September 11, 2001 Thomas L. Ghezzi, FCAS, MAAA Casualty Loss Reserve Seminar Call Paper Program Loss Reserving without Loss Development Patterns - Beyond Berquist Sherman

2 We used a few simplifications to keep this understandable We made up the data We select development factors based on the volume weighted average of the last three diagonals We tried to keep to a minimum the number of slides with lots of numbers that are hard to read

3 The data is constructed to allow for variations in reporting and payment patterns Ultimate losses based on hypothetical frequency and severity assumptions Annual trend of 5% per year  1% frequency  4% severity We include ten years in the data Ten year total ultimate losses of $766.5 million Hypothetical development patterns applied to the hypothetical ultimates to derive loss development data Variation in the patterns used to create hypothetical scenarios

4 We derived four scenarios to test the accuracy of various reserving techniques Scenario 1 (“Base Scenario”) - Stable settlement and reserving patterns Scenario 2 - Case reserve strengthening Assumes about six months acceleration in reporting pattern Scenario 3 - Settlement rate acceleration Assumes about six month acceleration in claim settlement and loss payment patterns Scenario 4 - Case reserve strengthening and settlement rate acceleration Assumes about six month acceleration in reporting and payment patterns

5 The loss reporting and payment patterns underlying the base scenario are as follows

6 In a stable environment, loss reserving is easy. An incurred loss triangle might look like this...

7 … and a paid triangle might look like this...

8 … and simple projections all give the same result

9 Introducing changes to the settlement and case reserving patterns expose weaknesses in traditional loss development analyses Scenario 2 - Case Reserve Strengthening Traditional loss development factor (LDF) projection based on incurred data will underestimate the amount of strengthening This results in over- projection of ultimate losses Ten year total projection is $796.0 million  $29.5 million higher than the actual ultimates of $766.5 million The misestimate for 12 months alone causes the projected ultimates to be too high by 17.8% ($111.4 m vs $94.5 m)

10 Changes in the settlement rate and payment patterns can be even more significant of a distortion Scenario 3 - Settlement Rate Acceleration Traditional LDF projection using paid losses results in over-projection of ultimate losses Ten year total projection is $840.7 million  $74.2 million higher than the actual ultimates of $766.5 million This error causes a 38% over-projection on the latest year ($130.8 m vs $94.5 m)

11 Loss reserving in a changing claim settlement or case reserving environment requires advanced techniques, and significant judgment Berquist-Sherman (PCAS LXIV, p123) Judgmental adjustments to “prior diagonals” to approximate the settlement rate and or case reserve levels on the current diagonal Adjusted Actua l Adjusted Loss Development Factors Adjusted loss development pattern applied to the unadjusted (actual) data

12 The techniques in this call paper adjust the latest diagonal instead of the prior data Ultimate Closed Claim Severity Technique Projects ultimate losses using traditional methods Calculates implied unpaid loss triangle Repeat this approach for claims to get estimated unclosed claims triangle Ratio of the unpaid loss triangle to unclosed claim triangle gives the estimated unclosed claim severity triangle minusequals Projected Ultimates Paid to Date Estimated Unpaid

13 The unclosed claim severity triangle is used to estimate the latest diagonal severities consistent with the historical data

14 When there are changes in patterns, this method replaces the “distorted” latest diagonal with an adjusted diagonal consistent with prior periods

15 The second new technique in this paper does not use loss development factors for any year Incremental Closed Claim Severity Method Calculates incremental paid losses and closed claims for each year between evaluation points Calculates incremental closed claim severity triangle The historical incremental closed claim severities are used to estimate future incremental severities Historical closed claim data is used to estimate future incremental closed claims Increm. Paid Losses Increm. Closed Claims Increm. Closed Claims Severity divided by equals

16 The “sumproduct” of severities and closed claims “below the diagonal” provides an estimate of the remaining closed claim severities by year

17 When there are changes in patterns, this method mostly avoids the “distorted” diagonals

18 These severities are used to estimate ultimate losses

19 In summary, the new methods provide significant improvement in projection accuracy As with all techniques, they produce the correct result in a stable environment With changes in case reserve adequacy and/or settlement rates, they are much more accurate

20 All methods work when life is stable and predictable

21 But the adjusted methods are more accurate when things are changing

22 These new techniques do not necessarily produce a better adjustment than the traditional advanced techniques. However... They may be more understandable to company management They allow explicit reflection of known changes in mix of business or other factors that affect trend They allow easy combination of case reserve and settlement rate adjustments They work equally well with calendar year changes and accident year changes They reflect recent claim frequency experience They provide reasonableness testing for more traditional methods

23 We used many simplified approaches and assumptions. Refinements are possible Use unpaid claim severities instead of unclosed More sophisticated forecasting techniques Blending with “post-change” experience Reasonableness testing implied loss ratios, severities, pure premiums Sensitivity testing