Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation
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 def...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2019-10-01
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| Series: | Risks |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-9091/7/4/107 |
| _version_ | 1818924122873266176 |
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| author | Clive Hunt Ross Taplin |
| author_facet | Clive Hunt Ross Taplin |
| author_sort | Clive Hunt |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-20T02:20:19Z |
| format | Article |
| id | doaj.art-e8a90da8142f456eabf609ae779ba4c9 |
| institution | Directory Open Access Journal |
| issn | 2227-9091 |
| language | English |
| last_indexed | 2024-12-20T02:20:19Z |
| publishDate | 2019-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Risks |
| spelling | doaj.art-e8a90da8142f456eabf609ae779ba4c92022-12-21T19:56:50ZengMDPI AGRisks2227-90912019-10-017410710.3390/risks7040107risks7040107Aggregation of Incidence and Intensity Risk Variables to Achieve ReconciliationClive Hunt0Ross Taplin1Private Practice, Perth, WA 6009, AustraliaSchool of Accounting, Curtin Business School, Curtin University, Bentley, WA 6102, AustraliaThe 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.https://www.mdpi.com/2227-9091/7/4/107meanbasel accordifrs 9credit riskinsurance riskattributionprobability of defaultloss given default |
| spellingShingle | Clive Hunt Ross Taplin Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation Risks mean basel accord ifrs 9 credit risk insurance risk attribution probability of default loss given default |
| title | Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation |
| title_full | Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation |
| title_fullStr | Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation |
| title_full_unstemmed | Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation |
| title_short | Aggregation of Incidence and Intensity Risk Variables to Achieve Reconciliation |
| title_sort | aggregation of incidence and intensity risk variables to achieve reconciliation |
| topic | mean basel accord ifrs 9 credit risk insurance risk attribution probability of default loss given default |
| url | https://www.mdpi.com/2227-9091/7/4/107 |
| work_keys_str_mv | AT clivehunt aggregationofincidenceandintensityriskvariablestoachievereconciliation AT rosstaplin aggregationofincidenceandintensityriskvariablestoachievereconciliation |