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END OF EXAMINATION

1

Part 6, Fall 2006: MULTIPLE CHOICE ANSWERS

ANSWER #1: C.

ANSWER #2 E

ANSWER #3 D.

ANSWER #4 E.

ANSWER #5: C.

ANSWER #6 B.

ANSWER #7: D.

ANSWER #8: B:

ANSWER #9: D:

ANSWER #10: A.

ANSWER #11 D.

ANSWER #12: E.

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Number 13

The reserve valuation process has 4 phases:

Review the data: observe the available data to detect anomalies or trend. Observe the rate

of development of losses, the smoothness of losses and the presence of large losses. Apply the reserving techniques: apply the reserving methods to the data to get reserve

estimates

Compare results and choose an indicated reserve: Compare and reconcile the resultsobtained. Understand the differences between the varying results. Make your choice ofthe best reserve estimates.

Monitor results: Observe the emergence of loss over time to validate the results. The besttool to review the results is the comparison of actual vs. expected losses.

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Number 14

Model answer #1

RY 12 24 36 Ult

2002 .11

2003 .25 .132004 .32 .26 .276 .1442005 .33

Sample Calc: .276 = (1 - .32 - .26) x (.25 / (.25+.13) )

Future claims closed in interval

24-36: .276 (1500) = 41436-Ult: .144 (1500) = 216

Future AVG claim cost by interval

24-36: 2100 (1.045) = 2194.50

36-Ult: 2500 (1.1)^2 = 3025

Estimated Reserve: 414(2194.50) + 216(3025) = 1,561,923

Carried Reserve: (1500)(1600) (1500)(.32)(.385) 1500(.26)(1420) = 1,661,400

Reserve Equity: 1,661,400 1,561,923 = 99,477

Redundant

Model answer #2

1) Calculate the portion of claims closed for report year 2004

PC(24-36) = (1-.32-.26) x (0.25 / (1-.35-.27) ) = .2763PC(36-ULT) = 1-.32-.26-.2763 = .1437

2) Projection of claims closed in interval for report year 2004

CC(24-36) = 1500 x PC(24-36) = 414CC(36-ULT) = 1500 x PC(36-ULT) = 216

3) Calculate the average paid costs for report year 2004

APC(24-36) = 2100 x (1 + 4.5%) = 2194.5APC(36-ULT) = 2500 x (1 + 10%)^2 = 3025

4) Calculate the amount of overall reserve for report year 2004

Overall Reserve = (Future Closed Claim) x APC= 414x2194.5 + 216x3025= 1,561,923

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5) Equity Position

The Carried Reserve = 1600x1500 1500x(385x.32 + 1420x.26)= 1,661,400

Equity Position = 1,661,400 1,561,923

= 99,477

The reserve has a redundancy

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Number 15

Model answer #1

a. Link Ratio Est. (with reform)Ultimate Loss = Repd Loss x Ult LDF

= 35M x 1.0 / % repd= 35M x 1.0 / 0.63= 55.55M

b. BF Est. (with reform)Ultimate Loss = Repd Loss + IBNR Est.

= Repd Loss + Expected Losses x % unreported= 35 + 50M x (1 0.63)= 53.5M

c. Bayesian Cred Est. (with reform)Ultimate Loss = x/d (Z) + (1-Z)Y, where Z = VHM/(VHM + EVPV)

Z = 14.3 / (14.3 + 57) = 0.2= 35M/0.63 (0.2) + (1 0.2) 50M= 51.11M

d. The least squares method is appropriate when the losses fluctuate due to randomvariation, not when tort reform causes the flucuations

Model answer #2

a. Link Ratio Ult LossUltimate Loss = Repd Loss / RLay

= 35M / 0.63= 55.55M

b. BF ULt LossUltimate Loss = Reported Losses + Expected Losses x (1 - % reported)

= 35M + 50M x 0.37= 53.5M

c. Bayesian Cred Est.L = x/d (Z) + (1-Z) E[Y], Z = VHM/(VHM + EVPV)

Z = 14.3 / (14.3 + 57) = 0.2006= 55.55M x (0.2006) + (1 0.2006) x 50M

= 51.11M

d. Because there has been a change in the loss emergence patter. Historical data is nolonger representative of future experience

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Number 16

Model answer #1

a) BF Reserve = 9,000,000 x (1-1/1.25) = 1,800,000BF Ult. Losses = 1,800,000 + 8,000,000 = 9,800,000

GB Reserve = 9,800,000 x (1-1/1.25) = 1,960,000

b) The Benktander method generally has a lower mean squared error than the Bornheutter-Ferguson method, and is a better linear approximation of the exact Bayesian procedure. Italso gives more weight to emerged losses.

c) The Benktander method generally has a lower mean squared error than the chain laddermethod, and is a better approximation of the exact Bayesian procedure. It also gives moreweight to the a priori estimation.

