Optimization of a Technology Stock Portfolio Using the Markowitz Model

Abstract

The rapid rise of artificial intelligence (AI) has significantly increased both opportunities and risks in the technology sector. A core challenge in investment lies in selecting an optimal portfolio that balances returns and risks according to investors’ preferences. This paper applies Harry Markowitz’s mean-variance portfolio optimization model to analyze the optimal asset allocation among three leading U.S. technology companies—NVIDIA, Microsoft, and Apple—whose stock prices exhibit relatively high volatility. However, the traditional Markowitz model relies on variance as a symmetric risk measure, which fails to reflect investors’ concern about downside losses and extreme market events. To address this limitation, this study incorporates two complementary risk metrics into the Markowitz framework: Semi-variance, which focuses exclusively on downside volatility, and Value-at-Risk (VaR), which quantifies potential extreme losses under extreme market conditions. Using daily closing stock price data of the three companies from July 1, 2024, to August 29, 2025 (sourced from Yahoo Finance), and under the constraints of a $1 billion investment budget, an 8% annualized portfolio return target, and a ban on short selling, this study constructs and compares three optimized portfolios. The results indicate that the VaR-optimized portfolio effectively mitigates extreme risks, while the semi-variance-optimized portfolio better addresses downside volatility, and the traditional variance-covariance-optimized portfolio prioritizes return potential. This research enhances the applicability of the Markowitz model to AI-driven volatile tech markets and provides practical guidance for investors with different risk tolerances.