Sample Essay Solutions
CAS Exam 6
Fall 2003
20 - Response 1
Paid ALAE to Paid Loss
AY
12
98
24
36
48
0.0750
0.0810
0.0822
0.0950
99
0.0625
0.0854
0.0942
00
0.0598
0.0657
0.0711
01
0.0669
0.0819
02
0.0663
Paid ALAE to Paid Loss ATAs
AY
12-24
98
24-36
36-48
48-Ult
1.0800
1.0148
1.0000
1.0085
1.0000
1.0117
1.0000
99
1.3664
1.1030
00
1.0987
1.0822
01
1.2240
Selected
3 yr Avg
1.2297
1.0884
Ultimate Loss = 10,680
Ultimate Paid ALAE to Paid Loss Ratio = (0.0663)(1.2297)(1.0884)(1.0117) = 0.0898
Ultimate ALAE = (10,680)(0.0898) = 959
ALAE Reserve = 959 – 630 = 329
20 - Response 2
Ratio Paid ALAE to Paid Loss
AY
98
99
00
01
02
12
0.0625
0.0598
0.0669
0.0663
= 630/9500
24
0.0750
0.0854
0.0657
0.0819
36
0.0810
0.0942
0.0711
48
0.0822
0.0950
24-36
1.0800
1.1030
1.0822
36-48
1.0148
1.0085
48-Ult
=0.0950/0.0942
Paid to Paid Development
12-24
AY
98
99
00
01
1.3664
1.0987
1.2242
3 yr Avg
Cumulative
1.2298
1.3541
1.0884
1.1011
1.0117
1.0117
1.0000
1.0000
AY
2002
Ult P-to-P
Ratio
0.0898
Ult
Loss
10,680
Ult
ALAE
958.82
Paid
ALAE
630
= 0.0663 x 1.3541
= 0.0898 x 10680
Therefore, ALAE reserve for AY 2002 @12/31/02 = 958.82 – 630 = 328.82
21 - Response 1
Reserve at 12 mos for AY2002 = 16.5M - 3M = 13.5M
Age
12
24
36
48
60
ult
Ending Reserve
13.5M
13.5m X .9 = 12.15M
12.15M x .6 = 7.29M
7.29M x.55 = 4.0095M
4.0095M x .4 = 1.6308M
0
Paid on Prior Year End Reserves
3M
13.5M x .55 = 7.425M
12.15M x .55 = 6.6825M
7.29M x .5 = 3.645M
4.0095M x 2.56608M
1.6308M x 1.03 = 1.651914M
AY2002 ultimate loss = sum of paid on reserve = 24,970,494
21 - Response 2
AY2002 Reserve at Dec 31, 2002 = Incurred - Paid = 16.5M - 3M = 13.5M
AY2002 Reserve Development @12:
@24:
@36:
@48:
@60:
@72:
13,500,000
13,500,000 x 0.9 = 12,150,000
12,150,000 X 0.6 = 7,290,000
7,290,000 X 0.55 = 4,009,500
4,009,500 X 0.4 = 1,603,800
0
AY2002 Paid Losses
13,500,000 X 0.55 = 7,425,000
12,150,000 x 0.55 = 6,682,500
7,290,000 X 0.5 = 3,645,000
4,009,500 X 0.64 = 2,566,000
1,603,800 X 1.03 = 1,651,914
@12:
@24:
@36:
@48:
@60:
sum of paid losses = 21,970,494
AY2002 ultimate = 21,970,494 + 3,000,000 = 24,970,494
22 - Response 1
A/Y
1997
1998
1999
2000
2001
’97
’98
’99
’00
’01
Earned
Exposures
100k
200k
200k
250k
300k
27 month
39 month
Ult
35k
65k
75k
85k
97k
55k
80k
85k
95k
66k
96k
102k
114k
x=27month/Earn Expos
.35
.325
.375
.34
X=.3475
.323
y=Ult/Earn Expos
.66
.48
.51
.456
Y= .5265
a) All-yr wtd Link Ratio
Link 27-ult = sum y/sum x = (.66+.48+.51+.456)/(.35+.325+.375+.34)
=2.106/1.39=1.515.
97,000x1.515=146,965
b) Budg’d Loss Estim
Will use our calc’d Y, that is average Ult LR for prior AY’s
Budgeted = (300,000)(.5265) = 157,950.