Model answer #2

a) R(BF) = U(0) x qk qk = 1-1/LDF = 1-1/1.25 = 0.20 = % unreported= 9M x 0.20 U(0) = initial estimate = 9M= 1.8M Ck = paid losses = 8M

U(BF) = R(BF) + Ck R Reserves= 1.8M + 8M = 9.8M U Ultimate Loss

R(GB) = U(BF) x qk = 9.8M x 0.20 = 1.96M

b) It represents an improvement because the BF method uses an estimate of inicial losses only tocalculate the reserve amount. It does not give much to the ultimate. The Benktander method

uses the BF ultimate as the starting point, and has lower mean square error in most cases.

The chain ladder method gives full credibility to the reported losses with no consideration ofultimate expected losses. The Benktander gives weight to both estimates and actual reportedlosses. It also has lower mean square error in most cases

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Number 17

Model answer #1

A1. Use paid ALAE to paid loss development ratios to develop the ultimate paid ALAE to paidloss ratios, then apply these ratios to the ultimate loss to project ALAE IBNR reserve.

A2. Develop ALAE separately by triangle method.

B1. Develop paid ALAE ratio to paid loss ratio would be appropriate, since it recognizes therelationships between the two, and also uses the paid ALAE data. The issue that should beemphasized is if ultimate loss projection has an error, then the ALAE projection will be in errortoo.

B2. Develop ALAE separately may not be appropriate, since the ALAE payment should berelated to paid loss.

Model answer #2

A1. You could develop ALAE separately from loss to see these changes and adjust appropriatelyfor them.

A2. You could take the ratio of paid ALAE / paid loss at each development period and calculatedevelopment factors between these ratios to see the changes and allow the new ratios ofALAE/loss to come through and develop a more appropriate ultimate ALAE / ultimate loss ratio.

B1. Developing ALAE separately from loss may not be appropriate since you can have bigswings in the ultimate ALAE / ultimate loss ratios. It does, however allow you to see changes inALAE patterns and adjust accordingly.

B2. This method is appropriate unless the development of the ALAE / loss ratios are changingsignificantly over time, then adjustments would have to be made.

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Number 18

Model answer #1

a. paid to paid ratio.

ratio = paid ULAE/paid loss = .045ratio * (1 - %@closing) * case reserves + ratio * IBNR reserves.045 * (1 - .3) (12,000,000) + .045 (4,000,000) = 558,000 = ULAE reserve

b. ratio = paid ULAE/ (paid loss + %@opening (Change in reserves))= 900,000/(2,000,000 + .3 (2,400,000) = .033

Change in reserves = (12M + 4M) (10M + 3.6M) = 2,400,000

.033 (.7) (12,000,000) + .033 (4,000,000) = 409,200 = ULAE Reserve

c. *Doesnt take into consideration open claims at the end of the year

*Will overstate reserves if company is growing

Model answer #2

a. ULAE pd/loss paid = 90/2,000 = .045.045 * (4,000,000 + .7 * 12,000,000) = 558,000

b. Incurred loss at 2005 =Change in Reserve = (12,000,000 + 4,000,000 10,000,000 3,600,000) = 2,400,000ULAE Paid/(paid loss + .3*2,400,000) = 90/(2,000 + .3*2,400) = 0.0330.033*(4,000,000 + 0.7 * 12,000,000) = 409,200

c. 1. When the company is growing, use [sic] paid to paid ratio to estimate ULAE will overestimate the ULAE ratio

2. If the claim department change [sic] the claim settlement pattern, the paid to paid ratio willchange. The estimate of ULAE based on historical paid to paid will not be accurate.

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Number 19

Model answer #1

a)

case rsv = Rptd - Paid case / open clm

AY 12 24 36 AY 12 24 362003 11,700 20,000 17,100 2003 0.39 0.50 0.8552004 24,600 26,250 2004 0.41 0.5252005 18,880 2005 0.472

