1. Allocating the Cost of Capital CAS Spring Meeting – 2002 Panelists Glenn Meyers – Insurance Services Office Dan Isaacs – Conning and Company Robert Butsic – Fireman’s Fund Insurance Company

2. Allocating Capital is Controversial A policy written with a monoline automobile insurance company with $100 million of surplus is not as well protected as a policy written with a large multiline insurance company with $100 million allocated to its automobile line of insurance.” -- Chuck McClenahan I agree with Chuck on this.

3. How do people use allocated capital? Really allocating the cost of capital. Use it to set profitability targets.

4. Why Allocate the Cost of Capital? Allocating the cost of capital is an internal management tool that relates an underwriting division’s financial goal to the insurer’s corporate financial goal. Any method that makes economic sense is OK.

5. Economic Sense ??? Let P = Profit and C = Capital. Then adding a line/policy makes sense if:  Marginal return on new business  return on existing business.

6. OK - Set targets so that marginal return on capital equal to insurer return on Capital? Before I answer this, let’s discuss a property of capital requirements. Let C[X] = Capital Required to Insure X Getting C[X] is the hard problem! C[X] should satisfy the subadditivity axiom: C[X+Y] < C[X] + C[Y] The subadditivity axiom means that diversification is good.

7. OK - Set targets so that marginal return on capital equal to insurer return on Capital? The sum of marginal capitals is less than the total capital! By Subadditivity

8. Conclusions: Marginal cost of capital provides a floor on the allocated cost of capital. At least one underwriting division must have an allocated cost of capital greater that that floor. Deciding who pays more by how much is a problem. Look at business plans.

9. One Way of Allocating the Cost of Capital The Gross-Up Solution –Multiply the marginal cost of capital times a factor so that sum of allocated cost of capital equals the total capital. Is this solution fudging?

10. An Insurer Business Strategy An insurer chooses to write the risks that yields the greatest return on marginal capital. If the insurer stays in business over the long run in a stable underwriting environment, two things will happen. –The insurer will make an adequate return on capital. –The insurer’s return on marginal capital will be equal for all risks.

11. An Insurer Business Strategy An insurer chooses to write the risks that yields the greatest return on marginal capital. The long-run effect of this strategy is the same as the Gross-Up solution. I originally derived the Gross-Up solution using Lagrange multipliers in a risk load setting.

12. The George Zanjani Example Division A –Expected return of 30 –Requires capital of 120 as a standalone Division B –Expected return of 15 –Requires capital of 120 as a standalone Combine A and B –Expected return of 45 –Requires total capital of 150

13. The George Zanjani Example Division A –Expected return of 30 –Requires capital of 120 as a standalone Division B –Expected return of 15 –Requires capital of 120 as a standalone

14. The George Zanjani Example It makes sense to combine A and B. –ROE for A = 30/120 = 25% –ROE for B = 15/120 = 12.5% –ROE for A+B = 45/150 = 30%

15. The George Zanjani Example Marginal capital for A and B is 30 Gross-Up allocated capital = 75 for both A and B A’s ROE = 30/75 = 40% B’s ROE = 15/75 = 20% B does not meet overall target of 30% Do we “fire” B?

16. The George Zanjani Example A capital allocation leading to “correct” economic decision –Allocate capital of 100 to A –Allocate capital of 50 to B Both allocations are above the marginal capital “floor.” ROE = 30% for both A and B

17. An Important Qualification Duration Capital must be held longer for some lines of insurance. Allocating the cost of capital must take duration into account. Discussed in “Risk and Return” session. http://www.casact.org/pubs/forum/01spforum/meyers/index.htm

18. Summary Capital allocation really means allocating the cost of capital. Marginal capital provides a floor for allocated capital. I provided a business strategy for which allocating capital is in proportion to marginal capital is appropriate. Zanjani provides a business strategy where allocating in proportional to marginal capital is wrong. Now let’s look at other strategies.