Sparse and Group Regression models in Portfolio Optimization

Introduction

This repo contains the implementation of models studied, analysed and proposed in "The effects of Sparse and Group Regression models in Portfolio Optimization".

This implementation focuses on finding the effects of Sparse and Group regression approaches to portfolio optimization problems in finance.

Motivation

Current approaches to portfolio optimization consider stocks as individual entities, and do not exploit the grouping/classifying information available (e.g. Financial Sectors, Industries, Type, etc).

This paper proposes a novel approach to Index Tracking - namely, a sparse, group and sparse group approach.

Implementation

This repo contains the implementation of the following models:

Feature Regression Models

• Absolute Values
• Conditional-Value-at-Risk (CVaR) Optimization
• Norm-Constrained CVaR Optimization
• Lasso

Group Regression Models

• Group Selection
• Group Lasso
• Sparse Group Lasso

Requirements

This implementation requires the CVX library for solving the convex optimization problems.

Usage

Tests were built to provide intuition when implementing the Sparse Group Regression model into a set of data, however, understanding on these models is required for an effective use;