22 - Response 2
A/Y Earned
Exposures
1998 100k
1998 200k
1999 200k
2000 250k
2001 300k
27 month
39 month
35k
65k
75k
85k
97k
55k
80k
85k
95k
From AY1997 - AY2000: Xbar = 1/4 x (35+65+75+85) = 65 x 10^3
From AY1997 - AY2000: Ybar = 1/4 x (55+80+85+95) x 1.2 = 94.5 x 10^3
C = Y bar/X bar = 94.5/65 = 1.453846
For AY 2001: ultimate loss = incurred @27 x C = 97,000 x 1.453846 = 141,023
23 - Response 1
a.
Accident Year
1999
2000
2001
2002
Age to Age Factors
24 - 36
36 - 48
1.5
1.1
1.4
12 - 24
2
1.75
1.5
Selected Factor
To Ultimate
48 - Ult
1.75
2.930813
1.45
1.67475
1.1
1.155
1.05
1.05
CY 2002
Incurred Loss
400
450
490
825
Ultimate Loss
IBNR
1172.325
772.325
753.6375
303.6375
565.95
75.95
866.25
41.25
IBNR Reserve
1193
b.
AY
1999
2000
2001
2002
EP
1000
1000
1500
1800
ELR
75%
75%
75%
75%
EL
750
750
1125
1350
FU
1.05
1.155
1.67475
2.930813
IBNR Reserve =
IBNR
35.71
100.65
453.26
889.38
1479
c.
Two reasons to use Bornhuetter-Ferguson method over the incurred age to age:
1. Data lacks credibility (i.e. no data volume)
2. Loss development patterns are volatile (i.e. large standard error between selected
factors and age to age factors derived from data
23 - Response 2
a.
Accident Year
1999
2000
2001
Average
99
00
01
02
Age to Age Factors
24 - 36
36 - 48
1.500
1.100
1.400
12 - 24
2.000
1.750
1.500
1.750
IL
825
490
450
400
1.450
Age
48
36
24
12
1.100
LDF
1.050
1.155
1.675
2.931
IBNR(f)
.050
.155
.675
1.931
48 - Ult
1.050
IBNR
41.25
75.95
303.75
772.40
1193.35
b.
ELR = 0.75
99
00
01
02
BF = EP x ELR x (1 - 1/LDF)
EP
1000
1000
1500
1800
1479.11
c.
1. volatile line of business
2. new line of business
ELR
0.75
0.75
0.75
0.75
(1 - 1/LDF)
.0476
.1342
.4030
.6588
IBNR
35.70
100.65
453.38
889.38
24 - Response 1
A.
I) Natural Disasters: The event/loss module is more complex than the insurance
module. Indeed losses depend on complex meteorological (hurricane) or geological
(earthquake) models that must calculate how a given structure will be affected. By
contrast, policy forms are standard and calculating the insured loss knowing the total loss
is easy.
II) Pollution Events: The insurance module is more complex. Losses can be
relatively easily modeled with the usual techniques but the insured loss depends on the
outcome of the judicial process. In particular, the existence of liability can be denied, the
indemnity is unknown (depends on verdict), and the allocation of losses to accident years
is somewhat arbitrary. Aggregate limits or drop-down clauses complicate the issue
further.
B. The insurance module uses the underlying losses and the policy terms as an input to
calculate the insured losses.
C. For older accident years, policy terms (deductible and limit) may not have been
recorded electronically. A solution is to generate stochastically the policy terms based on
a survey of the policy forms in force at the time losses may have occurred.
25 - Response 1
The period of the contract must be at least 13 months.
The insurer must not be able to cancel or increase the premium to the contract during the
period.
25 - Response 2
The policy term >= 13 months.
The insurer neither can cancel the policy nor increase the policy premium during the
policy term.
