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

Jianuo Li (), Mingyue Tian (), Yanxin Zhang () and Yimin Nie ()
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Jianuo Li: Linden Hall School for Girls
Mingyue Tian: Lingnan College, Sun Yat-Sen University
Yanxin Zhang: University of Macau, Faculty of Business Administration
Yimin Nie: Fuzhou University, School of Economics and Management

A chapter in Proceedings of the 2026 3rd International Conference on Applied Economics, Management Science and Social Development (AEMSS 2026), 2026, pp 147-162 from Springer

Abstract: 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.

Keywords: Portfolio Optimization; Markowitz Model; Index Model; Efficient Frontier; Risk-Return Trade-off (search for similar items in EconPapers)
Date: 2026
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DOI: 10.2991/978-94-6239-672-2_15

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