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Contingent Commissions and Market Cycles. Lan Ju Mark Browne University of Wisconsin-Madison. Question. Do profit-based contingent commissions dampen the underwriting cycle?. Simple Illustration. Underwriting Margin. NC. C. Soft Mkt. Hard Mkt. Time. - PowerPoint PPT Presentation
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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 !
2007 ARIA Meeting, Quebec City
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
2007 ARIA Meeting, Quebec City
Example
$2,500,000 premiums written
Current year limited loss ratio is 30%
Contingent commission
= $2,500,000 * 0.0192 = $48,000
2007 ARIA Meeting, Quebec City
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)
2007 ARIA Meeting, Quebec City
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 !
2007 ARIA Meeting, Quebec City
Monitoring by Motivated Brokers
Insurer
Brokers
Contingent Comm.
Good Business
Clients
Identify Insurer
Long-TermRelation
2007 ARIA Meeting, Quebec City
PNC
Another Description
SLNC
SNCSNC’D SC’ SC
SLC
P
Q
PNC’
PC’
PC
2007 ARIA Meeting, Quebec City
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 !
2007 ARIA Meeting, Quebec City
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
2007 ARIA Meeting, Quebec City
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
2007 ARIA Meeting, Quebec City
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 !