Dynamic Financial Analysis (DFA) Capital Allocation CAS Loss Reserve Seminar September 11, 2001

1. Dynamic Financial Analysis (DFA) Capital Allocation CAS Loss Reserve Seminar September 11, 2001 John J. Kollar

2. Insurer Value • Value as a function of present and expected earnings. • Variability of earnings requires more capital. • Capital = Cost = Business Expense • More capital means higher costs.

3. Increasing Insurer Value • What insurer operating strategy gives the largest expected return on capital? • Allocate capital to line of insurance to reflect the line’s contribution to the overall cost of capital. • Focus on lines with the greatest expected return on allocated capital relative to risk. • Reduce capital needs by exiting lines with poor returns relative to risk.

4. Increasing Insurer Value (cont’d) • Reduce capital needs by buying reinsurance. • Reinsurance stabilizes earnings. • Reinsurance is a cost. • Cost of reinsurance vs cost of capital? • How much and what reinsurance?

5. Dynamic Financial Analysis (DFA) • Definition: a process to analyze property/ casualty underwriting and investment risks • DFA meets analytic needs in changing economy • How: computer modeling to perform economic & p/c scenario testing (simulations) • Output: Possible future financial results • distribution of capital, income, etc.

6. DFA Applications • Determine the amount of capital. • Evaluate reinsurance/capital mix. • Allocate (cost of) capital by line, etc. • Set profitability targets by line, etc. • Determine pricing. • Select an investment strategy. • Plan growth - profitability vs risk.

7. DFA Benefits • Understanding risks and their impact on financials • Comprehensive/integrated/holistic risk treatment • Rating agency review • Regulatory review • Merger/acquisition valuation

8. Variability of Earnings • Key cause is the volatility of losses • Line, size, etc. • Correlation between lines • Extended settlement for long-tailed lines

9. Loss Volatility Requires More Capital } More Capital Less Capital } Expected costs

10. { Capital }Capital Low Risk Low Risk High Risk High Risk Total Total The Effect of Correlation Low Correlation High Correlation

11. Short vs Long-Tailed Lines Short-Tailed Lines Release most capital at the end of 1st year. Long-Tailed Lines Release a portion of capital at the end of each year. Year 1 Year 2 Year 3 Year 4 Year 1 Year 2 Year 3 Year 4

12. Constructing ISO Underwriting Risk Model (URM) • Claim severity distribution for ISO lines • Property Size of Loss Database (PSOLD) • Increased Limits Factors • Claim severity distributions for other lines • Workers compensation  Independent state rating bureaus • Fidelity & Surety  Surety Association of America

13. Constructing URM (Cont’d) • Calculate loss distributions by line. • Exclude “outlier” insurers. • Use data for many insurers. • Smaller insurer data has greater variability. • Include exposures, losses, claims. • Direct losses have greater variability than net. • Industry losses smooth out individual insurer differences. • Paid losses are less smooth over time.

14. Constructing URM (Cont’d) • Calculate loss distributions by line. • Use data for many years - separately  By insurer  By year  Settled claims  Open Claims  Untrended

15. Constructing URM (Cont’d) • Use industry data • By line • By settlement lag • Each claim To estimate industry parameters for claim severity distributions by maximum likelihood.

16. Constructing URM (Cont’d) • Use industry data • By insurer • By line • By settlement lag • Losses, claims, exposures, “net PPR” To estimate • Industry parameters for the claim frequency distributions by maximum likelihood  By line  By settlement lag • Correlations between lines

17. Constructing URM (Cont’d) • Estimate correlations between lines of insurance. • If bad things happen at same time, you need more capital. • Use data for many insurers to obtain reliable estimates.  Various size insurers

18. Constructing URM (Cont’d) • Develop covariance generators  Use common shock models.  Covariance generator measures magnitude of shock.  By line • “Estimating Between Line Correlations Generated by Parameter Uncertainty” • Glenn Meyers • http://www.casact.org/pubs/forum/99sforum/99sf197.pdf

19. Calculating an Insurer’s Underwriting Risk Via URM • Insurer input (minimum) • Premium by Annual Statement line  Use industry estimates for other parameters. • Insurer input (preferred) • Expected losses  By line  By settlement lag  Use catastrophe model as appropriate.  Use industry estimates for other parameters.  Can be adjusted by economic scenario generator.

20. Calculating an Insurer’s Underwriting Risk Via URM (Cont’d) • Policy Limits • Reinsurance • Use the collective risk model. • Separate claim frequency and severity analysis. • For each line of insurance: • Select a random claim count.  Use industry analysis of claim frequency. • Select random claim size for each claim.

21. Calculating an Insurer’s Underwriting Risk Via URM (Cont’d)  Use industry claim severity distributions.  Adjust for policy limits and reinsurance. • The aggregate loss for all lines = sum of all the random claim amounts for all lines. • Reflect the correlation of claim frequency across lines of insurance. • Repeat the above thousands of times (simulation) or use Fourier transforms to calculate the insurer’s aggregate loss distribution.

22. Underwriting Risk Measurement for DFA • Selected output from URM’s collective risk model. • Insurer’s aggregate loss distribution • Statistics for selected measure of risk  Tail value at risk, expected policyholder deficit, etc. • Aggregate loss distributions for subsets of insurer’s book of business  Can conduct marginal analysis.  What if insurer stops writing a line? • Input to DFA model