1. Cost of Capital Issues
April 16, 2002
John J. Kollar

2. Insurer Value Value as a function of present and future 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. Variability of Earnings
Key cause is the volatility of losses
Line, size, etc.
Correlation between lines
Extended settlement for long-tailed lines

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

7. Terrorism Loss Volatility
Expected Cost = ?
Greater Uncertainty
> > Capital

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

9. Terrorism Correlation/Concentration
Across Lines
Property
Liability WC
> > Capital
Charge more for account underwriting?

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

11. 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.

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

13. 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.

14. 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

15. 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

16. 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

17. Constructing URM (Cont’d)
Boundaries of Terrorism Risk
Unlimited today?
But shrinking
Terrorism Modeling (All Lines)
Making it measurable, sort of
Generating an all lines loss distribution
Like catastrophes, terrorism can cause many claims from the same event.

18. 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
 Unsettled claims by accident year.
 Use catastrophe model as appropriate.
 Can be adjusted by economic scenario generator.

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

20. 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.

21. Calculating an Insurer’s Underwriting Risk Via URM (Cont’d)
Selected output from URM’s collective risk model.
Insurer’s aggregate loss distribution
Statistics for selected measure of risk
 Standard deviation, tail value at risk, etc.
Aggregate loss distributions for subsets of insurer’s book of business
 Line
 State

22. Pricing - Capital Analysis
Determine (range of) expected cost from aggregate loss distribution
Determine needed capital/insurance
Calculate/select expected cost
Incorporate cost of capital

23. Circle of Insurer Life Regulatory action Risk Management Underwriting
Concentration
Underwriting
Account underwriting