# Semi-Definite Programming For SMRPs

### Using SDP to create sparse mean-reverting portfolios (SMRPs) with variance constraints

#### Introduction

In the previous research article, we explored the use of Monte-Carlo Minimization (MCM) as a non-convex method for finding mean-reverting portfolios. Here we will use Semi-Definite Programming (SDP) to form mean-reverting portfolios with 2 major constraints. These are variance and sparsity.

SDP is a convex method which makes it a lot more robust compared to MCM. This means that it is far better suited to longer-term pairs trading portfolios as these prioritize forming robust portfolios whereas shorter-term portfolios are best built using models that can find more complex, but also shorter-lasting relationships.