s10614-025-10976-3
Saputra, A. S., Meylani, M., Nurfauziah, N., & Gunardi, A. (2024). Optimizing ESG Leaders’ stock portfolio on the Indonesia Stock Exchange (IDX): A Single Index Model analysis (2020–2023). E3S Web of Conferences, 593, Article 13001. https://doi.org/10.1051/e3sconf/202459313001
Senthilkumar, A., Namboothiri, A., & Rajeev, S. (2021). Does portfolio optimization favor sector or broad market investments? Journal of Public Affairs, 22(S1), Article e2752. https://doi.org/10.1002/pa.2752
Sharpe, W. F. (1963). A simplified model for portfolio analysis. Management Science, 9(2), 277–293. https://doi.org/10.1287/mnsc.9.2.277
Toma, A., & Fulga, C. (2018). Robust estimation for the single index model using pseudodistances. Entropy, 20(5), Article 374. https://doi.org/10.3390/e20050374
Wahid, A., & Kowalewski, O. (2025). Sustainable portfolio optimization: A multi-class framework for eco-friendly stocks. Research in International Business and Finance, 76, Article 102841. https://doi.org/10.1016/j.ribaf.2025.102841
Waluyo, D. E., Ramasamy, S., & Jamilah, S. F. (2025). Portfolio optimization using mean-variance model and single index model: Evidence from Indonesian and Malaysian capital markets. Asian Economic and Financial Review, 15(11), 1731–1747. https://doi.org/10.55493/5002.v15i11.5662
Wardhana, A. A., & Hersugondo. (2025). Environmental, Social, and Governance Disclosure Effects on Firm Value, Profitability, and Capital Structure in Indonesia. Economic and Business Horizon, 4(2), 431–448. https://doi.org/10.54518/ebh.4.2.2025.687
Yayasan KEHATI. (n.d.). SRI-KEHATI. Retrieved April 30, 2026, from https://kehati.or.id/investasi-hijau/sri-kehati/
Yusup, A. K. (2022). Mean-variance and single-index model portfolio optimisation: Case in the Indonesian stock market. Asian Journal of Business and Accounting, 15(2), 79–109. https://doi.org/10.22452/ajba.vol15no2.3.
