SparsePortfolioSelection

Description

SparsePortfolioSelection is a Julia package which computes sparse L2-regularized efficient Markowitz portfolios. Sparsity is enforced explicitly via a cardinality constraint (or by penalizing cardinality, if you edit one line of the code), which is implemented by decomposing the problem as a mixed-integer linear programming and imposing cuts via outer-approximation. The algorithm is warm-started using a quasi-ADMM method with random-restarts and subsequently solves quadratic programs at each iteration to generate cuts.

Development Notes

This package should be used at your own risk. If you run into any issues, please file them here.

A High-Level Overview

I gave a high-level talk on this package at INFORMS 2018. The slides are available here

Installation and set up

In order to run this software, you must install a recent version of Julia from http://julialang.org/downloads/. The most recent version of Julia at the time this code was last tested was Julia 1.2.0.

A number of packages must be installed in Julia before the code can be run. They can be added by running:

using Pkg' 'Pkg.add("JuMP, MathProgBase, CPLEX, Random, LinearAlgebra, Mosek, JLD, LaTeXStrings, DataFrames, Test, Suppressor, DelimitedFiles, CSV, StatsBase")

At this point, the file "core.jl" should run successfully.

Reproducing output from the paper

You can reproduce Tables 3-9 by running the script "createTablexResults.jl", where x is the relevant table number. Note that you will need to manually change the cardinality constraint right-hand-side value (i.e. run each script seperately for k=5, 10, 20), and change the file path to point to the right file on your system. Note that all experiments were run using Julia 1.2, JuMP.jl 0.18.5, CPLEX 12.8.0 and Mosek version 9.0. More up to-date versions of Julia, CPLEX or Mosek should be fine, but the code will not work with JuMP.jl 0.19 or higher (at least, without rewriting the code to be compliant with the new JuMP callbacks-feel free to open a PR if you would like to change this).

Data sources

Some of the instances in this package is sourced from this publicly available dataset. To make the user's life easier, we have included this data in the data/ folder.

Citing SparsePortfolioSelection.jl

If you use SparsePortfolioSelection.jl, we ask that you please cite the following paper:

@article{BCw_sparse2018,
	title = {A scalable algorithm for sparse portfolio selection},
	journal = {arXiv preprint arXiv:1811.00138},
	author = {Bertsimas, Dimitris and Cory-Wright, Ryan},
	year = {2018}
}

Another paper which could potentially be useful to look at is the following paper, which generalizes our approach to a broader class of MIOs with logical constraints.

Thank you

Thank you for your interest in SparsePortfolioSelection. Please let us know if you encounter any issues using this code, or have comments or questions. Feel free to email us anytime.

Dimitris Bertsimas [email protected]

Ryan Cory-Wright [email protected]