TrendAY 12 24

04 1.051 1.0505 1.151

paid / closed clm Trend

AY 12 24 36 AY 12 242003 0.726 0.838 04 1.05 1.052004 0.762 0.880 05 1.052005 0.800

Data should be adjusted for change in case rsv since trend of 15% for AY05 is greater than prioryrs and paid/closed trend

b)

restated casecase / openclm

AY 12 24 36 AY 12 24 36

2003 12,840 20,000 17,100 2003 0.428 0.50 0.8552004 27,000 26,250 2004 .450=.472/1.05 0.5252005 18,880 2005 0.472

restated incurredAY 12 24 36 indicated loss rsv = ult - paid

2003 41,880 61,900 82,900=(50880)(2.084) -32,000

2004 65,100 96,650 =73855 = rsv = case + IBNR2005 50,880

LDF 1.482 1.339 all yrs wtd avg2.084 1.406 1.05

c) Indicated rsv margin = Booked rsv Indicated = 58,700 73,855 = -15,155

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Model answer #2

a)Average paid losses on claims

closedTrend on avg paid losses on claims

closedAY 12 24 36 AY 12 24

2003 726 838 940 2003-04 1.05 1.052004 762 880 2004-05 1.052005 800

example: 41,900,000/50,000 = 838

Average case reserve on openclaims

Trend on avg paid losses on claimsclosed

AY 12 24 36 AY 12 24

2003 390 500 2003-04 1.05 1.052004 410 525 2004-05 1.15

2005 472

example: (61,900,000 - 41,900,000)/40,000 =500

All trends are consistent except for the case reserves for accident year 2005 at 12 months ofdevelopment. Therefore the data needs to be adjusted.

b)

Adjusted average case reserves on open claims Adjusted cumulative case reservesAY 12 24 36 AY 12 24 36

2003 428 500 2003 12,840 20,000 17,100

2004 450 525 2004 27,000 26,2502005 472 2005 18,800

example: 472/1.05=450Average case reserves * # of open

claims

Cumulative Reported Losses Loss development factorsAY 12 24 36 AY 12-24 24-36 36-ult

2003 41,880 61,900 82,900 2003 1.478 1.339 1.052004 65,100 96,650 2004 1.4852005 50,800 simple avg 1.4815 1.339 1.05

= paid + case reserves

AY 2005 Ultimate losses = 50,880,000 * 1.4815 * 1.339 *1.05

= 105,978,711

Indicated loss reserve = 105,978,711 - 32,000,000 =73,978,711

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c)indicated loss reserve margin = actual carried reserve indicated reserve= 58,700,000 73,978,711= -15,278,711

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Number 20

Model answer #1

a. It is important to know about any changes made to claims department processes. Thiswill affect claim closure patterns, reserve adequacy among other things.

It is important to talk with underwriting so that you know about any changes in the mixof business or new exposures. These will also affect loss emergence and lossmagnitudes.

b. 1) Has there been a change in priorities as far as settling large claims versus smallclaims?

2) Has there been a change in philosophy regarding trivial or very small claims?

Model answer #2a. claims handling practices may have changed over the experience period.

For example, change in priority on small vs. large claimsChange in procedures for handling small claimsIncrease or decrease in number of adjustersChange in amount of assistance from outside claims adjusters

These changes can have an impact on the timing of loss and LAE payments and theultimate amount of the loss and LAE.

b. Underwriting policies and procedures may have changed over experience period.

a. 1) Has there been a change in priority in handling small vs. large claims?2) Has the caseload per claim department adjuster changed?

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Number 21

Model answer #1

1. Develop the triangle of number of closed claims to the number of ultimate claims.2. Assuming the current diagonal represents the current settlement pattern, use that

pattern to recalculate the closed claims triangle.3. Use a function that relates the paid losses to the number of closed claims to restate

paid losses, based on the recast closed claim triangle from step #2.

Model answer #2

First, you need to calculate disposal ratios for the latest calendar year (cumulative closedclaims over ultimate claim count). You use this latest diagonal as a base and work backwardsto restate the cumulative closed claims for the whole triangle (take the disposal ratios timesult reported claims for each accident year). You then interpolate between these newcumulative closed claims versus the original closed claims and adjust the original cumulative

paid losses accordingly.

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Number 22

Model Answer #1

1. The claims department may have had a backup of claims after a catastrophe or majorevent. One would not want to project this pattern into the future

2. A new type of claim may emerge that was not present in the past (for example, asbestos).You would not want to use older year settlement patterns in the future

3. A large loss could impact one years losses. This one loss should not be used to projectinto the future.

Model answer #2

1. Legal environment changes- Juries may start awarding larger payments to the claimant.

2. Claims department philosophy changes- claims department may settle larger claims first or slow down or speed up.

3. Changes in exposures

- If the type of exposures underlying the losses are different than historical

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Number 23

Model answer #1

a) PDLD1= (BP/L1+ CL1/L1*LCF)*TM[18,000/70,000 + .99*1.12]*1.04 = 1.421

1.421*70,000 = 99,470

b) PDLD2= (CL3-CL2)/(L3-L2) * LCF * TM={(.9*100,000-.95*90,000)/10,000 * 1.12 * 1.04 = .52416={(.82*110,000-.9*100,000)/10,000 * 1.12 * 1.04 = .023296Retro Future Adjustments = (10,000)(.52416) + (10,000)( .023296)=5475

c) As losses develop over time, more will hit the per-accident limit and retro maximum,lowering the capped losses as a % of total loss.