26 - Response 1
Created Year
99
00
01
02
Case O/S
12
4000
6000
8000
10000
Created Year
99
00
01
Simple Avg
Rem on O/S
12-24
0.6
0.6
0.6
0.6
Created Year
99
00
01
02
Loss Disposed of (diff in case o/s from 1 interval to next)
12-24
24-36
36-48
48-60
1600
800
800
1200
2400
1200
1200
1200
3200
1600
1600
1600
4000
2000
2000
2000
F-Ratios
0.056
24
2400
3600
4800
6000
36
1600
2400
3200
4000
48
800
1200
1600
2000
24-36
0.667
0.667
36-48
0.5
48-60
0
0.667
0.5
0
0.078
X
894 = 4000(0.056) + 2000(0.078) + 2000(X) + 2000(0.152)
894 = 684 + 2000x
210 / 2000 = x x = 0.105
F ratio for 36-48 mo = 0.105
0.152
60
0
0
0
0
26 - Response 2
Created Year
99
00
01
Case Outstanding remaining reserve factors:
12-24
24-36
36-48
48-60
0.6
0.667
0.5
0
0.6
0.667
0.6
0.600
0.667
0.5
0
Completion of Created Yr 2002 Reserves
Created Yr
2002
12
10000
24
6000
36
4000
48
2000
60
0
Disposed Reserves for Created Yr 2002:
Created Yr
2002
12-24
4000
24-36
2000
36-48
2000
Therefore,
894 = 0.056 * 4000 + 0.078 * 2000 + X * 2000 + 0.152 * 2000
X = 0.105 = 36-48 F-ratio
48-60
2000
27 - Response 1
Cumulative Reported Claims
Cumulative Closed Claims
Loss
Year
2000
2001
2002
Loss
Year
2000
2001
2002
12
60
72
90
24
100
120
150
36
100
120
150
12
40
48
60
24
80
96
120
36
100
120
150
As of December 31, 2003
Cumulative Cumulative
Loss Claims
Claims
Claims
Incremental Weighted
Year Reported
Closed
Open
Reports
Claims*
2000
100
100
0
0
0
2001
120
120
0
0
0
2002
150
120
30
60
90
As of December 31, 2004
Cumulative Cumulative
Loss Claims
Claims
Claims
Year Reported
Closed
Open
2000
100
100
2001
120
120
2002
150
150
Incremental Weighted
Reports
Claims*
0
0
0
0
0
0
0
0
0
*Weighted Claims = Incremental Reports + Open Claims
(90)(500)(1+x) = 51,300
45,000x = 51,300
x = 1.14
14% trend applied.
Estimated
Ultimate
Claims
100
120
150
27 - Response 2
Calendar Year 2003
(1)
Loss Claims
Year Reported
2000
2001
2002
(2)
Claims
Open @
Beg Yr
0
0
60
(3)
(4)
Claims
Open @
End Yr
Claims
Closed
0
24
30
0
0
30
(5)
Weighted
Claims*
0
0
0
0
0
90
Weighted Claims = (1) + (4)
In CY 2004, no new claims are reported and there are no open claim, so weighted
claims equal to zero.
12/31/02 ULAE reserve = weighted claims x average 12/31/02 ULAE paid per open
claim x (1 + trend rate)
51,300 = 90 x (500) x (1 + trend rate)
trend rate = 14%
28 - Response 1
Counterparty
SE
MSP
Expiration
Length
3
4
Mean Default
Time
2.21
2.8
# of Remaining
Coupons
1
2
Probability of
Default
.0019
.013
Mean Default Time SE = (1*.04 + 2*.07 + 3*.08) / (.04 + .07 + .08)
Mean Default Time MSP = (1*.22 + 2*.28 + 3*.29 + 4*.51) / (.22 + .28 + .29 + .51)
Total Reserves = (.0019)*(50,000,000*(1+.045 * (1))* (1 - .85) +
(.013)*(22,000,000*(1 + .052*(2))* (1 - .85) = 14,891.25 + 47,361.6
Reserves over outstanding = 62252.85 / 72,000,000 = .00086
28 - Response 2
Company PAR
SE
MSP
Exposure Coupon
50,000,000 3
22,000,000 4
.045
.052
Default
Rate
.19%
1.3%
Mean
time to
Default
2.21
2.8
# annual Reserve
interest
payments
1
14,891.25
2
47,361.6
Default Rate A rated = .04% + .07% + .08% = .19%
Default Rate BBB rated = .22%+.28% + .29% + .51% = 1.30%
Mean Default Time SE = (1*.04 + 2*.07 + 3*.08) / (.04 + .07 + .08)
Mean Default Time MSP = (1*.22 + 2*.28 + 3*.29 + 4*.51) / (.22 + .28 + .29 + .51)
