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49 Sample Solutions Exam 5, May 2008 Released: August 18, 2008

50 Exam 5, Question 1 1. Must have fortuitous losses If losses are possible, they should occur by chance alone. Intentional losses are not insurable. 2. Independent and not catastrophic This must hold so that a single loss event will not make an insurer or an entire industry insolvent due to a single occurrence. 3. Affordability Policyholders must be able to afford the coverage; some coverages like flood insurance, are not supplied by the private market because they are prohibitively expensive.

51 Exam 5, Question 1 1. Definite and measurable Losses should be definite in time, cause, and location and should be measurable. 2. Fortuitous losses Losses should be accidental and unexpected. 3. Pure risk There should be no chance of profit No speculation

52 Exam 5, Question 2 a. The principle of indemnity asserts that an insured should be compensated only for the value of the loss. b. Ex: Actual cash value If an insured could get replacement cost rather than actual cash value, they may be more likely to submit fraudulent claims. Ex: Any deductible or coinsurance Since insured is partly responsible for loss, they will be less likely to intentionally cause loss or put themselves or their property in danger of loss.

53 Exam 5, Question 3 a. Large settlement that will be paid in installments for a predetermined amount of time and total dollar amount. b. c. 1. Claimant receives monthly payments tax free 2. Claimant is guaranteed payment 1. Insurer able to settle claim quicker 2. Insurer able to purchase annuity to cover payments for less than the total dollar amount to be paid to claimant

54 1. May not be legal to insure property Ex. Illegal narcotics held for sale Exam 5, Question 4 2. Property may not be covered by perils insured against Ex. Crack in building foundation 3. Property may be more advantageously insured elsewhere Ex. Automobile

55 Exam 5, Question 5 a. 1. Provide additional limits above an underlying policy s per occurrence limit 2. Provide coverage for some claims not covered by the underlying policy terms, subject to a self-insured retention b. Drop-down coverage occurs when an umbrella takes over as the primary policy, either through reduction/exhaustion of the underlying policy s aggregate limits or when the umbrella covers a claim not covered under the underlying policy s terms, subject to a self-insured retention.

56 Exam 5, Question 6 UM Coverage cannot be stacked, so the most that will be paid is the highest available limit of $250,000. UM does not cover property damage, so Susan s car is not covered. Susan s policy is primary, so it pays $100,000. Subject to the limit of 250,000 overall, Bob s UM coverage pays 250, ,000 = 150,000

57 Exam 5, Question 7 Coverage A limit $200,000 Deductible 1,000 Coverage B limit $200,000 * 10% = $20,000 Coverage C limit $200,000 * 50% = $100,000 Coverage D limit $200,000 * 30% = $60,000 Dwelling: Coverage A will cover the replacement cost, which is $150,000 - $1,000 (deductible) = $149,000 Contents: Coverage C will cover the actual cash value which is $90,000 Detached Garage: Coverage B will cover the replacement cost which is $20,000 (reach the limit) Detached Shed: Coverage B will cover, but the limit has been reached, no payments. Additional Living Expense: Coverage D will cover $25,000 The insurer will pay $149,000 + $90,000 + $20,000 + $25,000 = $284,000

58 a. Paula s PAP - Collision Deductible = Other than collision Deductible = 250 Exam 5, Question 8 Car is stolen, there is a waiting period of 48 hours for transportation expense. The transportation expense will be maximum $20 day, maximum 600 in total. Taxi fares: 1 st day $30 not covered 2 nd day $30 not covered 3 rd day $30 cover $20 \ 4 th day $30 cover $20 > Total taxi = $60 5 th day $30 cover $20 / Remaining 28 days (3 days + 30 days 5 days) = every day <$20 a day. Total Transportation = = 605 capped at $600. Car s damage (other than collision) = 10,000 deductible 250 = 9,750 Total payment = ,750 = 10,350 b. First day taxi $30 no coverage Waiting Period for transportation = 24 hours Second day taxi $30 capped at $20 Rental 545 Total transportation = 565 Damage to Car = 10,000 deductible 500 = 9,500 under collision coverage Total payment = 10,065

59 Exam 5, Question 9 1. Mediation Both parties to a claim agree to bring in an outside party who helps to facilitate the communication and settlement of the claim. 2. Arbitration When the coverage is in dispute, both parties to a claim agree to submit all the evidence to an arbitrator to determine if coverage exists. 3. Pretrial settlement conference The judge of the case will meet with attorneys of both parties 2 to 3 weeks before the trial to discuss evidence, stipulate damage amounts and attempt to settle before the case goes to trial.

