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Open AccessArticle

Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation

by Clive Hunt 1,* and Ross Taplin 2,*
1
Private Practice, Perth, WA 6009, Australia
2
School of Accounting, Curtin Business School, Curtin University, Bentley, WA 6102, Australia
*
Authors to whom correspondence should be addressed.
Risks 2019, 7(4), 107; https://doi.org/10.3390/risks7040107
Received: 22 August 2019 / Revised: 9 October 2019 / Accepted: 21 October 2019 / Published: 25 October 2019
The aggregation of individual risks into total risk using a weighting variable multiplied by two ratio variables representing incidence and intensity is an important task for risk professionals. For example, expected loss (EL) of a loan is the product of exposure at default (EAD), probability of default (PD), and loss given default (LGD) of the loan. Simple weighted (by EAD) means of PD and LGD are intuitive summaries however they do not satisfy a reconciliation property whereby their product with the total EAD equals the sum of the individual expected losses. This makes their interpretation problematic, especially when trying to ascertain whether changes in EAD, PD, or LGD are responsible for a change in EL. We propose means for PD and LGD that have the property of reconciling at the aggregate level. Properties of the new means are explored, including how changes in EL can be attributed to changes in EAD, PD, and LGD. Other applications such as insurance where the incidence ratio is utilization rate (UR) and the intensity ratio is an average benefit (AB) are discussed and the generalization to products of more than two ratio variables provided. View Full-Text
Keywords: mean; Basel Accord; IFRS 9; credit risk; insurance risk; attribution; probability of default; loss given default mean; Basel Accord; IFRS 9; credit risk; insurance risk; attribution; probability of default; loss given default
MDPI and ACS Style

Hunt, C.; Taplin, R. Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation. Risks 2019, 7, 107.

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