LargeScale Regularized Portfolio Selection Via Convex Optimization During the past years, statistical regularization methods have shown their advantages for portfolio selection in various aspects like stabilizing the portfolio weights, selecting sparse portfolios, and reducing the portfolio turnovers. In this paper, a regularized portfolio selection model is proposed based on the sorted (or ordered weighted) l 1  norm. The proposed model is general to incorporate both the Markowitzxe2x80x99s meanvariance portfolio problem and the index tracking portfolio problem. To be capable of handling largescale portfolio selection (i.e., the asset universe is large), an efficient algorithm based on the alternating direction method of multipliers is developed. Numerical simulations validate the benefits of the proposed model and the high efficiency of the algorithm.

Global minimum variance portfolios under uncertainty: a robust optimization approach This paper presents new models which seek to optimize the first and second moments of asset returns without estimating expected returns. Motivated by the stability of optimal solutions computed by optimizing only the second moment and applying the robust optimization methodology which allows to incorporate the uncertainty in the optimization model itself, we extend and combine existing methodologies in order to define a method for computing relativerobust and absoluterobust minimum variance portfolios. For the relative robust strategy, where the maximum regret is minimized, regret is defined as the increase in the investment risk resulting from investing in a given portfolio instead of choosing the optimal portfolio of the realized scenario. The absolute robust strategy which minimizes the maximum risk was applied assuming the worstcase scenario over the whole uncertainty set. Across alternate time windows, results provide new evidence that the proposed robust minimum variance portfolios outperform nonrobust portfolios. Whether portfolio measurement is based on return, risk, regret or modified Sharpe ratio, results suggest that the robust methodologies are able to optimize the first and second moments without the need to estimate expected returns.