Proceedings of the 2026 3rd International Conference on Applied Economics, Management Science and Social Development (AEMSS 2026)

<Previous Article In Volume
Next Article In Volume>

A Comparative Study of the Markowitz and Index Models Under Various Constraints: An Empirical Analysis Based on 20 Years of Data for 21 Stocks

Authors
Jianuo Li1, *, Mingyue Tian2, Yanxin Zhang3, Yimin Nie4
1Linden Hall School for Girls, Lititz, 17543, PA, USA
2Lingnan College, Sun Yat-Sen University, Guangzhou, 510275, China
3Faculty of Business Administration, University of Macau, Macau, 999078, China
4School of Economics and Management, Fuzhou University, Fuzhou, 350108, China
*Corresponding author. Email: Jessie.ljn08@gmail.com
Corresponding Author
Jianuo Li
Available Online 12 May 2026.
DOI
10.2991/978-94-6239-672-2_15How to use a DOI?
Keywords
Portfolio Optimization; Markowitz Model; Index Model; Efficient Frontier; Risk-Return Trade-off
Abstract

This paper examines portfolio optimization using both the Markowitz Model (MM) and the Index Model (IM), with a focus on the S&P 500 Index and 21 of its OEX constituent stocks over a 20-year sample period. Daily prices were converted into monthly returns, resulting in over 200 months of data. Using Excel Solver and SolverTable, we estimated expected returns, variances, and covariance matrices, and then applied quadratic optimization under multiple constraints. Specifically, we analyzed five cases: (1) Regulation T constraint, (2) box constraint, (3) no constraint, (4) no short-selling, and (5) exclusion of the index. The results highlight differences between MM, which captures full pairwise correlations among assets, and IM, which simplifies by linking returns to the market index. Empirical findings suggest that while unconstrained portfolios offer the highest potential returns, they produce extreme weights and higher risks. In contrast, IM portfolios demonstrate more stability and improved efficiency under conservative conditions, making them more suitable for investors with regulatory or practical limitations.

Copyright
© 2026 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Download article (PDF)

<Previous Article In Volume
Next Article In Volume>
Volume Title
Proceedings of the 2026 3rd International Conference on Applied Economics, Management Science and Social Development (AEMSS 2026)
Series
Advances in Economics, Business and Management Research
Publication Date
12 May 2026
ISBN
978-94-6239-672-2
ISSN
2352-5428
DOI
10.2991/978-94-6239-672-2_15How to use a DOI?
Copyright
© 2026 The Author(s)
Open Access
Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

Cite this article

risenwbib
TY  - CONF
AU  - Jianuo Li
AU  - Mingyue Tian
AU  - Yanxin Zhang
AU  - Yimin Nie
PY  - 2026
DA  - 2026/05/12
TI  - A Comparative Study of the Markowitz and Index Models Under Various Constraints: An Empirical Analysis Based on 20 Years of Data for 21 Stocks
BT  - Proceedings of the 2026 3rd International Conference on Applied Economics, Management Science and Social Development (AEMSS 2026)
PB  - Atlantis Press
SP  - 147
EP  - 162
SN  - 2352-5428
UR  - https://doi.org/10.2991/978-94-6239-672-2_15
DO  - 10.2991/978-94-6239-672-2_15
ID  - Li2026
ER  -