1 CAS Ratemaking Seminar, Salt Lake, Utah March 13-14, 2006 RCM-2: Town Hall Session: Logic, Fallacies, and Paradoxes in Risk and Return Analysis in Ratemaking: Town Hall Meeting Moderator/Host/Panelist/ Referee Robert F. Wolf, FCAS, MAAA Director, Navigant Consulting, Inc. Panel Louise Francis, Consulting Principal, Francis Analytics & Actuarial Data Mining, Inc. Glenn G. Meyers, Chief of Actuarial Research and Assistant Vice President, ISO Russ Bingham, Director of Research, The Hartford Financial Services Group

2 Common Basis Robert F. Wolf, FCAS, MAAA Director, Navigant Consulting Inc.

3 CAS Statement of Principles “The underwriting profit and contingency provisions are the amounts that, when considered with net investment and other income, provide an appropriate total after-tax return.” What is Our Goal?

4 Two Issues –What’s appropriate? Risk charge for “random variation from the expected costs” must be “consistent with the cost of capital” Included in underwriting profit provision –How do you measure return? Return on what? What is Our Goal?

5 Assets Liabilities Capital Let K = Policyholder Supplied Funds = Premiums Less Loss Payments Let S = Shareholder Supplied Funds= Capital to Support Insurance Operations K S K+S Supplied Funds

6 Marginal Balance Sheet Impact Let R A = Return on Assets which supplied by both policyholders and shareholders. R L = Cost of Float. Investing policyholder Supplied funds until needed. R E = Cost of Capital. Shareholders Return on their investment K+S K S Returns R A Costs R L Costs R E

7 Marginal Balance Sheet Impact This relationship develops into the generally accepted view that an insurance company is a levered trust. K+S K S Returns R A Costs R L Costs R E Levered Trust (K+S)R A = KR L + SR E Re-Arranging S(R E –R A ) = K(R A –R L ) Let P = Premium R U = - (K/P) R L (S/P)(R E –R A ) = (K/P)R A +R U

8 Cost of Capital

9 Niche 1 Niche 2 Niche 3 Premium Discounted Combined Ratio R u =1-Disc CR xxx Total xxx Needed Capital xxx REQ CAPITAL Marginal Capital Who Cares? Now we are talking An insurer chooses to write the risks that yields the greatest return on marginal capital. In the long run, in a stable underwriting environment, the insurer will make an adequate return on capital and the insurer’s return on marginal capital will be equal for all risks.

10 Capital Allocation is necessary The best way to make risk-based portfolio composition decisions Critical element of financial product pricing Standard language of management Capital Allocation makes no sense All of the company’s capital is available to support each policy No capital is transferred at policy inception Capital is transferred via reserve strengthening How can we resolve this paradox and move forward? The “Allocating Capital “ Paradox

11 Insurance Capital is a Claims Paying Reservoir –Subject to unpredictable future inflows and outflows Likelihood and magnitude of drawdowns Co-incidence with other drawdowns Systemic shocks Huge mismatch: –Cost of Capital = Current Expense –Current underwriting activities are exposing future capital Capital is a holistic portfolio phenomenon – not meaningfully divisible –Can we allocate life to our organs? –Can we allocate the WhiteSox success to each player?

12 Myers-Read

13 Myers-Read 2003 ARIA prize winning paper Presented at 2003 Spring Meeting Also invited discussions by many CAS researchers Butsic applied it to Cat Reinsurance pricing in 1999 Reinsurance Call Paper program (prize- winner) Buckle up…

14 Myers-Read – Summary Focus on Value of Default Option of Insurer >Function of surplus, covariance of losses and assets Marginal default value for LOB i depends on required capital for LOB i, covariance, portfolio mix Covariances all add up, so marginal default values all add up under certain assumptions (stay tuned) Use this to determine unique allocation formula Elegant mathematics in a multi-variate LogNormal

15 Myers-Read – Critiques G. Meyers: demonstrates ISO insurer distributions are not homogeneous Introduces heterogeneity multiplier to make things add up A way to “make it work” S. Mildenhall: adds up if and only if distributions are homogeneous –Defined as straight linear scaling with volume, no shape change Not true for most Insurance distributions

16 Myers-Read – Critiques G. Venter: 1)Time period for option = ? 2)Sensitive to extreme tail – difficult to estimate 3)Seems like other additive methods (see RMK) 4)Aimed at allocating frictional costs of holding capital, but used as denominator in RORC formula

17 Merton-Perold

18 Merton-Perold – Summary Capital allocation to segments is meaningless Capital is held at the company level Each segment receives a guarantee from the parent company Price of guarantee could be observable in market Cost of guarantee represents risk capital Opposed to allocation exercises: –Guarantee only has meaning at company level –Order dependence

19 Mango

20 Shared Asset Usage Shared Asset Reservoir, Golf Course, Pasture, Forest, … User Community Asset owners control access rights to preserve asset, control against over-use Access Users have their own interests, often cannot see larger picture Uses are classified as either CONSUMPTIVE or NON-CONSUMPTIVE

21 Consumptive and Non-Consumptive Consumptive Permanent transfer of control of a portion of the asset to the user Aggregation risk from over- depletion Examples: –Water from reservoir –Fisheries –Timber Non-Consumptive Temporary partial transfer of control of a portion of the asset to the user Aggregation risk from exceeding capacity Examples: –Golf course –Campsites –Hotel

22 Typical Insurance Capital Allocation Required t=5 Written Premium t=5 Required Capital Formula Changes in Required Capital are attributed to imputed capital transfers to and from the Owner But no such transfers ever take place!

23 The Capital Hotel Occupancy has a time dimension and an amount dimension Return is equivalent of rental fees  should also be linear with time and amount There are also clearly opportunity costs, since occupancy of capacity (rooms) precludes it from use by others

24 Insurer Capital Is A Shared Asset Shared Asset Reservoir, Golf Course, Pasture, Hotel, … Insurer Capital User 1 User 2 User 3 User 4 Asset Owners: Control Overall Access Rights Preserve Against Depletion From Over-Use Consumes On Standalone Basis Tunnel Vision - No Awareness Of The Whole Consumes On Standalone Basis Tunnel Vision - No Awareness Of The Whole

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26 EXAMPLES

27 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

28 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

29 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%

30 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?

31 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

32 Does this example apply to insurance? Not really – Insurance decisions are made in smaller chunks. Suppose the Divisions A and B consist of a bunch of individual insurance policies. You can devise a more profitable strategy where you write a few more polices in Division A, and fewer in Division B. The Zanjani example turns capital allocation upside down by forcing you to allocate capital in proportion to the risk load.