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‘‘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