‘‘Reinsurance Bad Debt’Reinsurance Bad Debt’

ByBy

Peter Matthews & Paul Murray Peter Matthews & Paul Murray

CAS Reserving SeminarCAS Reserving Seminar

September 18th 2000September 18th 2000

Reinsurance Bad Debt

Reserve for the risk of non-realisation of the full value of current and

projected reinsurance recoveries

Security Risks

• Slow payments

• Disputes

• Liquidations

• Run-offs

• Inadequate commutation receipts

• Non-payment by intermediaries

USA Insolvencies v Combined Loss Ratios

Source: A.M.Best-Insolvencies / Swiss Re - Loss Ratios

69 8

11

27

54

30

25

42

54

38

44

63

37

18

79

24

8

0

10

20

30

40

50

60

70

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99

Year

Num

ber

of In

solv

enci

es

90

95

100

105

110

115

120

Com

bine

d Lo

ss R

atio

s

?

Combined Loss Ratio

Source: A.M.Best

Historical USA Insolvency Rate

-

0.50

1.00

1.50

2.00

2.50

80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

Year

Inso

lven

cy R

ate

%

0

10

20

30

40

50

60

70

Num

ber o

f Ins

olve

ncie

s

Annual Insolvency Rate %

Broad Brush Approach 1

Bad Debt =

% of Future R/I Recoveries

+Ledger Unpaid Balance Write-Off

Broad Brush Approach 2

• Assume X% future annual default rate (say 1%)

• Discount future R/I recoveries at X% p.a. (PV1)

• Bad Debt =Undiscounted Future R/I Recoveries -PV1 + Ledger Unpaid Balance Write-Off

Broad Brush ApproachAdvantages Disadvantages• Easy to calculate and

explain

• No need to understand R/I program

• Not reinsurer specific

• Difficult to justify

• No use of R/I structure

• No use of agency security ratings (AM Best, S&P, Moody’s)

• Cannot measure or change influence of any one individual reinsurer

• Cannot react to individual large loss scenarios

• Cannot be used for commutation purposes

A More Detailed Approach

• Understand outwards programs

• Estimate ultimate outwards claims recoveries

• Identify the reinsurers behind each outwards contract

• Allocate security risk factor to each reinsurer

• Sum over all reinsurers and contracts

Structure of Outwards Reinsurance Program

Property XL

Property

Property QS

General XL

Whole Account XL

Casualty XL

Casualty

Casualty QS Aviation

Marine

0.0

0.1

0.4

0.9

1.6

2.5

3.6

4.9

6.4

8.1

US Dollars(Millions)

0.0 1.0 2.0 3.0 4.0 5.0

Reinstatements

Casualty Account - 1997

1.50 xs 1.00

1.50 xs 2.501.50 xs 2.50

1.50 xs 4.001.50 xs 4.00

1.00 xs 5.501.00 xs 5.50

1.00 xs 6.501.00 xs 6.50

1.00 xs 7.501.00 xs 8.50

0.75 xs 0.25

0.0

0.1

0.4

0.9

1.6

2.5

3.6

4.9

6.4

8.1

US Dollars(Millions)

0.0 1.0 2.0 3.0 4.0 5.0

Reinstatements

Casualty Account - 1997Evented Losses

1.50 xs 1.00

1.50 xs 2.501.50 xs 2.50

1.50 xs 4.001.50 xs 4.00

1.00 xs 5.501.00 xs 5.50

1.00 xs 6.501.00 xs 6.50

1.00 xs 7.501.00 xs 8.50

0.75 xs 0.25

Cover Remaining

Loss 1

Loss 2

Loss 3

Loss 4

Loss 5

Loss 6

Loss 7

0.0

0.1

0.4

0.9

1.6

2.5

3.6

4.9

6.4

8.1

US Dollars(Millions)

0.0 1.0 2.0 3.0 4.0 5.0

Reinstatements

Casualty Account - 1997Paid and Outstanding Aggregate Losses

Cover Remaining

O/S

Paid

Loss Types

• Projected Events – Hurricanes, Earthquakes, Air Disasters

• Aggregate Losses – Asbestos by Insured

• Evented Losses not individually projected

• Attritional Losses – Quota Share

Estimate R/I Recoveries

• Projected events• Aggregate losses• Other evented losses

• Attritional losses

• Review results

- Apply Class Incurred to Ultimate Factors and present to R/I Program

- Apply Class Incurred to Ultimate Factors and present to Proportional R/I Program

}Present to R/I Program

Most Recent R/I Years

• Review earlier years experience

• Apply expected recovery loss ratios

• Discuss and review results with underwriters

Calculate R/I Reserve

• For each R/I contract calculate:

Reserve = (O/S + IBNR)

less

Future Reinstatement Premiums

equals

R/I Reserve

0.0

0.1

0.4

0.9

1.6

2.5

3.6

4.9

6.4

8.1

US Dollars(Millions)

0.0 1.0 2.0 3.0 4.0 5.0

Reinstatements

Casualty Account - 1997Aggregate Losses

1.50 xs 1.00

1.50 xs 2.501.50 xs 2.50

1.50 xs 4.001.50 xs 4.00

1.00 xs 5.501.00 xs 5.50

1.00 xs 6.501.00 xs 6.50

1.00 xs 7.501.00 xs 8.50

0.75 xs 0.25

Cover Remaining

IBNER High

IBNER Medium

IBNER Low

O/S

Paid

0.0

0.4

1.2

2.4

4.4

6.8

9.6

12.8

16.4

20.4

US Dollars(Millions)

