Comparative Analysis of Portfolio Optimization Between Markowitz Model And Single Index Model

Yiyun Chen; Zi Liu; Zhijie Zou

doi:10.54691/bcpbm.v38i.4226

Authors

Yiyun Chen
Zi Liu
Zhijie Zou

DOI:

https://doi.org/10.54691/bcpbm.v38i.4226

Keywords:

Markowitz Model; Single Index Model; Portfolio optimization.

Abstract

The key factors which investors consider when investing are the risks and returns of the assets. Moreover, they may determine efficient investment portfolios using some financial models. The goal of this paper is to compare the various optimal portfolios constructed using the Markowitz Model and the Index Model and give possible explanations for the results. The data selected for this paper are stocks from ten companies, which are Adobe Inc., International Machines Corporation, SAP SE, Bank of America Corporation, Citigroup Inc., Wells Fargo & Company, The Travelers Companies, Southwest Airline Corporation, Alaska Air Group Inc., and Hawaiian Holdings Inc. The companies are selected from the technology sector, financial services sector, and the industrial sector of the economy in order to simulate real investment decisions. In specific, twenty years of total daily return data from the companies and the S&P 500 index are collected. The statistical analysis shows that the expected return of the optimal portfolio calculated by the Single Index Model is always higher than that of the Markowitz Model. The assumption, that all stocks are independent of each other, made by the Single Index Model may provide a partial explanation for the difference in the expected returns. Nonetheless, the specific effect of the difference is yet to be examined.

Downloads

Download data is not yet available.

References

Qu, K., Tian, Y., Xu, J., & Zhang, J. (2021, December). Comparison of the Applicability of Markowitz Model and Index Model Under 5 Real-World Constraints for Diverse Investors. In 2021 3rd International Conference on Economic Management and Cultural Industry (ICEMCI 2021) (pp. 1323-1332). Atlantis Press.

Susanti, E., Ervina, N., Grace, E., & Siregar, L. (2021). Comparison Analysis Of Optimal Portfolio Formation Results Using Single Index Model With Markowitz Model During The Covid 19 Pandemic In LQ 45 Index Company. International Journal of Educational Research & Social Sciences, 2(5), 1146-1156.

Patel, A. K. (2017). Construction of Optimal Portfolio Using Sharpe’s Single Index Model and Markowitz Model: An Empirical Study on Nifty50 Stocks. Available at SSRN 3259328.

Putra, K. A. A. S. P., & Dana, M. (2020). Study of Optimal Portfolio Performance Comparison: Single Index Model and Markowitz Model on LQ45 Stocks in Indonesia Stock Exchange. American Journal of Humanities and Social Sciences Research (AJHSSR). Retrieved September 7, 2022, from chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/https://www.ajhssr.com/wp-content/uploads/2020/12/ZE20412237244.pdf.

Varghese, J., & Joseph, A. (2018, May 15). A Comparative Study on Markowitz Mean-Variance Model and Sharpe’s Single Index Model in the Context of Portfolio Investment. PESQUISA. Retrieved September 7, 2022, from chrome-extension://efaidnbmnnnibpcajpcglclefindmkaj/http://pesquisaonline.net/wp-content/uploads/2018/05/A-Comparative-Study-on-Markowitz-Mean-Variance-_pesquisa_May-2018.pdf.

Hanif, A., Hanun, N. R. & Febriansah, R. E. (2021). Optimization of the stock portfolio using the Markowitz model in the era of the covid-19 pandemic. TIJAB (The International Journal of Applied Business), 5(1), 37-50. Submission Date:03/02/2021Acceptance Date:16/04/2021 https://www.e-journal.unair.ac.id/TIJAB/article/view/25228/14028

Leung, P.-L., Ng, H.-Y., & Wong, W.-K. (2012, October 1). An improved estimation to make Markowitz’s portfolio optimization theory users friendly and estimation accurate with application on the US stock market investment. View of optimization of stock portfolio using the Markowitz model in the era of the COVID-19 pandemic. Retrieved September 7, 2022, from https://www.sciencedirect.com/science/article/abs/pii/S0377221712002792.

Chen, Z., Li, H., Li, Z., & Yin, L. (2022). Analysis of Ten Stock Portfolios Using Markowitz and Single Index Models. Proceedings of the 2022 7Th International Conference on Social Sciences And Economic Development (ICSSED 2022). doi: 10.2991/aebmr.k.220405.202.

Lee, H. S., Cheng, F. F., & Chong, S. C. (2016). Markowitz portfolio theory and capital asset pricing model for Kuala Lumpur stock exchange: A case revisited. International Journal of Economics and Financial Issues, 6(3), 59-65.

Wu, M., Imran, M., Feng, Y., Zhang, L., & Abbas, M. (2017). Review and Validity of Capital Asset Pricing Model: Evidence from Pakistan Stock Exchange. International Research in Economics and Finance, 1(1), 21. doi: 10.20849/iref. v1i1.267.

Džaja, J., & Aljinović, Z. (2013). Testing CAPM model on the emerging markets of the Central and Southeastern Europe. Croatian Operational Research Review, 4(1), 164-175.

Andrea Frazzini, & Lasse Heje Pedersen (2010). Betting Against Beta Journal of Financial Economics.