SE Reserve = (50,000,000*1*.045 + 50,000,000)*.0019 * (.15) = 14,891.25
MSP Reserve = (22,000,000*2*,052 + 22,000,000)*.013*(.15) = 47,361.6
Reserves over Par Outstanding = (14,891.25 + 47,361.6) / (72,000,000) = .086%
29 - Response 1
1. To pay for future losses covered by policy.
2. To provide funds for return to policyholders in the case of cancellation
3. To purchase reinsurance, if necessary.
29 - Response 2
1. To fund the purchase of reinsurance
2. To properly recognize income
3. Required by regulators/statutes
30 - Response 1
Statement Billing – the insurer sends statement to the agent and the agent reconciles the
statement with his records.
Account Current Billing – the agent sends a statement to the insurer and subsequently
remits payments. The insurer reconciles the statement with its records.
30 - Response 2
Item Basis
Account Current
Difference – Account current is a statement that summarizes activity during a certain
time frame. Item basis means a separate bill for each item, not summarized.
31 - Response 1
Assumption: The reinsurer is Authorized to do business in the state the primary insurer is
domiciled.
1st step: Need to know if the ratio of Rein Recov on Paid >90 days / (Total Rein Recov on
Paid + $ received in prior 90 days) >= 20%
Ratio = 200,000/(900,000 + 100,000) = .2
Because ratio >= 20%, penalty = .2 * Total $ owed primary insurer from reinsurer = .2 *
(900,000 + 800,000 + 700,000 + 500,000 + 5,000 – 100,000) = 561,000
31 - Response 2
Overdue/(recoverable on Loss and LAE + paid in last 90 days) =
200000/(900000+100000) = 20%
This is >= to 20%, so
Penalty = 20% x (900,000 + 800,000 + 700,000 + 500,000 + 5,000 – 100,000) = 561,000
32 - Response 1
SAP measures results on a calendar year basis.
Lloyds measures results on an underwriting year basis which develops over three years.
SAP: There is an urgency to close the books timely, even through the use of estimations.
Lloyds: There is no urgency to close the books, earned premium and incurred losses are
not known until the end of the third year.
SAP: Unearned premiums and ultimate losses are accrued each year.
Lloyds: Accruals for unearned premiums are never established and accruals for ultimate
loss are known at the end of the third year.
SAP: Premium written is recorded gross of commissions.
Lloyds: Premium written is recorded net of commissions.
32 - Response 2
US:
Use calendar year basis
Record the written premium gross of commission
Always urgent to close the books at the end of the year
Set up unearned premium reserve
Lloyds:
Use underwriting year basis
Record the written premium net of commissions
Never urgent to close the books at the end of the year
Never set up unearned premium reserve
33 - Response 1
a) Ledger = 40,000 + 20,000 = 60,000
Ledger assets are assets that are recorded on the books of the company.
b) Non-ledger = (44,000 – 40,000) = 4,000
Non-ledger assets: implicit adjustments
c) Assets not admitted = 7,000
Non-admitted assets: assets not allowed as per SAP
d) Net admitted assets = Ledger + Non-ledger – Non-admitted
= 60,000 + 4,000 – 7,000
= 57,000
33 - Response 2
a) Ledger assets: Purchase price of common stock + Agents balances due and payable
= 40,000 + 20,000 = 60,000
b) Non-ledger assets = unrealized gain of common stock
= 44,000 – 40,000 = 4,000
c) Assets Not Admitted = Agents’ Balances Outstanding beyond the 90th day = 7,000
d) Net Admitted Assets = Ledger Assets + Non-ledger assets – Assets Not Admitted
= 60,000 + 4,000 – 7,000
34 - Response 1
a.
Company A and C
Company A’s loss ratio adjustments indicate that reserves on prior years swing up and
down. It is likely that they have been decreasing the adequacy of reserves on prior years
to make their loss ratio look lover and have increased their reserve adequacy on prior
years to increase their loss ratio. They have done this to make their calendar year loss
ratios look stable.
Company C is growing steadily. From this we must conclude that their reserves on prior
years are growing exponentially as well. A change of 4.3% in 2002 equals $1226, while
an increase of 4.3% in 1997 equals only $581.
b.
1) IRS – pressure to book reserves at profitable levels so pay taxes early
2) Attorneys have brought insurance companies to suit over unsubstantiated claims
that rate are excessive due to inflated reserves.
c.
