A Comparative Study of the Markowitz Model and the Single Index Model under Bull and Bear Market Scenarios

The quest for the optimal balance between risk and return remains a pivotal area of research within modern portfolio theory. As two traditional approaches, the Markowitz model and the single-index model embody distinct philosophies: precise calculation versus simplified approximation. The Markowitz model delves deeply into the covariance relationships between assets, laying the foundation for modern portfolio theory; the single-index model enhances practical applicability by streamlining the estimation process of the covariance matrix. This study constructs the efficient frontier, global minimum variance portfolio, and optimal risky portfolio under both the Markowitz model and single index model using data from 21 selected sample stocks. Empirical testing and comparisons are conducted across various scenarios using metrics such as the Sharpe ratio and Sortino ratio. Empirical results indicate that the single-index model demonstrates superior risk-adjusted returns and robustness across most market conditions. Whilst the Markowitz model theoretically achieves greater diversification, cumulative estimation errors may lead to comparatively weaker performance in empirical outcomes. These findings not only assist investors in model selection across dynamic market environments but also inform future research on expanding constraints and incorporating factor models.