60 Exam 5, Question 10 a. b. 1. Assigned Risk Plans 2. Reinsurance Facility 1. Once applicant has been rejected as voluntary risk, they can apply for coverage through assigned risk plan. Such applicants are then randomly assigned to insurers (typically based on voluntary market share) who have to accept them & handle them in the usual way (i.e. insurer retains all premiums & losses for assigned risk) 2. With a reinsurance facility, insurers accept all risks, but can cede undesirable risks to reinsurance facility. Facility results are pooled among all insurers. c. already covered in answers to b) but for clarity s sake: 1. Luck of the draw (i.e. insurers responsible for assigned risks) 2. Losses (or profits) shared among insurers

61 Exam 5, Question 10 a. b. c. 1. Assigned risk plan 2. Joint underwriting association 1. Insureds have proof of rejection from the voluntary market. Insurers participating have no choice which risk to select. Risk is assigned to them and they are responsible for losses of risks assigned to them. They are responsible for insurer function of risk assigned to them. 2. Servicing insurers are appointed. Insureds are not really assigned to any single insurer though servicing carriers will handle the insurer functions. 1. Profits and losses from policies you own. Not shared with others. 2. Profits & losses shared based on premium volume in voluntary market.

62 Exam 5, Question 11 a. b. 1. Independent agency system 2. Exclusive agency system 3. Direct writers Ownership of expiration producers may or may not own the expirations of the policies they produce; independents own, exclusive & direct do not own; when you own the expiration, you can shop the policy to any insurer you want. Contractual relationship producers may be employees, i.e. paid by salary by the insurer, or an independent contractor (usually paid by some type of commission); independents are independent contractors, as are exclusive, while direct writers are employees of insurer.

63 Exam 5, Question 12 a. 1. Verifiable can the insurance company determine if the information provided is accurate? 2. Practical Is the exposure base easy to estimate, or does it require costly inspections? 3. Varies with hazard Does the exposure base increase and decrease as the actual exposure does? b. Exposure base number of credit cards 1. Verifiable through credit services 2. Practical since credit checks are fairly inexpensive 3. Varies with hazard to the extent that more credit cards generally means more credit carts that can have their information stolen by an identity thief.

64 Exam 5, Question 13 a. Written Premium are the dollar amounts charged by an insurer for policies written during a specific time period. The total policy premium is included in the written premium. b. Earned Premium is the amount of the policy premiums that have been exposed to risk during a specified time period. Earned Premium is directly proportional to the portion of the policy period covered by the insurer during the specified time period. c. Unearned Premium is the portion of policy premium that has yet to be exposed to risk as it covers a future time period during which the policy will be in-effect. d. In-force Premium is the total written premium of all policies in effect at a specific point in time.

65 Exam 5, Question 14 Assume policies are written uniformly throughout policy period. Use geometric relationship OLF = Current Rate Level CY/PY Rate Level a CY On Level Factor = 1.00 x.92 (1-(1/2)(5/6) 2 )(1.00)+(1/2)(5/6) 2 (.92) 2006 CY On Level Factor = b PY On Level Factor = = x.92 (1/2)(1/6) 2 (1.00)+(1-(1/2)(1/6) 2 )(.92) = x.92 (1/6)(1.00)+(5/6)(.92) = PY On Level Factor = 1.00 x.92 1 x.92 =1.000 c. Extension of exposure method re-rates each policy at current rate level. This may be preferable to the parallelogram method since it does not require policies to be written uniformly throughout policy period.

66 Exam 5, Question 15 a. Past rate changes Make a direct adjustment to historical premium and restate it at the current rate level. b. Step 1: 112 = Step 2: The trend period: 7/1/2007 7/1/2009, 2 years Trend factor = = The trend factor to 2006 calendar/accident year x =

67 Exam 5, Question 16 a. Trend will decrease. Premiums for coverage with $1000 deductible < than for $250 deductible. If more customers buy $1000 deductible coverage, premiums will go down b. Frequency will also go down as losses below $1000 are not reported and paid for by insured c. If $1000 deductible policy is priced inadequately, profitability will go down if more insureds start committing at $1000 deductible.

68 Exam 5, Question 17 a CY incurred losses = $ CY incurred losses: $500 + $3500 $3000 = $1000 for loss #1 total paid + change in reserve $ $ $1000 = $15000 for loss #2 total paid + change in reserve so 2007 CY incurred losses = $ $15000 = $16000 b AY incurred losses as of 12/31/2008 = $500 + $ $3000 = $ AY incurred losses as of 12/31/2008 = $ $ $1000 = $15000 c. Since both losses come from PY 2006, 2006 PY incurred losses as of 12/31/2008 = $ $15000 = $ PY incurred losses as of 12/31/2008 = $0 d. One advantage is that premiums and losses can be matched using policy year incurred losses. One disadvantage is that policy year data is the least mature and least responsive compared to CY or AY data.

