ERM-101-12: Measurement and Modeling of Dependencies in Economic Capital

📗erm-101-12
📖erm-learning-obj-2
📖erm-learning-obj-5

#1

Reading Source: https://www.actuaries.org.uk/system/files/documents/pdf/sm20100510.pdf

Topics Covered in this Reading:

  • Correlation as the Simplest Type of Dependency
    • Dependency Structures
    • What do we mean by Dependency?
    • Pearson Correlation Coefficient
    • Spearman Coefficient
    • Kendall Tau Correlation
    • Numerical Example
  • Risk Aggregation
    • Risk Aggregation Framework
    • Risk Aggregation Methodologies
    • Simple Summation
    • Fixed Diversification Percentage
    • Variance-Covariance Matrix
    • Copulas
    • Causal Modelling
    • Natural Catastrophe vs Reinsurance Credit Risk Aggregation

ERM-101-12: Measurement and Modelling of Dependencies in Economic Capital, Ch.3
#2

I’m looking for someone to comment on when we would use Spearman Rho or Kendall Tau as a measure of correlation instead of Pearson Rho.
I’m also curious about which is more commonly used in the variance covariance approach to aggregating risk capital? The reading indicates that correlations are estimated using conventional techniques, but also that tail/quadrant correlations are used as an alternative.


#3

The Pearson Rho is the most commonly used in the variance covariance approach. It is simple to calculate and more well-known.

Spearmen Rho or Kendall Tau calculate the correlation based on the rank, and not the specific values. Therefore, these two measures are less impacted by outliers. So with a data set with a few large outliers, perhaps these would be preferred to Pearson Rho.

Does anyone else have any other situations where Spearman Rho or Kendall Tau may be preferred?