A Descent Algorithm for Constrained LAD-lasso Estimation with Applications in Portfolio Selection

Yue Shi, Chi Tim Ng, Zhiguo Feng, Ka Fai Cedric Yiu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

4 Citations (Scopus)


To improve the out-of-sample performance of the portfolio, Lasso regularization is incorporated to the Mean Absolute Deviance (MAD)-based portfolio selection method. It is shown that such a portfolio selection problem can be reformulated as a constrained Least Absolute Deviance problem with linear equality constraints. Moreover, we propose a new descent algorithm based on the ideas of ‘nonsmooth optimality conditions’ and ‘basis descent direction set’. The resulting MAD-Lasso method enjoys at least two advantages. First, it does not involve the estimation of covariance matrix that is difficult particularly in the high-dimensional settings. Second, sparsity is encouraged. This means that assets with weights close to zero in the Markovwitz's portfolio are driven to zero automatically. This reduces the management cost of the portfolio. Extensive simulation and real data examples indicate that if the Lasso regularization is incorporated, MAD portfolio selection method is consistently improved in terms of out-of-sample performance, measured by Sharpe ratio and sparsity. Moreover, simulation results suggest that the proposed descent algorithm is more time-efficient than interior point method and ADMM algorithm.

Original languageEnglish
Pages (from-to)1988-2009
Number of pages22
JournalJournal of Applied Statistics
Issue number11
Publication statusPublished - 18 Aug 2019


  • constrained LAD Lasso
  • MAD-Lasso
  • nonsmooth optimality conditions
  • portfolio selection
  • Sharpe ratio
  • sparsity

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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