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

74 RISKINESS LEVERAGE MODELSexpected underwriting return after rental cost of capital to allocatedrisk capital. It is assumed that expense items like overheadand taxes, as well as returns from any capital excess of the ratingagency required capital or from riskier investments that wouldrequire additional rating agency capital, would be handled withincorporate planning.RROC represents the expected return for exposing capital torisk of loss, as the cost of benign rental of capital has alreadybeen reflected. It is analogous to the Capital-Call Cost in theEVA approach, here expressed as a return on capital rather thanapplied as a cost. In the discussion of Tail Value at Risk, it wasobserved that Venter has noted that co-XTVAR may not allocatecapital to a line of business that didn’t contribute significantly toadverse outcomes. In such a situation, the RORAC calculationbased upon riskiness leverage models may show the line to behighly profitable, whereas RROC may show that the line is unprofitablebecause it did not cover the mean rental cost of ratingagency capital.In the EVA approach, risk preferences are reflected in thefunction selected and parameterized in computing the Capital-Call Cost. In the RROC approach, risk preferences are specifiedin the selection of the riskiness leverage model used to measurerisk. This riskiness leverage model in practice would be parameterizedto equal the total capital of the company, which wouldbe maintained to at least cover rating agency capital required tomaintain the desired rating. Both approaches utilize the RMKalgorithm for allocating risk (measured as a Capital Call Cost inEVA and as risk capital in RROC) to line of business.5. SIMULATION EXAMPLEThe RORAC and RROC approaches were tested and the resultsare summarized in the attached exhibits. Exhibit 1.1 summarizesthe examples tested, including underlying assumptions,while Exhibit 1.2 summarizes the technical differences between