Generate Sector-Correlated Equity Returns and GBM Price Paths

Summary

This document explains how to create synthetic equity price scenarios with a sector-based correlation structure. Assets are assigned to sectors; pairwise correlations are sampled from different ranges for same-sector, ordinary cross-sector, and selected negatively related sector pairs. The matrix is then adjusted to be positive semi-definite and normalized to have unit diagonal values.

Correlated geometric Brownian motion paths are generated by applying a Cholesky factor of that matrix to independent normal shocks, then using the shocks in a discretized GBM price update. The example describes visualizing the correlation matrix and sample paths, and inspecting summary statistics. Synthetic scenarios can support portfolio stress testing, backtest debugging, and model development, but the article does not validate their realism against historical returns. GBM also imposes simplified return dynamics, and the generated correlation structure depends on chosen sector assignments and sampling ranges.

Key ideas

• Sector assignments can create higher within-sector correlations and distinct cross-sector relationships.
• Eigenvalue adjustment and diagonal normalization make a sampled matrix suitable as a correlation matrix.
• Cholesky decomposition converts independent normal shocks into shocks with the target correlation structure.
• The resulting correlated shocks can drive multiple discretized GBM price paths.
• Synthetic data is useful for controlled scenarios, but its realism depends on the modeling assumptions.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.