69 Exam 5, Question 18 a. Basic limits trend: All but the $20K loss are already at the cap. So the BL trend is simply ( *1.1)/( ]-1=1% b. Excess limits trend is [( ]*1.1-50*4)]/[ ]-1=27% c. When loss trends are negative.

70 Exam 5, Question 19 a. Min: 50/100 =.5 =.75 35% of workers earn the minimum limitation. 2/3.667 Max: 67/100 =.667 = % of workers earn at least the maximum weekly 2/3.667 benefit. 42% - 20% = 22% of wages are unaffected by min/max limits Current Effective Comp Rate =.35(.5) +.40(2/3) +.22(2/3) =.5883 Revised Min: 50/100 =.5 =.75 35% of workers earn at or below minimum 2/3.667 weekly benefit. Revised Max: 100/100 = 1.00 = % of workers earn at least the maximum 2/3.667 weekly benefit 81% - 20% = 61% of wages unaffected by limitations. Revised Effective Comp Rate =.35(.5) +.09(1.00) +.619(2/3) = % Change in Effective Comp Rate = = 14.16% b. Incentive effects are the human behavioral responses to changes in the direct effects of increasing or decreasing benefit levels, compensation rates, etc. c. Because increasing the maximum benefit increased the effective compensation rate, we might expect to see longer duration injuries, since injured workers are receiving more benefit, they have less incentive to return to work. We would also expect an increase in claims, since workers will be paid more for injuries, they will report more injuries.

71 Exam 5, Question 20 Lag Report Year Lag A B C D 1 A C D E 2 A D E E 3 A E E E 4 A E E 5 A E 6 A a. Occurrence policy in $2000 = All A s b. 1st year claims made = B c. 2 nd year claims made = All C s d. 3 rd year claims made = All D s e tail policy = All E s

72 Exam 5, Question 21 a. Retroactive date is a date which activates the claims made policy. Claims occurred on or after that date and reported during the policy period will be covered by the CM policy. b. Extended reporting period extends the periods for the claims to be reported under CM policy after the policy period ends. Claims occurred during the policy period and reported before the extended reporting period ends will be covered by CM policy.

73 Exam 5, Question 22 a. Complement = (present rate) x (last trend)t x (1+ requested change) (1+ approved change) T= time in trend from 1/1/07-1/1/09, 2 years = 200 (1.1) 2 (1.20) = (1.15) b. Advantage: unbiased as it s based on current rates which are assumed to be unbiased. Disadvantage: may be inaccurate if process variance in losses is high.

74 Exam 5, Question 23 a. A fixed expense is an expense that is incurred that does not vary with premium. A variable expense is an expense that is incurred that varies with the amount of premium. b. Fixed exp ratio =.6(100k) +.5(66k) +.25(40k) = =.1 1m 1m 1m var. exp ratio =.4(100k) +.5(66k) + 110k +.75(40k) = =.2 1m 1.1m 1.1m 1m Rate = LR + Fixed Exp ratio 1 V Q Rate = = 13.3% increase c. Rate changes impact the fixed expenses as a percent of premium because the premium the ratio is applied to is different than contemplated in the ratio itself. If there had been a large rate increase after the fixed ratio was calculated the estimated fixed expenses would be higher than actual.

75 Exam 5, Question 24 Using McClenahan s notation F = 16 V = 15% Q = 3% R = 300 so R = P + F 300 = P + 16 I V Q P=230 If P = P x 1.1 = 230 x 1.1 = 253 then R = =

76 Exam 5, Question 25 a. TLR = = 0.77 b. Old TLR = = Therefore effect = = -1.3% 0.77 c. Experience Rate Change = = -5.3% 0.76 d. Overall Rate Change = (0.72) (0.76) 1 = -6.5% (0.76) (0.77)

77 Exam 5, Question 26 a. Compute the on level earned premium (OLEP) OLEP for CY/AY 2006 = Earned exposures x present rate = 345,704 x 110 = 380, OLEP for CY/AY 2007 = 396,714 x 110 = 436, Trend the premium at 3% between the average earned date in historical period to the exposure period. Trend period for CY/AY 2006 = 7/1/06 to 1/1/2010 = 3.5 years Trend period for CY/AY 2007 = 7/1/07 to 1/1/2010 = 2.5 years CY/AY 2006 projected premium at present rates = 380,274.4 x (1.03) 3.5 = 421,723 CY/AY 2007 projected premium = 436,385.4 x (1.03) 2.5 = 469,854 AY b. Link Ratio ,200 = , We can see the change in case reserving practices from the link ratios. We will use the link ratios below the solid line. Develop losses to ultimate AY 2006 ultimate losses = 240,000 x LDF x LDF x LDF x LDF 63-ultimate = 240,000 x 1.1 x 1.05 x 1 x 1 = 277,200