Model answer #2

a) [(18,000+(70K)(.99)(1.12)](1.04) = 99,441

b) P2=[18K+(90K)(.95)(1.12)](1.04) = 118,310Plast=[18K+(110K)(.82)(1.12)](1.04) = 123,785123,785-118,310= 5,475

c) As policy matures more of the loss development is eliminated by plan maximums andminimums, and the per-accident limitation. In particular, much of the development atlater maturities is above the per-accident limitation.

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Number 24

Model answer #1

a. Because of the volatility in the data: AY2002: 12-24 a-t-a factor = 20.889. The level ofreported loss in 2003 is quite different than in the other years.

b. 1. The 20.889 dev. Factor could have been caused by an unusual large loss.2. The unusual level of reported loss in 2003 could have been caused by a catastrophe

affecting many insureds.c. The loss event module will model loss event and the insurance module will apply the

policy terms of all the policies in the been estimated to genterate estimated insured loss.The loss event module will require many data external to the insurance field.

d.

Model answer #2

a. Losses are very volatile + there seems to be one large loss in the experience. A LDF of 21 isprobably not appropriate for most years & has a large impact on the selected 12-24 monthfactor.

b. 1. Large loss.

2. A catastrophe in 2003 that impacted a number of insureds (e.g. hurricane).c. > Simulate loss events using external data such as geological & meteorological dagt if youare looking at property losses resulting from hurricanes.

> Use the policy forms to determine what losses would have been sustained if the lossevent occurred. Use this information to project future losses using the current policy forms.

d. Event ModuleInsurance ModuleInsured Losses> Estimated insured losses are a function of the event module (which uses external dat tosimulate the event) & the insurance module, which looks at the policy forms to determine thelosses that would be incurred if the event happened.

Loss event

module

Insurance

module

Insured loss

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Number 25

Model Answer #1

A. Not a good fit chart shows that the data is skewed to the right.B. It is somewhat typical of ELRF models. The skewness is correct, but ELRF models

typically show a downward slope indicating that small values are underpredicatedand large values overpredicted.

C. Model the logarithms of the data.

Model answer #2

A. There are more positive values than negative values, so it is skewed to the right. Thismeans the standard errors are not normally distributed so it is a poor fit.

B. This is typical since the ELRF models do not necessarily have errors that arenormally distributed.

C. Use a logartithmic model and determine the trends across accident, payment, and

development periods.

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Number 26

Model Answer #1

1. Bias is consistent over time (i.e. same bias appears in all year & across all companies)2. User understands the bias

3. User can adjust the bias to reflect their own bias (i.e. they have the info they need toreplace the bias with their own)

Model answer #2

1. The user knows the bias exists.2. The user can adjust for the bias.3. The bias is consistently applied.

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Number 27

Model answer #1

A. Tax Authorities modified SAP

Regulatory/NAIC SAP

Investor/SEC GAAP

Management modified SAP or GAAP or a combination, depending upon managementpreference & the companys situation

B. Advantage of 1 set of accounting rules:Reduced cost & confusion in the creation of info (i.e. no need to spend time calculating &reconciling estimates under multiple systems).

Disadvantage:Need to make compromises to make the info apply to all users, so these compromisesmake the info suboptimal to some.

Model answer #2

A. Regulators SAPInvestors GAAPTax authorities modified SAPManagement SAP, GAAP, or some other set of rules depending on the purpose.

B. Having one set of rules would simplify the job of the accountants and simplify theaccounting information systems needed to keep track of everything.

However, compromises would have to be made such that the final resulting statements Income Statement, Balance Sheet, etc. may not provide useful information to any set ofusers.

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Number 28

Model answer #1

A:1. To ensure that theres sufficient funds to return to the policyholders in the

event of cancellation of all policies.2. To match income with expenses.

B.1. Seasonal Contracts Insurance contracts that insures only snowmobiles

since snowmobiles are only used during winter months, the exposure ishigher during winter.

2. Extended Warranty Contracts The exposure is usually higher toward theend of the contract as this is when mechanical failure will tend to happen.

C.For extended warranty contracts, the company may lower rates in the first fewyrs since no losses have emerged and favorable results are showing under thepro-rata method. Rates then become too low when losses emerge in the later yrs

which will cause the company to lose money..

