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Allocating the Cost of Capital CAS Spring Meeting – 2002 Panelists

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. Allocating Capital is Controversial.

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Allocating the Cost of Capital CAS Spring Meeting – 2002 Panelists

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  1. Allocating the Cost of CapitalCAS Spring Meeting – 2002Panelists 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? • Use it to set profitability targets. • Really allocating the cost of capital.

  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? By Subadditivity • The sum of marginal capitals is less than the total capital!

  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 QualificationDuration • 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.

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