CLOSING THE BOOKS WITH PARTIAL INFORMATION By Joseph Marker, FCAS, MAAA CLRS, Chicago, IL, September 2003

2 Closing the Books with Partial information - CLRS 2003 Outline This presentation discusses the setting of Loss and LAE reserves when a “fresh” reserve analysis is not available. Shows one method in detail. Discusses this method in relation to others. Shows how method addresses Management’s reserving issues.

3 Closing the Books with Partial information - CLRS 2003 Importance of Loss and LAE Reserve This reserve is: The largest liability on the balance sheet. The balance sheet item with the greatest uncertainty. Subject to scrutiny at least quarterly.

4 Closing the Books with Partial information - CLRS 2003 Information Available at Closing Often the books are closed with no “fresh” reserve study done in time for the closing, such as  At quarter end, when reviews are not done every quarter,  At quarter end, if a “fresh” reserve review cannot be done in time.  At monthly intervals, if reviews are done every quarter. From here on, assume that we are dealing with quarterly closings.

5 Closing the Books with Partial information - CLRS 2003 Information Available at Closing At closing time, various levels of information may be available: 1. A full reserve review on data as of the current quarter, or 2. No reserve review, but actual loss development through the current quarter, e.g.: Paid and outstanding loss and loss expense by accident year. Paid and outstanding claim counts. Earned premiums and earned exposures. 3. Loss payment and written premium information only. This discussion assumes that information described in (2) is available.

6 Closing the Books with Partial information - CLRS 2003 Example: Company XYZ Company XYZ is closing its books as of 3/31/2003. A full loss reserve review is available as of 12/31/2002. Exhibit 1 shows an example of a “Roll Forward” calculation. Method compares expected and actual development during the quarter. Uses this information to modify the Selected Ultimate Loss

7 Closing the Books with Partial information - CLRS 2003 Expected Loss Development: Exhibit 1 Exhibit 1 determines the expected 1 st quarter development and payments. Shows the “chain ladder” methods (paid and incurred) through 12/2002. Separates expected development into current quarter vs. future. Requires the Selected Ultimate Loss by accident year as of 12/2002. LDF for 1 st quarter may need to be interpolated from annual factors.

8 Closing the Books with Partial information - CLRS 2003 Expected Loss Development: Exhibit 1 Calculation of 1 st Quarter Expected development Future development on each accident year equals selected ultimate minus developed loss to date (12/31/2002) The expected proportion developing in 1 st quarter is given by: [ LDF (to quarter end) – 1.0 ] divided by [ LDF (to ultimate) – 1.0 ] We need to know the proportion of the annual development expected in the 1 st quarter.

9 Closing the Books with Partial information - CLRS 2003 Expected Loss Development: Exhibit 1 Calculation of 1 st Quarter Loss Development Factor If quarterly LDFs are available, use those. If only annual LDFs are available, use interpolation. Most difficult to assess for the immediate past accident year. Reference: Richard E. Sherman, “Extrapolating, Smoothing, and Interpolating Development Factors,” PCAS LXXI (1984), pages

10 Closing the Books with Partial information - CLRS 2003 Expected Loss Development: Exhibit 1 Limitations of Exhibit 1: l Uses only the standard age-to-age LDF methods. l Does not estimate the loss amount for the current partial accident year. Exhibit 1 can also project claim counts.

11 Closing the Books with Partial information - CLRS 2003 Exhibit 2: Actual Development Exhibit 2 brings in the actual paid and developed loss for the quarter. Differences between actual and expected development lead to recalculation of the ultimate loss.

12 Closing the Books with Partial information - CLRS 2003 Revising the Selected Ultimate Loss: XYZ Company Exhibit 2 “Roll Forward” Loss Adjustment Mechanism: For Incurred Method, Ultimate Loss = Previous Ultimate Loss plus the difference between Actual and Expected 1 st Quarter development. For Paid Method, use Actual minus Expected payments to adjust the loss. Key observations about this adjustment mechanism: For Incurred Method, the Ending IBNR at 3/2003 depends only on expected development. For Paid Method, the Ending Total Reserve depends only on the expected payments.

13 Closing the Books with Partial information - CLRS 2003 Closing the Books with Partial information - CLRS 2003 Comments on Exhibit 1 Ultimate Loss If the “tail” is lengthening, this procedure understates reserves compared to fresh analysis. More stable, less responsive than fresh analysis. May be used to “screen” lines of business for deeper analysis when actual and expected development vary significantly.

14 Closing the Books with Partial information - CLRS 2003 Comments on Exhibit 1 Ultimate Loss Management relates well to the concept of comparing Actual and Expected development. Since IBNR is determined independently of actual development, reserve discussions can begin before the quarter end.

15 Closing the Books with Partial information - CLRS 2003 Current Accident Year We have not discussed setting reserves for the current accident year To do this, use exhibits where projections are based on: l Bornhuetter-Ferguson methods rather than straight LDF methods l Pricing projections will likely be the key information used. Common methods for estimating the current accident year are l Fix the loss ratio based on pricing studies l Using the loss ratio and the projected development pattern, adjust the loss ratio by the difference between actual and expected emergence. l Use frequency-severity methods and track claim count reporting.

16 Closing the Books with Partial information - CLRS 2003 Current Accident Year Calculation is tricky for 2 nd and 3 rd quarter reserves. LDFs account for future losses for the entire accident year. IBNR reserve includes only future development on losses with accident dates in the partially completed year.

17 Closing the Books with Partial information - CLRS 2003 Summary When closing the books without a current reserve evaluation, use the actual development to date to modify previous reserve estimates. Deal with quantities that make sense to management, such as Actual versus expected development. Keep the explanatory exhibits simple and few. Use the exhibits to involve other disciplines in explaining variances.

18 Closing the Books with Partial information - CLRS 2003

19 Closing the Books with Partial information - CLRS 2003