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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.
Market risks account for an integral part of life insurers' risk profiles. This paper explores the market risk sensitivities of insurers in two large life insurance markets, namely the U.S. and Europe. Based on panel regression models and daily market data from 2012 to 2018, we analyze the reaction of insurers' stock returns to changes in interest rates and CDS spreads of sovereign counterparties. We find that the influence of interest rate movements on stock returns is more than 50% larger for U.S. than for European life insurers. Falling interest rates reduce stock returns in particular for less solvent firms, insurers with a high share of life insurance reserves and unit-linked insurers. Moreover, life insurers' sensitivity to interest rate changes is seven times larger than their sensitivity towards CDS spreads. Only European insurers significantly suffer from rising CDS spreads, whereas U.S. insurers are immunized against increasing sovereign default probabilities.
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.