Abstract
This paper studies the mean-variance (MV) portfolio problems under static and dynamic settings, particularly for the case that the number of assets (p) is larger than the number of observation times (n). We prove that the classical plug-in estimation seriously distorts the optimal MV portfolio in the sense that the probability, that the plug-in portfolio will outperform the bank deposit, tends to 50% for p>>n and a large n. We investigate a constrained l1 minimization approach for directly estimating effective parameters appearing in the optimal portfolio solution. Similar to the Dantzig Selector, the estimator is efficiently implemented with linear programming and the resulting portfolio is called the linear programming optimal (LPO) portfolio. We derive the consistency and rate of convergence for the LPO portfolios. The LPO procedure essentially filters out unfavorable assets based on the MV criterion, resulting in a sparse portfolio. The advantages of the LPO portfolio include the computational superiority, its applicability for dynamic portfolio problems and non-Gaussian distributions of asset returns. Simulations validate the theory and its finite-sample properties. Empirical studies show that the LPO-based portfolios outperform the equally weighted portfolio, the MV portfolios using shrinkage estimators and other competitive estimators.
Published Version
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