Model answer #2

A.1. To withhold premium to pay for cancelled policies.2. To match revenue with expenses.

B1. Aggregate excess policies More likely to hit retention later in the cycle

when more losses have occurred.2. Warranty Contracts One would expect more failures (hence more costs

later in the term).

C.1. Pro-rate means earning premium evenly. At earlier dates (such as warranty

above) expected losses are low, you may stupidly believe you are profitableand start writing more policies or worse, lower rates.

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Number 29

Model answer #1

a) Ceded Premium = 0.75 * 80 = 60

Ceded Unearned Premium = 0.75 * 40 = 30Ceded Loss Reserves = 0.75 * 40 = 30Ceding Commission = 0.3 * 60 = 18

Net Cash = Cash Ceded Premium + Ceding Commission = 100 60 +18 = 58Net Unearned Premium = Unearned Premium Ceded Unearned Premium = 40 -30 = 10

Assets

Cash 58Total Assets 58

Liabilities and Policy Holder Surplus

Unearned Premium 10Loss Reserve 10Total Liabilities 20Policy Holder Surplus 38Total Liab & PHS 58

PHS = Total Assets Total Liab = 58 20 = 38

b) Yes surplus went from 20 to 38 after reinsurance thanks to the ceding commission.

Model answer #2

a) AssetsCash 58Total Assets 58

Liabilities & SurplusUnearned Premium 10 = 0.25% of 40Loss Reserves 10 = 0.25% of 40Total Liabilities 20Policyholder Surplus 38 = 58 -20

Total Liab & Surplus 58

WP to reins 60Ceding Commission to Primary = 60 * 0.3 = 18Cash = 100 60 +18 = 58

b) Yes the policyholder surplus has increased from 20 to 38 due to the ceding commission

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Number 30

Model answer #1

a) Although the company cedes away profitable business the insurer achieves surplus relieffrom the quota share contact. There is a limitation about premium/surplus ratio. The

insurer needs surplus relief to increase its surplus and decrease the premium to surplusratio,

b) To qualify for reinsurance accounting, two conditions must be met:a. Reinsurer assumes a significant reinsurance loss from the reinsurance portion of

the insurance contractb. It is reasonably possible that the reinsurer will suffer a significant loss

Since we have a very profitable book of business here, it is unlikely the treaty will meetthe 2ndcriteria unless due to a condition in 113 If the reinsurer assumes almost all theloss from the reinsurance portion of the insurance contract then the contract could stillqualify for reinsurance accounting.

Model answer #2

a) Premium to surplus ratio should not be greater than 3:1 to avoid the attention of theregulators

So the ceding insurer, by ceding away premiums (thus reducing written premium) andreceiving ceding commission (thus increasing surplus) can bring its premium to surplusratio down to an acceptable level, even if it has to cede profitable business.

b) 1. Reinsurer must assume significant insurance risk2. There must be a reasonable possibility of significant loss to the reinsurer from thetransaction.

The reinsurer must demonstrate that these conditions are met. It is probable that they willin this case because a profitable book of business does not mean losses are improbable.

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Number 31

Model answer #1

a. When the reinsurer assumes all of the insurance risks from the ceding co. and cedingco. is no longer liable for unpaid claims or services due to policyholders.

b. Both underwriting risk and timing risk must exist for reinsurer to assume significantrisk.

c. Sliding Scale Commission or Retro Prem If reinsurer requires insurer to pay

additional prem, is premium paid a high % of losses. limits reinsurers possibility

of incurring a significant loss.

Loss sensitive provisions such as loss corridors where the ceding companyreassumes part of the loss.

Model answer #2

a. When the responsibilities of the primary insurer are extinguished (i.e. a novation)

b. If either

The probability of significant variation in the amount or timing of payments is remote.

The contract allows for a delay in the timely payment of reimbursement from reinsurer tocedant.

Provisions that allow for additional premium to be paid by the insurer to reinsurer basedon the experience of the contract (i.e., retro premium policies)

Carryforward provisions that allow experience to be carried forward into subsequentterms

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Number 32

Model answers #1

Part a1. External Context Identify strength, weakness, opportunity or threats to enterprise. One

thing could be the threat of being sued for a defective equipment.2. Internal Context Overall objective of the enterprise.3. Risk Management Identify the risks that the company can face. Fire exposure to the

company; need to buy insurance.Part b

1. Consult with experts in the field, internal lawyers, etc to determine the legal climate &evaluate the likelihood of adverse changes in judicial rulings & jury awards in tort cases.

2. Discuss risk tolerance with management to evaluate the range of financial results thatwould be preferred & evaluate the performance of other companies prod. liab. lines todetermine a range of reasonability.

