Beating the correlation breakdown, for Pearson’s and beyond

Robust inference and flexible scenarios and stress testing for financial portfolios by JD Opdyke, Chief Analytics Officer, Sachs Capital Group Asset Management, LLC.

JD Opdyke

Chief Analytics Officer, Sachs Capital Group Asset Management, LLC.

We live in a multivariate world, and effective modelling of financial portfolios, including their construction, allocation, forecasting, and risk analysis, simply is not possible without explicitly modelling the dependence structure of their assets.Correlation/concordance matrices like Pearson’s product moment correlation [1], Kendall’s Tau [2], and Spearman’s Rho [3] play a fundamental and central role here. As the scaled version of the variance-covariance matrix, Pearson’s rightly shapes our views and measurements of risk, diversification, and optimal construction and allocation in a very wide range of settings, from Markowitz efficient frontiers [4], to Black-Litterman scenarios [5] and fully flexible views [6], to BIS guidance on stress tests [7]. And while the limitations of Pearson’s are arguably often overstated [8] and/or misrepresented [9], when rank-based approaches are more appropriate, Kendall’s and Spearman’s are very widely used alternatives relied upon in all major financial settings [10].Why, then, are these ubiquitous measures of correlation and dependence structure rarely treated in practice as rigorously estimated parameters like any others in these models? Why are values used for their cells in specified scenarios almost always ‘qualitative’ and informed by ‘judgment’ (if not arguably ad hoc) rather than probabilistically measured based on quantitatively determined finite sample distributions? When quantitative estimates are used, why are they rarely, if ever, associated with finite sample confidence intervals, both at the level of the entire matrix and that of the individual correlation cells, simultaneously and consistently? And why do these questions still apply to almost all stress tests ([11-14] are partial exceptions), even after major global financial crises and dramatically increased regulatory oversight worldwide? The latter is especially troubling given the widely documented ‘correlation breakdowns’ that occur during such times of extreme market stress [7,15-18], which is when risk analytics, and the (sometimes dire) consequences of the methods chosen for portfolio construction and allocation, matter the most [19-22].Methodologically, I believe there are four major reasons for this less-than-ideal state of affairs, and only one approach that solves them all simultaneously.

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References

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