If the loss reserve indicates that claims adjusters reserves are too large or too small, they
may make adjustments for this, which will distort the patterns, and increase/decrease
reserves thus further affecting CY U/W results.
34 - Response 2
a.
Company A is likely to have impact their CY results with their reserving practices
because they have not been consistent.
Company B is consistently underreserving with relatively stable writings, therefore, their
CY underwriting results are probably not affected.
Company C has consistently underreserved, but they have been growing, so this will
impact their CY underwriting results.
b)
1) IRS – if reserves increase, taxes decrease
2) Trial Lawyers – believe that insurance companies inflate reserves in order to
obtain larger rate increases.
c)
A claim adjuster must use consistent method in setting case reserves. If they know
reserving results, they might attempt to adjust their methods, which will throw reserving
off.
The results of loss development studies used to determine the overall adequacy of
company case reserves should not be divulged to claim adjusters. Inevitably, this would
lead to changes in individual case reserving practices.
35 - Response 1
a. Situation involving possible loss and uncertainty that will be decided when certain
future events occur or fail to occur
b. 1. Information existing before financial statement date indicates asset impaired or
liability incurred at financial statement date
2. Amount of loss can be reasonably estimated
35 - Response 2
a. A situation or condition which given the occurrence (or non-occurrence) of a
future event could cause an asset to be impaired or a liability to be incurred.
b. It must be “probable” that an asset has been impaired or a liability incurred as of
the date of the financial statements; the amount must be reasonability estimable.
36 - Response 1
Advantages
1) Intermediary will get quote from several different reinsurers and try and find the
best rate on the desired coverage.
2) Intermediary will research solvency of reinsurer for insurers to make sure it is as
solvent as the company would like to deal with
Disadvantages
1) May slow down communication between insurer and reinsurer since
communications go through intermediary instead of directly between insurer and
reinsurers
2) Intermediary charges a commission or fee
36 - Response 2
Advantages
1) An intermediary has access to numerous reinsurers and therefore may be able to
negotiate better terms for the primary insurer
2) Intermediaries generally either have themselves or have access to a great deal of
information and expertise which can be of value to the primary insurer.
Disadvantages
1) The intermediary adds a third party to a transaction which may increase delays in
cash flow and information flow.
2) The risk of insolvency of the intermediary can be significant for both the primary
insurer and the reinsurer.
37 - Response 1
CMP Liability
Loss
1
2
3
Limit % Ceded =400K/Limit
100K
0
1M
400/1000=40%
2M
400/2000=20%
%Retained = (1-ceded)
$ Retained
100%
100K
60%
500K x 60% = 300K
80%
1M x 80% = 800K
1.2M
CMP Property
Loss $ Retained
1
1M + 1M = 2M
2
1M
3
1M
All Other
30M
Total
34M
Total Combined before CAT Cover = 34M + 1.2M = 35.2M
After CAT cover, retained = 1M + (31M – 1M)*10% + (35.2M – 31M) = $8.2M
37 - Response 2
CMP Liability
Ceded: Loss 1 $0, Loss 2: 40% reinsured, $200K, 20% reinsured $200K = $400K
Property
Ceded $3M since it is a per occurrence only one limit is paid
Catastrophe:
Liability retained = $1.2M
Property retained = $36M
Total retained = $37.2M
Loss Reinsured = $30M * 90% = $27M
Total Loss Retained = $37.2M - $27M = $10.2M
38 - Response 1
A.
Sunset Clause – limits the time that primary insurer can report claims to reinsurer after
treaty ends.
Sunrise Clause – provides extended reporting period – say for example, after sunset
clause takes effect.
B.
1. As and endorsement to treaty – basically extending the sunset clause to prolong
reporting period
2. As a separate contract – let sunset clause end reporting period, then a new contract
takes effect and “carries over” claims to a new reporting period allowance.
38 - Response 2
A)
Sunrise – this clause extends the reporting period beyond the sunset clause.
Sunset – After a designated period of time past the expiration of the policy, no more
claims can be reported.
B)
As an endorsement
As a separate contract
39 - Response 1
A. Policies attaching (policies effective or renewed during contract term)
Ceded Amount
Occurrence 1
Occurrence 2
Occurrence 3
Occurrence 4
Not Covered
$400,000 above retention
$0 (did not reach attachment point)
$20,000 above retention
$420,000 ceded to reinsurer.
