2007 ARIA Meeting, Quebec City

Contingent Commissions and Market Cycles

Lan Ju

Mark Browne

University of Wisconsin-Madison

2007 ARIA Meeting, Quebec City

Question

Do profit-based contingent commissions dampen the underwriting cycle?

2007 ARIA Meeting, Quebec City

Simple Illustration

Time

C

NC

Soft Mkt Hard Mkt

Underwriting Margin

2007 ARIA Meeting, Quebec City

Background on Contingent Commission Compensation Structure to Brokers - Direct Commissions (Traditionally) - Contingent Commissions Profit-based Volume-based ( PSA )

Current Issue: - RIMS against supplemental commissions

Focus !Focus !

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A Portion of Contingent Commission Bonus Matrix

Current Year Limited Loss Ratio(%) <30 30.1- 34 34.1- 37 37.1- 40 40.1- 43 43.1- 46

Premiums Written($)

<249,999 0.00 0.00 0.00 0.00 0.00 0.00

250,000-499,999 0.80 0.71 0.63 0.56 0.50 0.45

500,000-999,999 1.18 1.06 0.95 0.86 0.77 0.70

1,000,000-1,999,999 1.74 1.58 1.44 1.31 1.19 1.08

2,000,000-2,999,999 1.92 1.74 1.58 1.44 1.31 1.19

3,000,000-3,999,999 2.11 1.92 1.74 1.58 1.44 1.31 Source: CNA 2006 Addendum to Agency Agreement

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Example

$2,500,000 premiums written

Current year limited loss ratio is 30%

Contingent commission

= $2,500,000 * 0.0192 = $48,000

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Relevant Literature – Market Cycles Rational Expectation Theory: Perfect market - Cummins and Outreville (1987)

Capacity Constraint Theory: Not perfect market - Winter(1988, 1991a, 1994) - Gron (1994) - Cummins and Danzon(1992) - Doherty and Garven(1995)

Risky Debt Theory: Insurer’s default risk - Harrington et. al. (1988,1994, 2004, 2005) - Cummins and Danzon(1997)

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Harrington (2004 & 2005)

Proxy: Loss ratio development = Developed loss ratios -

Originally reported loss ratios

Argument: - Premium growth in the soft market is positively

correlated with loss ratio development - Excessive price cuts in the preceding soft market are

associated with upward claims costs development in the subsequent hard market Trigger the formation of hard market !

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Monitoring by Motivated Brokers

Insurer

Brokers

Contingent Comm.

Good Business

Clients

Identify Insurer

Long-TermRelation

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PNC

Another Description

SLNC

SNCSNC’D SC’ SC

SLC

P

Q

PNC’

PC’

PC

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Hypothesis and Data

Data: - NAIC 1997-2005 - 5-year loss development - Focus on latter part of soft market 97-00

Hypothesis: - Insurers who pay greater contingent commissions are associated with smaller loss ratio development Cycles are dampened !

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Modeling (Firm-Specific Approach)

Problem: Endogeneity

LRDi,t = α + β1LnGrowthi,t + β2CONCOMi,t

+ β3ROAi,t + β4RBCi,t + β5Herfindahli,t + β6Longtaili,t + β7Sizei,t + β8Stocki,t+ β9Groupi,t + εi,t

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First-Stage: Tobit Regression

CONCOMi,t = α + β1ROAi,t + β2 RBCi,t + β3 Herfindahli,t + β4Longtaili,t + β5Sizei,t + β6 Stocki,t

+ β7Groupi,t + εi,t

Second-Stage: IV Regression (Primary Interest) LRDi,t = α + β1LnGrowthi,t + β2 PredCONCOMPredCONCOMi,ti,t + β3ROAi,t

+ β4RBCi,t + β5 Herfindahli,t + β6 Longtaili,t + β7 Sizei,t + β8Stocki,t + β9Groupi,t + εi,t

Two-Stage Regression

2007 ARIA Meeting, Quebec City

IV Regression (97-00, N=3,043)

Covariates Estimate Robust Std. Error

Intercept -0.3667 0.4376

LnGrowth 0.1644 0.09321*

PredCONCOM -10.1420 1.2252***

ROA -0.3368 0.08665***

RBC 0.000548 0.000732

Herfindahl -0.2769 0.1378**

Longtail -0.1551 0.09797

Size 0.03487 0.02072*

Stock 0.1514 0.01584***

Group 0.01540 0.05907

-2log likelihood 9181.1

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Conclusion

Consistent with Prior Literature:

Stronger Premium Growth Greater LRD New Findings:

Greater contingent commission payments

Less severe upward loss development Further Research:

- Longer period of data

- Incorporate multi-period theoretical model

2007 ARIA Meeting, Quebec City

Thank You !