A Study of Short Sale Constrained Portfolios Based on the Mean-Variance Model in the U.S. Stock Market

With the continuous development of the stock market, achieving a balance between return and risk through the optimization of investment portfolios has become one of the core concerns for investors. This paper studies the problem of optimal stock portfolio selection using the mean-variance framework. Building on the mean-variance model proposed by Markowitz, numerous subsequent studies have extended this foundation, including the introduction of solution-based approaches and the establishment of mean-variance models under novel risk perceptions. This study selects 12 U.S. stocks (ABBV, ADBE, AMD, etc.) and uses the closing prices on the first trading day of each month from January 3, 2022, to February 3, 2025, as sample data. By calculating monthly stock growth rates, expected returns, and the covariance matrix, and applying the solution algorithm of the mean-variance model, the efficient frontier of the investment portfolio is derived. Under the practical market constraint of a short-sale prohibition, iterative calculations are performed. The optimal frontier portfolio corresponding to an expected return of 0.013 is obtained, providing a quantitative reference for investors to balance return and risk and to formulate investment strategies in actual stock investment.