B. Losses occurring
Ceded Amount
Occurrence 1
Occurrence 2
Occurrence 3
Occurrence 4
$200,000 above retention
$400,000 above retention
$0 (did not reach attachment point)
Not Covered
$600,000 ceded to reinsurer.
40 - Response 1
PL
DWP)
500K
1M
2M
5M
10M
15M
25M
Exposure Factor
0
0
(1.35 – 1.18)/1.35 = .1259
(1.71 – 1.18)/1.71 = .3099
(1.8 – 1.18)/1.8 = .3444
(1.8 – 1.18)/1.88 = .3298
(1.8 – 1.18)/1.99 = .3116
Exposure Premium (Exposure Factor x
279,750
2,789,100
1,601,460
354,535
444,965
5,469,810
Exposure rate = (5,469,810/DWP) x ELR x ECO/XPL Factor x Expense Load
= (5,469,810/22,375,000) x (1-.12-.03-.05-.25) x 1.15 x (1/(1-.2))
= 19.33%
40 - Response 2
Policy Limit
(000)
DWP
(000's)
Exposed Premium
Factor
500
1,000
2,000
5,000
10,000
15,000
500
3,500
2,222
9,000
4,650
1,075
1-1.18/1.35=.126
1-1.18/1.71=.310
1-1.18/1.8=.344
(1.8-1.18)/1.88=.330
(1.8-1.18)/1.99=.312
Exposed
Premium
(1) X (2)
279,972
2,790
1,599.6
354.75
445.356
5,469.858
Expected Loss Ratio = 1-(.12+.03+.05+.25)=.55
Reinsurance expected loss = .55 X 5,469,858=3,008,422
Total expected loss including ECO/XPL=3,008,422 X1.15=3,459,685
Note: ALAE load is included in ILF's
Total Subject premium assuming all DWP is included = 22,375,000
Loss Rate = 3,459,685/22,375,000= 15.46%
Final Gross indicate rate = 15.46%/(1-.2) = 19.33%
41 - Response 1
1. ALAE is excluded totally from subject loss
1
2
3
Loss
600,000
50,000
200,000
Ceded Loss
400,000
0
100,000
500,000
2. ALAE is included in loss to subject limit and retention
1
2
3
Loss&ALAE
960,000
200,000
600,000
Ceded Loss
400,000
100,000
400,000
900,000
3. ALAE is proportionally allocated by loss amount
1
2
3
Loss
600,000
50,000
200,000
Ceded Loss
400,000
0
100,000
thus total ceded loss & ALAE
1
640,000
2
0
3
300,000
940,000
ALAE Allocated to reinsurer
360,000 x 400/600 = 200,000
0 x 150,000 = 0
400,000 x 100/200 = 200,000
41 - Response 2
1. Don't pay ALAE
Claim
1
2
3
Loss
600,000
50,000
200,000
Ceded Loss
400,000
0
100,000
500,000
2. Include ALAE with the losses
Claim Loss&ALAE
1
960,000
2
200,000
3
600,000
Loss&ALAE in 400k x 100k
400,000
100,000
400,000
900,000
3. Pay ALAE in equal proportion to losses
Claim
1
2
3
claim
1
2
3
Loss
600,000
50,000
200,000
Portion of loss in layer
400,000/600,000 = 2/3
0/50,000 = 0
100,000/200,000=1/2
Portion of ALAE paid
2/3 (360,000) = 240,000
0 (150,000) = 0
1/2 (400,000) = 200,000
paid loss & ALAE in Layer
400,000 + 240,000
640,000
0+0
0
100,000 + 200,000
300,000
940,000
42 - Response 1 (Time Factor = .500)
Assuming all ground up loss of $20,000,000 from 7/1/02 catastrophe is from policies
with effective dates during treaty period.
Reinsured loss = 15M xs 10M = 20M – 10M = $10,000,000
75% Pro-Rata to Amt = 10M/15M = (66.7%)(75%) = 50%
Pro-Rata to time = 50% (7/1 is halfway between 1/1 & 12/31)
Reinstatement Premium =
=
($2,000,000) (.5) (.5)
$500,000
42 - Response 2 (Time Factor = .750)
Reinstatement Prem = % of Loss x Annual Prem x Amount Factor x time left
% of Loss = 10,000,000/15,000,000 = 2/3
time left = 75%, since this is a risk attaching treaty!