Part c1. Retail Risks company chooses to finance the loss from its own surplus

2. Transfer Risks purchase insurance to shift the exposure

Model answer #2

Part a1. internal context company governing structure2. external context companys relationship w/ stockholders3. risk management context What current risk management procedures are in place

Part b1. Look at historical data for similar equipment to see incidence of suits, damages, etc.

2. Seek expert advice from panel of surgeons who perform those procedures to have themassess potential for damages.

Part c1. Retain risk self insurance2. Transfer risk buy insurance

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Number 33

Model answer #1

a) One of a kind competitor is strategic risk.Response is to create a new, non-overlapping business design/plan

b) Since the competitor is looking for large deductible policy market share, the small insurercould try to capitalize and grow in the small deductible market share

Competitor should shift its business plan and offer better quality of service for the pricecharged, i.e. not focus only on cheapest price

Model answer #2

a) The strategic risk is a one-of-a-kind competitorThe counter measure is to develop a new non-overlapping business plan

b) The small insurer could offer changes in terms and conditions that may not bring muchadditional cost, but might entice insureds

The small insurer could offer better claims management, or even an emergency hotlinenumber

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Number 34

Model answer #1

1. Future rate level: a distribution of future rate level due to how many new competitorswill enter the market.

2. Future loss level: a distribution of future losses based on different weather scenarios.3. Interest rates: future interest rate changes that might affect investment income.4. Customer retention level: distribution of whether customers will renew their policies in

the future based on different pricing scenarios.

Model answer #2

1. Premium rates: premium rates able to be charged2. Market share: market share should vary as new competitors enter; inversely correlated

with premium rates3. Demand for the reinsurance product: total number of potential customers

4. Frequency and severity of covered perils: weather patterns, building codes and otherfactors influencing expected loss may be changing.

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Number 35

Model answer #1

If they scan the horizon and can see before everybody else that a threat is imminent they cancome up with strategies that not only will see the company through the difficult times, but also

will give it an edge over competitors. The key is to be a risk shaper rather than a risk taker anduse risk to your advantage.

Model answer #2

Like the example given in the paper of Bill Russell not only dominating in the level of reboundshe was able to get but also immediately looking to see which of his teammates he should pass theball to, strategic risk management can be used proactively instead of reactively. By concentratingon the areas of focus given by Slywotzky and Drzik and implementing quick countermeasures orhedges against things going sour, a manager may forestall a detrimental development or elsemitigate the results of something out of his control.

The key is to recognize potential downfalls and implement strategies to cope with them beforethey come to pass.

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Number 36

Model answer #1

a) 1 - Primary insurer is not accustomed to writing large home values or business on thecoast, so it has the risk of underpricing its business.

2 Reinsurer priced its excess of loss treaty according to the current policy limit profileand geography of exposures. Changes to these could result in unanticipated loss and lossespenses.

b) Insurer may look to reinsurer for guidance on pricing this unfamiliar type of business.Moreso, insurer could seek out facultative reinsurance for the extremely different riskswhere there is a coverage gap.

Reinsurer may wish to renegotiate terms of the treaty, at the very least price according toliberalized guidelines.

Model answer #2

a) Primary should be concerned about catastrophes with liberal coastal restrictions. Therecould be increased total losses for a large number of properties at once. This will hurtwith frequency of claims but also have less profit sharing from reinsurer.

Reinsurer should be concerned about increase in mix and value of homes. There nowcould be more losses in the excess portion and the insurer premiums to reinsurer may notbe adequate.

b) The reinsurer may want to get retrocessional reinsurance and cede layers above theirs toother reinsurance companies.

The primary insurer could get Cat coverage to protect itself.

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Number 37

Model answer #1

A.)A hurricane could result in many of the policies under the treaty experiencing losses andcausing big losses to the insurer because:

a. The per-occurrence limit could be penetrated making the insurer retain more than40%.

b. Maximum per-risk limit can easily be penetrated since the insurer offersexposure up to $25 million.

B.) Insurer needs to purchase:a. Catastrophe reinsurance attaching at $20 million.b. Excess of loss per-risk reinsurance attaching at $5 million, both with appropriate

coinsurance provisionsC.) -- Variable Quota Share: of retention can vary depending on the insured value and a

lower % is used for higher valued policies-- Surplus Share: insurer retains certain amount of insured value (a line) and cedescertain number of lines to reinsurer.

Both offer a ceding commission.

Model answer #2

A.)a. The per-risk limit of the treaty is $5M, but the range of insured values is up to

$25M. This means that individual losses between $5M and $25M will not bereinsured.

b. The per-occurrence limit is $20M, which could be reached by accumulation ofsmall or large losses that result from a hurricane.

