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

62 RISKINESS LEVERAGE MODELSACKNOWLEDGEMENTThe author wishes to thank Rodney Kreps, Donald Mango, andGary Venter for their very helpful review and comments. Any errorsare the responsibility of the author.1. INTRODUCTIONRodney Kreps begins his paper by describing the genericproblem as a situation where a company holds a single pool ofshared capital to support a number of random liabilities and assets.The reserves are ordinarily meant to support their meanvalue, while the surplus is meant to support their variabilityaround their means. Kreps, and by reference Gary Venter [5],first allay actuarial concerns about allocation of capital (discussedin [3]) by pointing out that return on equity (ROE) methodsof computing pricing risk loads are really allocating the returnon capital. If a line of business is returning 10% on allocatedcapital, one should ask whether this is a sufficient return to compensatethe providers of that capital. Kreps then enumerates twodesirable qualities for allocable risk load (the product of allocatedsurplus and a target rate of return):1. It should be allocable down to any desired level.2. It should be additive, in that risk load or capital allocatedto components of the portfolio sum to the total risk loador capital need for the portfolio. This would be true forsubsets of the portfolio as well.Kreps does not insist that a risk load or capital allocationmethod satisfy all the requirements for a coherent risk measure[1], as he believes the risk measure should emerge from the fundamentaleconomics of the business rather than the desired mathematicalproperties. Thus, Value at Risk (VAR) and Tail Valueat Risk (TVAR) are both examples of riskiness leverage models,while VAR is not a coherent risk measure [1] and TVAR is well