1988 1990 1992 1994 1996 1998

Casualty Account - All YearsUltimate Loss Experience

Cover Remaining

IBNER High

IBNER Medium

IBNER Low

O/S

Paid

0.0

0.8

3.2

6.4

10.8

16.0

US Dollars(Millions)

0.0

2.0

4.0

Reinstatements1988

1991

1994

1997

Casualty Account - All YearsUltimate Loss Experience

Cover Remaining

IBNER High

IBNER Medium

IBNER Low

O/S

Paid

0.0

0.4

1.2

2.4

4.4

6.8

9.6

12.8

16.4

20.4

US Dollars(Millions)

1988 1990 1992 1994 1996 1998

Casualty Account - All YearsAll Reinsurers

REINSURER J

REINSURER I

REINSURER H

REINSURER G

REINSURER F

REINSURER E

REINSURER D

REINSURER C

REINSURER B

REINSURER A

Unknown

0.0

0.4

1.2

2.4

4.4

6.8

9.6

12.8

16.4

20.4

US Dollars(Millions)

1988 1990 1992 1994 1996 1998

Casualty Account - All YearsReinsurer A

45.8%

70.0%

53.1% 52.1% 48.5%36.3%

51.3%

45.5% 56.4%

74.5% 75.1% 73.6% 67.8%

42.5%

51.2%

48.9%

49.8% 57.9%

Other Contracts

Cover Remaining

Other Security

IBNER High

IBNER Medium

IBNER Low

O/S

Paid

1,400.0

1,600.0

1,800.0

2,000.0

2,400.0

2,800.0

US Dollars(Thousands)

Jan-1990 Apr-1990 Jul-1990 Oct-1990 Jan-1991

Casualty Account - All YearsReinsurer A (Zoomed)

500 xs 1,000

53.1%

1,000 xs 1,500

1,000 xs 2,500

45.5%

1,000 xs 1,500

1,000 xs 2,500

56.4%

1,000 xs 1,500

1,000 xs 2,500

500 xs 1,000 500 xs 1,000 500 xs 1,000

1,000 xs 1,500

1,000 xs 2,500Other Contracts

Other Security

IBNER Medium

IBNER Low

O/S

Paid

© English Matthews Brockman 2000

Basic Summary of Agency Rating Categories

Security Level

Secure 1 AAA extremely strong A++ superior Aaa exceptional2 AA very strong A+ superior Aa excellent3 A strong A, A- excellent A good4 BBB good B++, B+ very good Baa adequate

Vulnerable 5 BB marginal B, B- fair Ba questionable6 B weak C++, C+ marginal B poor7 CCC very weak C, C- weak Caa very poor

7+extremely poor/weak, understate supervision, liquidation,rating

suspended, not rated

S & P A M Best Moody's

Allocate Security Levels

Reinsurer Security Level S & P Description

A 3 Strong

B 1 Extremely Strong

C 2 Very Strong

D 6 Weak

E 4 Good

F 5 Marginal

0.0

0.4

1.2

2.4

4.4

6.8

9.6

12.8

16.4

20.4

US Dollars(Millions)

1988 1990 1992 1994 1996 1998

Casualty Account - All YearsReinsurer Security

Disasterous

Very Weak

Weak

Marginal

Good

Strong

Very Strong

Extremely Strong

Unknown

Source: Standard & Poor's

Sample Default Rates (%)Mean Term Years

Security Level

1 2 3 4 5 6 10 15+

1 .0 .0 .1 .1 .2 .4 1.0 1.1

2 .0 .0 .1 .2 .4 .5 1.0 1.1

3 .1 .1 .2 .4 .6 .8 1.8 2.3

4 .2 .4 .7 1.2 1.7 2.2 3.7 4.2

5 .9 3.0 5.2 7.3 9.3 11.2 15.1 16.8

6 4.7 9.9 14.3 17.4 19.7 21.3 25.6 26.4

7 18.9 26.0 31.0 35.1 39.0 39.9 42.7 42.7

Sample Class Bad Debt Default %s

Property Aviation Marine Casualty

Security Level

Mean Term 2 yrs 3 yrs 4 yrs 10yrs

1 Extremely Strong

.0 .1 .1 1.0

2 Very Strong .0 .1 .2 1.0

3 Strong .1 .2 .4 1.8

4 Good .4 .7 1.2 3.7

5 Marginal 3.0 5.2 7.3 15.1

6 Weak 9.9 14.3 17.4 25.6

Calculate Bad Debt

• Select the bad debt factor for each reinsurer appropriate to each class of business.

• Apply the bad debt factor for each respective reinsurer to the reinsurance reserves within each contract.

• Sum over all contracts, all programs and all years.

0.0

0.4

1.2

2.4

4.4

6.8

9.6

12.8

16.4

20.4

US Dollars(Millions)

1988 1990 1992 1994 1996 1998

Casualty Account - All YearsEstimated Recoveries and Bad Debt

Cover Remaining

Paid

Good Debt

Bad Debt

Sensitivity of Bad Debt to Rating Selection

0%

100%

200%

300%

400%

500%

600%

+2 +1 0 -1 -2

Security Level

Per

cen

tag

e o

f O

rig

inal

Detailed ApproachAdvantages

Disadvantages• Closer to reality• Better understanding of R/I

program• Auditable• Allocation by reinsurer• Principal to principal set-off• Better feedback to Underwriters

and Management• Better actuarial advice w.r.t.

processing and purchasing of reinsurance

• Observe aging of bad debt

• Time and effort

Future Developments

• Use in DFA models• Test a wide variety of scenarios and stochastic

parameters• Interact with underwriting cycle and catastrophe

expectations• Optimisation and pricing of future reinsurance

programs

Conclusion

“Winning is not about doing one thing 100% better, but doing 100 things 1% better”

Dennis Conner