COMPARATIVE ANALYSIS OF OPTIMAL PORTFOLIOS: A MATHEMATICAL AND EMPIRICAL REASSESSMENT OF THE MARKOWITZ AND SHARPE MODELS
Keywords:
Markowitz Mean-Variance Optimization, Sharpe Single-Index Model, Estimation Risk, Efficient Frontier, Bias-Variance Trade-off.Abstract
The evolution of Modern Portfolio Theory (MPT) is fundamentally defined by the tension between theoretical completeness and practical implementability. This research provides a rigorous comparative analysis of the two primary paradigms in asset allocation: the Markowitz Mean-Variance framework and the Sharpe Single-Index Model (SIM). While the Markowitz approach offers a theoretically complete representation of the opportunity set through the full variance-covariance matrix, its practical application is frequently hindered by the "curse of dimensionality". We examine how the quadrating expanding parameter space of the Markowitz model exacerbates estimation risk, transforming the framework into an "error maximizer". Conversely, the Sharpe SIM provides computational parsimony and structural stability by imposing a diagonal residual covariance structure, effectively serving as a form of implicit regularization. This article delineates the structural trade-offs between estimation accuracy (variance) and specification error (bias).
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