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

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.

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.

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?

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

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

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

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

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

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

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.

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

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.

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

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

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

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.

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.

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.

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.

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

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

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