A Linear Portfolio Optimizer to Mean-Variance Optimization

In Markowitz portfolio optimization problems, the estimation of the inverse covariance matrix is not trivial and could even be intractable when the dimension is very high. In this article, we propose a linear portfolio optimizer (LPO) to solve Markowitz optimization problems in both low-dimensional and high-dimensional settings. Instead of estimating the inverse covariance matrix directly, the LPO method estimates the portfolio weights directly through solving an l 1 constrained optimization problem. The resulting linear optimization can be solved very efficiently by implementing a DASSO algorithm. Moreover, the LPO estimator is shown to asymptotically yield the maximum expected return while preserving the risk constraint. Simulations on both synthetic data and empirical data from Fama-French and CRSP databases validate the performance of the proposed method in comparison with other existing proposals