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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Jianuo Li & Mingyue Tian & Yanxin Zhang & Yimin Nie, 2026. "A Comparative Study of the Markowitz and Index Models Under Various Constraints: An Empirical Analysis Based on 20 Years of Data for 21 Stocks," Advances in Economics, Business and Management Research,, Springer.
    • Handle: RePEc:spr:advbcp:978-94-6239-672-2_15
    DOI: 10.2991/978-94-6239-672-2_15
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