Sample Essay Solutions CAS Exam 6 Fall 2003
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 + 21301 − = 1,755 1.2 1 = 1700 + 21301 − = 2,410 1.5 1 = 1200 + 21301 − = 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.
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