Reinstatement Prem = 2/3 x 2,000,000 x .75 x .75 = 750,000
42 - Response 3 (Time Factor = .875)
The treaty will cover risk attached to the treaty –> coverage from policies written to
January 1st to December 31st.
On July 1st 2002, the unexpired portion of treaty coverage is 7/8 – that means that 1/8 of
the coverage provided by the treaty had expired.
Reinstatement Prm = 2,000,000 x (10M/15M x .75) x 7/8 = 875,000
43 - Response 1
Fire Exposure Rate:
$100,000 as a %
Limit
of limit
100,000 100/100=1.00
200,000 100/200=0.50
250,000 100/250=0.40
$200,000 as a %
of limit
200/100=2.00
200/200=1.00
200/250=0.80
Fire Exposure
Factor
1-.845=0.155
.845-.623=0.222
.768-.564=0.204
Exposed Fire Prem.
0.155(5m)=775,000
0.222(5m)=1,110,000
0.204(5m)=1,020,000
Total=2,905,000
Therefore,
Fire Exposure Rate=2,905,000/15,000,000(0.60)(1.08)(1/(1-0.25))(1.0)=0.1673
Therefore,
Overall Rate=(Fire Rate)(35m/100m)+(Wind Rate)(15m/100m)+(Other
Rate)(50m/100m)
0.908=(0.1673)(0.35)+0.042(0.15)+(other rate)(0.50)
Therefore Other Rate=
0.06629
43 - Response 2
Limit
Fire
Prem
100,000
200,000
250,000
5m
5m
5m
Ceding
Co Ret
% of
limit
100
50
40
Exp
factor
Ret+lim
% of pol
limit
Exp fctr
Exp.
Layer
Exp. Prem
.845
.623
.564
200
100
80
1.0
.845
.768
.155
.222
.204
775,000
1,110,000
1,020,000
2,905,000
Fire Exposure Rate= (2,905,000*.6*1.08*(1/(1-.25)))/15,000,000=.1673
Let x=”other” exposure rate.
.098=(.1673*35+.042*15+x*50)/(35+15+50)
x=.0663
44 - Response 1
(1)
(2)
Accident
Year
1998
1999
2000
2001
2002
Adjusted
Premium
8,500
9,000
9,500
9,600
12,100
(3)
Report
Lag
0.90
0.80
0.65
0.40
0.25
Sum
(4)
=(2) X (3)
Burned
Premium
7,650
7,200
6,175
3,840
3,025
Reported
Loss
8,500
6,500
4,500
2,300
1,500
27,890
23,300
ELR = Exp Loss Ratio = 23,300 / 27890 = 0.8354
(1)
Accident
Year
1998
1999
2000
2001
2002
(6)
=ELR x
(2)
Expected
Losses
7,101
7,519
7,936
8,020
10,108
(7)
= 1 - (3)
IBNR
Factor
0.10
0.20
0.35
0.60
0.75
Total IBNR Reserve
(sum of column 8)
(8)
= (6) x (7)
IBNR
710
1,504
2,778
4,812
7,581
17,385
(5)
44 - Response 2
S-B Method IBNR =
(Reported Loss) (Adjusted EP)(1-Lag)
--------------------------------------------------(Adjusted EP) - (Adjusted EP)(1-Lag)
(8500+6500+4500+2300+1500)[8500(.1)+9000(.2)+9500(.35)+9600(.6)+12100(.75)]
IBNR = -----------------------------------------------------------------------------------------------------(8500+9000+9600+12100) [8500(.1)+9000(.2)+9500(.35)+9600(.6)+12100(.75)]
(23,300)(20,810)
IBNR = ---------------------48,700 – 20,810
IBNR = $17,385.19
45 - Response 1
1. The reinsurer should assume a significant insurance risk (both underwriting risk
and timing risk) on the portion of the insurance under the contract.
2. It should be reasonably probable that the reinsurer realize a significant loss from
the transaction.
45 - Response 2
1. The reinsurer must assume significant insurance risk (u/w and timing risk)
2. reasonable possibility of realizing a significant loss.
