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

76 RISKINESS LEVERAGE MODELSfrom 17.50% to 17.88%, while RROC increases from 9.95% to10.05%.) However, in Example 3, a 50% quota share for line 1improves the portfolio RORAC measure by 47% (from 17.50%to 25.74%), RROC improves by 54% (from 9.95% to 15.36%),and risk capital needed to support the portfolio decreases by over40% (from $5.71 million to $3.39 million).Line 1 and the reinsurance line 4 were combined in calculatingreturns by line of business. It is interesting that the expectedreturns for lines 1 and 2 did not change very much with the purchaseof reinsurance, while the highly profitable returns for line3 declined because it is now contributing to more of the 1-in-50year adverse deviations. The portfolio returns with reinsuranceimproved because a smaller share of capital is now allocated tothe marginally profitable line 1 and greater shares of capital areallocated to the highly profitable lines 2 and 3 (this can be seenby reviewing the change in the distributions of allocated capitaldisplayed for the reinsurance examples at the bottom of Exhibit2). It is also interesting that returns for line 2 improve a littlebecause of its correlation with line 1 and because it has not beenallocated any of the cost of reinsurance.For the portfolio, Exhibit 2 also displays the Cost of CapitalReleased for the two reinsurance examples, which is the ratioof the cost of the reinsurance (decrease in expected profitabilitydue to reinsurer’s profit margin) to the decrease in capitalneeded to support the portfolio. The Cost of Capital Releasedwas modestly lower than the company’s net returns for the stoplossexample (12.6% versus 17.9% for RORAC, and 8.6% versus10.1% for RROC), but dramatically lower for the quota-share example(5.6% versus 25.7% for RORAC, and 2.1% versus 15.4%for RROC). Thus, the company’s cost to release over 40% of itscapital for other purposes was a small fraction of its net returnsfor both metrics in the quota-share example.However, the net capital allocated to the portfolio based on the150% of XTVAR standard is less than the mean rating agency requiredcapital computed for the RROC metric. It was determined