All practitioners involved with the (re)insurance chain of business practice risk ranking, including the insureds. The methodologies vary from theoretical, to empirical and simulation, to historical best practices and expert knowledge reliant. Regardless of the underlying theory one still needs a robust ranking metric. Here we will attempt to show that choosing a ranking metric can actually be done in a systematic manner. We will reuse and adjust ‘Mango and Mildenhall (2014)’ criteria for a capital allocation metric, and see if it fits to adopt it to selecting a risk ranking metric. We look at pure technical premium, variance, and tail value at risk (TVaR) and how they satisfy four selection criteria:
1. ‘Drill Down and Roll Up’ is the ability to back-allocate the top portfolio metric to risk components such as lines of business and single risks and reversely accumulate single and component risk ranking metrics to lines and business units. All three metrics satisfy this criteria. They are either additive or sub-additive which is sufficiently good for the practitioner.
2. “Focus on Downside in addition to Volatility”. Pure technical premium and variance, the latter being contained in the former, emphasize knowledge of volatility. While TVaR emphasizes worst case scenarios, which may lead to severe downside or even ‘utter ruin’ of the firm.
3. Perform Risk Ranking at Business Unit (BU) Level. The relative riskiness of a business unit or a single line is already implied in the accumulated total premium of the unit. The risk of the expected outcome and its variance is already priced into the total accumulated business unit premium. Premium and variance become unsuited as risk ranking measures because their relativity is already priced in by the insurer. On the other had the relative riskiness of TVaR by BU is not accounted in pricing. Practically it is not accounted in capital allocation in most or many cases, as the preferred metric is value at risk (VaR)
4. Stability and Robustness: Both metrics are affected by marginal impact to the book of business, because of dependences
among risks. A change to the profile of one risk factor affects the change of the risk profile of the whole portfolio both in terms of most likely outcomes and tail outcomes.
Lastly and overall TVaR meets ‘our criteria’ for a practical risk ranking metric in a more robust manner. The relative riskiness of other metrics is already implied in the price of insurance risk, thereby they become risk neutral and using them for ranking does not bring additional informational value to the underwriter or risk manager. TVaR being outside of the definition of the price of (re)insurance risk brings new information value to the ranking process.
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Location: Boston, MA, United States