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Sensitivity-implied tail-correlation matrices

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  • Paulusch, Joachim
  • Schlütter, Sebastian

Abstract

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.

Suggested Citation

  • Paulusch, Joachim & Schlütter, Sebastian, 2021. "Sensitivity-implied tail-correlation matrices," ICIR Working Paper Series 33/19, Goethe University Frankfurt, International Center for Insurance Regulation (ICIR), revised 2021.
    • Handle: RePEc:zbw:icirwp:3319
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    References listed on IDEAS

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    More about this item

    Keywords

    Risk aggregation; Capital allocation; Portfolio optimization;
    All these keywords.

    JEL classification:

    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation
    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill

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