B.)

a. The insurer can buy excess of loss reinsurance for the layer between $5M and$25M.

b. The insurer can buy catastrophe reinsurance to indemnify them against lossesfrom a hurricane. The catastrophe reinsurance would be cheaper if the quota-share agreement inures to its benefit.

C.)a. Surplus Share reinsurance: still provides a ceding commission and the insured

sets a retained line where it would wholly retain policies with limits below theline.

b. Variable Quota Share: this functions like surplus share. The insurer would seekreinsurance that enables it to retain low-limit policies. It is likely that this wouldstill provide a ceding commission.

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Number 38

Model answer #1

a) Excess of loss Dollar threshold above which the reinsurer has liability to the primaryinsurer (per claim or per occurrence)

Pro-rata Reinsurer pays on each claim from the first dollar

b) Excess of loss Percent of subject premium, charged for XOL cover

Pro-rata Reinsurer pays a given percentage of each claim and receives the samepercentage of premium. Ceding commission can play the pricing role assumed by the ratein a XOL treaty.

c) Excess of loss Premium charged by the primary insurer for the policies underlying thetreaty.

Pro-rata: subject premium is used in the context as well, but gross losses are directlyshared in the same proportion as premium

d) Excess of loss Percent of loss in reinsured layer that the primary insurer must retain.

Pro-rata the pro-rata percentage is the complement of the percent retained. Pro-rata is inessence a co-participation provision on the whole book from first dollar.

Model answer #2

a) Attachment point the primary insurer retains all of the losses below this point. No suchconcept in pro-rata as all losses, regardless of ground-up size, are ceded/retained using

the pro-rata percent.

b) Rate the percentage of subject premium ceded to reinsurer as premium for reinsurancecoverage. For pro-rata, reinsurance premium ceded percentage is the same as thepercentage of loss ceded

c) Subject premium the premium collected by the direct insurer on policies covered underreinsurance agreement. This is the same in pro-rata agreement.

d) Co-participation a percentage of the loss within the XOL coverage layer that theprimary insurer must retain. Similar to pro-rata percentage, except in XOL, it applies onlyto losses within reinsured layer and does not apply to premium.

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Number 39

Model answer #1

A. Use quota share that provides immediate surplus relief in the amount of cedingcommission.

B. Aggregate excess of loss it restricts exposures to a given amount of loss ratio

Per risk excess of loss it restricts the exposure excess of the attachment point

Model answer #2

A. Pro-rata reinsurance such as quota share reinsurance or surplus share reinsurancewould address the premium to surplus ratio issue because they provide surplus reliefin the form of a ceding commission.

B. Excess of loss reinsurance could address the issue of writing high valued homes since

it provides large line capacity. The primary will simply cede off the higher layers tothe reinsurer.

Aggregate XOL reinsurance can address the issue of having an acceptable loss ratio.Aggregate XOL reinsurance provides loss ratio stability because once retained lossesreach a certain level, the reinsurer begins offering protection.

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Number 40

Model answer #1

Limit Premium Premium in Layer

1 6M 02 8M 1.6 = 8 x 0.25 / 1.25

3 12 3.72 = 12 x 0.45 / 1.45

4 10 3.75 = 10 x 0.6 / 1.6

5 4 1.41 = 4 x 0.6 / 1.7

Total 10.48M

You didnt say what primary ELR is; Im assuming it is 100%.

Reinsurer needs to charge 10.48M / 0.6 / 0.9 = 19.407M

Model answer #2

Assuming the table haspurepremiums:

Limit1M No exposure2M 8M x (1 1 / 1.25) = 1.6M3M 12M x (1 1 / 1.45) = 3.724M4M 10M x (1 1 / 1.60) = 3.75M5M 4M x ([1.6 1] / 1.7) = 1.412MTotal 10.486M

Pure Premium = 10.486M

Premium = 10.486M / (1 0.4) / (1 0.1) = 19.418M

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Number 41

Model answer #1

A

[ ] ( )( )[ ] ( )

Kx

xx

unwindofPVonTax-LossFutureofPVratetaxResBasisTaxxx

5.836,1

.

)425(*35.0350,135.0*725.0*000,2

*

=

+=

+=

BInsurer is seller of Liabilities. Therefore insurer pays consideration.

Ambivalent point is max value seller is willing to pay. So given that $1.75 M < $1.86 M,insurer would regard $1.75 M consideration as better than break-even.

