Estimating Forward-Looking Stock Correlations from Risk Factors

Abstract

This study provides fully mathematically and economically feasible solutions to estimating implied correlation matrices in equity markets. Factor analysis is combined with option data to receive ex ante beliefs for cross-sectional correlations. Necessary conditions for implied correlation matrices to be realistic, both in a mathematical and in an economical sense, are developed. An evaluation of existing models reveals that none can comply with the developed conditions consistently. This study overcomes this pitfall and provides two estimation models via exploiting the underlying factor structure of returns. The first solution reformulates the task into a constrained nearest correlation matrix problem. This method can be used either as a stand-alone instrument or as a repair tool to re-establish the feasibility of another model’s estimate. One of these properties is matrix invertibility, which is especially valuable for portfolio optimization tasks. The second solution transforms common risk factors into an implied correlation matrix. The solutions are evaluated upon empirical experiments of S&P 100 and S&P 500 data. They turn out to require modest computational power and comply with the developed constraints. Thus, they provide practitioners with a reliable method to estimate realistic implied correlation matrices.

Keywords

• risk factors
• implied correlation
• equity risk
• factor analysis
• invertible matrix
• correlation matrix