Sensitivity-implied tail-correlation matrices - Joachim Paulusch; Sebastian Schlütter (Goethe University Frankfurt, International Center for Insurance Regulation (ICIR), 2021)
Tail-correlation matrices are an important tool for aggregating risk measurements across risk categories, asset classes and/or business segments. This paper demonstrates that traditional tail-correlation matrices|which are conventionally assumed to have ones on the diagonal|can lead to substantial biases of the aggregate risk measurement's sensitivities with respect to risk exposures. Due to these biases, decision-makers receive an odd view of the effects of portfolio changes and may be unable to identify the optimal portfolio from a risk-return perspective. To overcome these issues, we introduce the "sensitivity-implied tail-correlation matrix". The proposed tail-correlation matrix allows for a simple deterministic risk aggregation approach which reasonably approximates the true aggregate risk measurement according to the complete multivariate risk distribution. Numerical examples demonstrate that our approach is a better basis for portfolio optimization than the Value-at-Risk implied tail-correlation matrix, especially if the calibration portfolio (or current portfolio) deviates from the optimal portfolio.
Keywords: G22; G28; G32; 330; Risk aggregation; Capital allocation; Portfolio optimization