46 - Response 1
2 difference between commutation and M&A
(1) Buyer expects profit
(2) Liability is not extinguished as in commutation; buyer of M&A acquires liability
based on PV
46 - Response 2
(1) Desire profit, where commutation desires ambivalence point
(2) Does not extinguish liabilities, where commutation would sell outstanding
liabilities
47 - Response 1

1 
Ra = K a + R3 1 − 
fa 

R3 = ∑ K n f n
n
R3 =
R1999
R2000
R2001
1
[1200(1.8) + 1700(1.5) + 1400(1.2)] = 2,130
3
1 

= 1400 + 21301 −
 = 1,755
 1.2 
1 

= 1700 + 21301 −
 = 2,410
 1.5 
1 

= 1200 + 21301 −
 = 2,147
 1.8 
47 - Response 2
AY Expected Ult base on Inc Loss Development
1999 1400 x 1.2 = 1680
2000 1700 x 1.5 = 2550
2001 1200 x 1.8 = 2160
Average = 2,130
AY
1999
2000
2001
AY
1999
2000
2001
Initial Expected Losses
(1)
2130
2130
2130
Estimated Ultimate
1400 + 355 = 1,755
1700 + 710 = 2,410
1200 + 947 = 2,147
% Unreported
(2)
1 – 1/1.2 = 0.1667
1 – 1/1.5 = 0.3333
1 – 1/1.8 = 0.4444
IBNR
= (1) x (2)
355
710
947
48 - Response 1
1. Claim emergence can be forecast with reasonable accuracy.
2. Average claim costs are a function of those for the preceding quarter,
adjusted for inflation.
3. Closed claims are a function of claims closed in the future (pending + IBNR)
4. Inflation impacts a claim in the quarter of closure.
48 - Response 2
1. Inflation impacts cost at the time that the claim is closed (paid)
2. Claims closed in each quarter are dependent on claims closed in the future
(pending + IBNR)
3. The average severity is dependent on preceding quarter’s severity adjusted
for inflation.
4. Claims emergence can be forecast with reasonable accuracy.
49 - Response 1
1. There is a lack of direct association between occurrence and loss. Court decisions
may result in many policy years being simultaneously triggered.
2. A lack of historical data.
3. Losses are high severity and low frequency.
4. Only calendar year data may be available.
49 - Response 2
1. Loss development patterns are not stable.
2. These liabilities are of a relatively new type and not enough data is available.
3. Publicity surrounding the successful filing of claims may result in a “feeding
frenzy” of new claims.
4. There is no specific accident data and many policies can be triggered.
50 - Response 1
a.) Can evaluate the impact of structured settlements, commutations, etc. have on the
insurers operating results. Can help determine an optimal strategy in terms of
claims management practices.
b.) DFA (dynamic financial analysis) can show the rating agency that the company
has a good understanding of their exposures and makes decisions based on
rigorous analysis of various scenarios. The company can also construct models to
determine the probability that capital could fall below <X billion, which would
lead to a rating downgrade.
c.) DFA can help determine /evaluate merger & acquisition opportunities and how
these will affect company results & the competitive market. It can help determine
which opportunities provide the greatest risk or return so the company can
evaluate whether the acquisition is desirable.
50 - Response 2
a.) DFA can be used to help management better understand the costs, benefits and
risks associated with changing their claim handling practices.
b.) Rating agencies will look favorably on managements demonstration that
comprehensive risk management and risk analysis work has been done.
c.) M&A’s work best when synergies between companies are high and economies of
scale can be leveraged – DFA can help management analyze how entities will fit
together to best position themselves after M&A, or if M&A should happen.
51 - Response 1
a) Facultative: Allows 1 policy at a time to be ceded above the typical (desired) limit
b) Facultative: Allows individual exposure above desired limits but below reinsurance
attachment to be ceded.
c) Treaty: Allows large destabilizing (e.g. catastrophic) losses to be removed from
underwriting losses.
(It removes large aggregate losses)
51 - Response 2
a.
Facultative Reinsurance allows a primary insurer to write a policy limit that is
larger than they would be able to otherwise, perhaps with an excess of loss
contract.
b.
Facultative Reinsurance would allow a primary insurer to fill coverage gaps in
an existing reinsurance program by ceding risks not sufficiently covered by
the existing program
c.
Treaty reinsurance is more effective in stabilizing underwriting results
possibly by ceding a portion of large losses.