correlation – SITMO Machine Learning

Introduction

In quantitative finance, correlation matrices are essential for portfolio optimization, risk management, and asset allocation. However, real-world data often results in correlation matrices that are invalid due to various issues:

Merging Non-Overlapping Datasets: If correlations are estimated separately for different periods or asset subsets and then stitched together, the resulting matrix may lose its positive semidefiniteness.

Manual Adjustments: Risk/assert managers sometimes override statistical estimates based on qualitative insights, inadvertently making the matrix inconsistent.

Numerical Precision Issues: Finite sample sizes or noise in financial data can lead to small negative eigenvalues, making the matrix slightly non-positive semidefinite.

Correlation is everywhere in finance. It’s the backbone of portfolio optimization, risk management, and models like the CAPM. The idea is simple: mix assets that don’t move in sync, and you can reduce risk without sacrificing too much return. But there’s a problem—correlation is usually taken at face value, even though it’s often some form of an estimate based on historical data. …and that estimate comes with uncertainty!

This matters because small errors in correlation can throw off portfolio models. If you overestimate diversification, your portfolio might be riskier than expected. If you underestimate it, you could miss out on returns. In models like the CAPM, where correlation helps determine expected returns, bad estimates can lead to bad decisions.

Despite this, some asset managers don’t give much thought to how unstable correlation estimates can be. In this post, we’ll dig into the uncertainty behind empirical correlation, and how to quantify it.

Tag: correlation

Finding the Nearest Valid Correlation Matrix with Higham’s Algorithm

Introduction

Understanding the Uncertainty of Correlation Estimates