Portfolio optimization based on quadratic programming: a comparative risk-return analysis with mean-variance model under different time periods

This paper compares the specific performance of Markowitz’s mean-variance model and quadratic programming optimization model in different economic periods by means of empirical analysis. The paper compares and analyzes the return performance and risk assessment of the mean-variance model and the quadratic programming optimization model in different economic periods (including expansion, stabilization, recession, and recovery periods) by introducing various risk measurement tools, such as the lower semi variance, value-at-risk (VaR), and conditional value-at-risk (CVaR). The results of the comparative analysis show that the quadratic programming optimization model is more effective in controlling extreme risks and outperforms the mean-variance model during periods of high market volatility, while the difference in performance between the two models is small during periods of relative economic stability. By comparing the effective boundary images and Sharpe ratios of the quadratic programming model and the mean-variance model, this paper provides an effective reference basis for investors to choose appropriate optimization strategies in different economic periods.