PROCEEDINGS May 15, 16, 17, 18, 2005 - Casualty Actuarial Society

RISKINESS LEVERAGE MODELS 33There are several desirable qualities for an allocatable riskload formulation: (1) it should be able to be allocated to anydesired level of definition; (2) the risk load allocated for anysum of random variables should be the sum of the risk loadamounts allocated individually; (3) the same additive formulais used to calculate the risk load for any subgroup or group ofgroups.This means that senior management can allocate capital toregions, and then regional management can allocate their capitalto lines of business, and the allocations will add back up to theoriginal. Further, it also means that the lines of business will addto the allocations for total lines of business as seen at the seniormanagement level.Ultimately, the choice of the riskiness leverage function willreflect management attitudes toward risk. The intention of thispaper is to provide an interpretable framework for infinitelymany choices, all of which can be appropriately allocated. It willbe argued that the risk load must be considered in the context ofthe capital to support the risk.Once management has experimented with various riskinessleverage functions and found a formulation with which they arecomfortable, then it can be used to evaluate potential managementdecisions quantitatively. For example, buying reinsuranceor choosing between reinsurance programs can be framed byincluding the variables representing the reinsurance cash flows.The general effects from a well-designed program will be to increasethe mean cost–because the reinsurer needs to make aprofit, on average–and to decrease the risk load and its associatedcost–because the reinsurance is a good hedge againstsevere outcomes. If there is a net reduction in total cost, thenthere is an advantage to the alternative. It is worth noting that nofinancial information except the price is needed from the reinsurer.In particular, whatever return the reinsurer may think hewill get from the contract is irrelevant to the cedant’s decisionto buy or not.