Model answer #2

A

46.538,836,1

35.01

35.0*000,450,1250,701,1

'

750,14835.0*000,425

000,850,1

=

=

=

=

=

==

=

=

=

PointeAmbivalenc

1,701,250

148,750-1,850,000

UnwindonTax-PVsell)to(noteAmbivalencsSeller

UnwindRemainderIRStheofPVonTax

1,450,000

0.725*2,000,000ReserveBasisTax

LiabilityofPV

BIn (a) the sellers ambivalence point is $1,836,538.46 which is higher than $1.75 million.This deal is better for seller but worst for the buyer considering both have the same taxadvantage.

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Number 42

Model answer #1

(1) (2) (3) (4) (5) (6)

Cvg A Limit DWP $600,000 as

% of A Limit

$1,100,000 as

% of A Limit

Exposure Factor Exposure

Premium100,000 10M 600% 1100% 100-100=0% 0

200,000 15M 300% 550% 100-100=0% 0

500,000 20M 120% 220% 100-90%=10% $2M

1,000,000 30M 60% 110% 87.5%-45%=42.5%

$12.75M

Total 75M $14.75

(5) Exposure factor = difference in Cum Loss Distribution % for columns (4) and (3)Column (3) = 600,000 / cvg A limitColumn (4) = 1,110,000 / cvg A limit$1,100,000 = Retention + limit of Reins layer

Fraction of expected losses covered = Exposure Premium / DWP = 14.75 / 75 = 19.66%

Model answer #2

Limit % under @ 600K % under @1100K

Vlookups Exposed Premium

100K 600k/100k=6.000 1100/100=11.000 1 1 = 0 0

200K 600k/200k=3.000 1100/200=5.500 1 1 = 0 0

500K 600k/500k=1.200 1100/500=2.200 1 - .9 = .1 .1(20M)=2M

1000K 600k/1000k=.600 1100/1000=1.100 (.9+.85)/2 - .45 =.425

.425(30M)=12.75M

Total 14.75M

10M15M20M30M75M

% covered = 14.75M / 75M = .197

19.7% of total losses covered

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Number 43

Model answer #1

A. losses expected in 200 x 100 layer = 23,875 22,084 = 1,791

This is 1,791 = 7.33% of expected loss24,430

Reinsurance premium = 7.33% = 9.46% of expected loss1 - .15 - .075

= 2,311

B. Primary charged 24,430 x .95 = EL x inadequacy = 32,2341 - .24 - .04 inflation for expense & profit

C. Ceding percent = .0733* (b) = 2,362.8

It would be adequate but only because the primary insurer includes a high expenseratio. The reinsurance rate would need to be adjusted for primary inadequacy andexpense and profit then built up correctly.

Model answer #2

A. reinsurance covers loss from (100,000 to 300,000) layer.Expected loss: 23,875 22,084 = 1,791Reinsurer charge = 1,791 = 2,311

1 15% - 7.5%

B. primary insurer charge = 24,430 x 95% = 32,2341 24% - 4%

C. ceding percentage = 200 = 57.14%350

57.14% x 32,234 = 18,419 > 2,311

Much more than adequate for reinsurer. Because most loss is below the retention lineof 100,000 reinsurance premium should reflect such loss distribution.

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Number 44

Model answer #1

a) Retained amount = .35 * (10,000 + 5,500 + 7,000 + 600) = 8,085

b)

Policy AOI Retention Loss AmtRetained

Loss

A 200,000

60% =[1 - (4 *

20,000 /200,000)]

10,000 6,000

B 50,000 40%

5,500 2,200

C 20,000 100%

7,000 7,000

D 10,000 100%

600 600

15,800

Model answer #2

a) Retained amount = (1 - .65) * (10,000 + 5,500 + 7,000 + 600) = 8,085

b)

Policy AOI

Amount

covered % ceded Loss Amt

Retained

Loss

A 200,000 80,000 4 lines 40%

10,000 6,000

B 50,000 30,000 2 lines 60%

5,500 2,200

C 20,000 -too

small 0%

7,000 7,000

D 10,000 -too

small 0%

600 600

15,800

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Number 45

Model answer #1

a. The Stanard-Buhlmann method should receive more weight in recent Accident years.The chain ladder method can produce volatile results at early evaluations.

b. The chain ladder method should receive more weight in older years. The methodbecomes more stable as it ages and it is harder to on-level older premium as required bythe Stanard-Buhlmann method.

Model answer #2

a. More recent green years give more credibility to the SB estimate since the Chain Ladderestimate is subject to great variability due to sporadic loss emergence at this young age.

b. As data matures, assign more weight to Chain Ladder for the reason mentioned in part(A), and also because Stanard will become more error prone due to cumulative rate-

adjustments over many years.

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