Excerpt From The Economics of Capital Allocation (Also presented at Bowles Symposium)

1. Excerpt FromThe Economics of Capital Allocation(Also presented at Bowles Symposium) Glenn Meyers Insurance Services Office, Inc.

2. Summary of Myers/Read Result • Allocate capital in proportion to marginal capital. • Instantaneous marginal capital • Assumes capital is a continuous function of exposure.

3. Summary of Myers/Read Result • Define: If the random loss X = U·e for exposure measure e and random number U, then the distribution of X is homogeneous with respect to e. • If all losses are homogeneous with respect to exposures, the constant of proportionality in the allocation formula is equal to one. • Steve Mildenhall shows that this assumption is necessary and well as sufficient for the Myer/Read result to hold.

4. Is Homogeneity a State of Nature? • Homogeneity says that • This can be checked empirically. • Data set with 460 normalized deviations of 46 insurers, 10 years http://www.casact.org/pubs/forum/03spforum/03spf069.pdf • Form high and low expected loss groups of 230 observations each. • Empirically test to see if distributions of normalized deviations are identical.

5. If distributions are identical, then the QQ plot lies on line.

6. Range of Small E’s is greater than range of big E’s

7. What happens if you drop the homogeneity assumption? • Assume efficient company behavior • Company maximizes return on capital • Capital is a scarce resource (i.e. limited) • Return on marginal capital is equal for all lines. • If not you can replace exposure in one line with exposure in another line and increase return on capital • So far, similar to Myers/Read • If you drop homogeneity, the constant of proportionality is greater than one.

8. What happens if you drop the homogeneity assumption? Allocated Capital Equals Marginal Capital x Heterogeneity Multiplier • Allocation is unique and not arbitrary

9. Does dropping the homogeneity assumption make a significant difference? • Examples in papers by Meyers, Klinker and Lalonde • Reinsurance Call Paper Program – 2003 Spring Forum • Multiplier = 1.64 • Capital Management Call Paper Program To appear in 2003 Summer Forum • Multiplier = 1.50 for large insurer • Multiplier = 2.43 for small insurer

10. Further Discussion After Presentation • While acknowledging that homogeneity might be a problem with the theory, Professor Myers expressed some doubt that heterogeneity would be a problem with a reasonably sized insurer. • My assertion is YES. As evidence I offered the heterogeneity multipliers on the previous slide. I don’t think they made the point, so I am trying again.

11. Additional Details on the Small and Large Insurers • Total expected loss • $221 Million for small insurer • $2,215 Million for large insurer • Exposure of large insurer is exactly ten times that of the small insurer. • If homogeneity is even approximately true the QQ plot of the modeled normalized deviations of the two insurers should lie on the 45° line.

12. Range of small insurer is greater than range of large insurer