78 AY 2007 ultimate losses = 210,000 x 1.2 x 1.1 x 1.05 x 1 x 1 = 291,060 Loss trend is (.99)(1.02) Trend period for AY 2006: 7/1/06 1/1/2010 = 3.5 yrs Trend period for AY 2007: 7/1/07 1/1/2010 = 2.5 yrs AY 06 ultimate loss + ALAE = 277,200 x ((.99)(1.02)) 3.5 = 286,825 Loss + ALAE + ULAE = 286,825 (1.1) = 315,508 AY07 ultimate loss + ALAE = 291,060 x ((.99)(1.02)) 2.5 = 298,243 Loss + ALAE + ULAE = 298,243 x 1.1 = 328,067 c. CY/AY 2006 loss ratio = 286,825 (1.1) = ,723 weighted loss ratio 40% / 60% CY /AY 2007 loss ratio = 298,243 (1.1) = 69.8 W = 71.8% 469,854 Indicated Change Factor= Wtd LR + FE% = 71.8% + 8% = V Q Crd. Wtd. Indicated rate change = [1.064 x Z +(1-Z) ] - 1 = (1.064x ) -1 = = 4.8%

79 Exam 5, Question 27 a. Pure premium method is more appropriate than loss ratio method when current rate level premiums are difficult to calculate. b. Loss ratio method is more appropriate than pure premium method when a well defined and responsive exposure base is not present.

80 Exam 5, Question 28 a. 1. Verifiable initially the color may be easy to obtain from VIN number information. However, as cars age and get repainted, possibly a different color, someone would need to visually verify the color. 2. Administrative expenses the cost of running the VIN numbers or visually verifying the color may outweigh any value added to accuracy by including this variable b. 1. Privacy the color of your car should not invade privacy issues because people drive their car in public for everyone to see the color already. 2. Causality although the data may show some correlation between car color and losses, to the public, color of car is not a direct cause of loss.

81 Exam 5, Question 28 a. b. 1. Verifiable - color would be easy to verify 2. Objective Definition - color would also satisfy this criteria 1. Privacy - color would satisfy this criteria since color is not a very private issue 2. Controllability -the insured can choose the color of their car, so it is controllable

82 Exam 5, Question 29 a. ABC is going to attract lower cost insureds since the rate is going to be lower for them. XYZ is going to attract higher risks since their rate is lower as compared with ABC. XYZ will be adversely selected against. This will result in higher loss ratio for XYZ and can eventually have a problem of solvency. b. 1. Pricing - The companies can try to find a proxy (an estimate) for the abolished rating variable. 2. Marketing - When doing marketing to attract customers, the companies can try to not attract the people with the negative characteristic.

83 Exam 5, Question 30 We use Finger s notation. Note that since we only want indicated relativities & not rate indications, we don t need balanced adjustments or the offbalance factor. Territory Loss Ratio Preliminary Adjustment LR territory /LR total 1 420,000 = = , ,250,000 = =.971 1,680, ,000 =.8.8 = , TOTAL 2,030,000 =.766 2,650,000 Credibility Credible adjust (#claims/1082) =(A 1)Z + 1 (600/1082) = Territory Current Relativity Indicated Relativity x.6 = x 1 = x.52 = Credible adjustment territory Credible adjustment * base Current relativity

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85 Ter (1) Prem (2) Prem at Ter 2 Level Exam 5, Question 30 (3) Loss & ALAE (4) (3)/(2) LR (5) (4)/(4) 2 Ind Rels (6) Cred (7) Cred Wtd Rels 1 520, , , ,680,000 1,680,000 1,250, , , , New Rels Cred = sqrt(claims/1082) (7) = (5)(6) + (1-(6))(CurRel)

86 Ground up expected loss = x f(x) x Expected loss with $300 deductible Exam 5, Question 31 = 1000 x 2 _ dx 0 500,000 = 1 * x = , = (x 300) * f(x) dx Credit = = = 1000 (x 2 300x) dx ,000 = 1 x 3 150x , =

87 Exam 5, Question 32 a. E[LA 500 ] = 100 (0.2) (0.1) ( ) = 395 E[L] = 1,420 LER = 395_ 1,420 = = 27.82% b. Expected loss in excess of 500 = 350 (0.609) ( ) = ALAE = 350 (0.609) (0.1) = Fixed expenses = Variable underwriting expense provision = 22% Profit provision = 2% Premium for policy with 500 deductible = $272.20

88 Exam 5, Question 33 (A) (B) (C) (A) x (C)/(B) Class Premium Cur. Relativity New Relativity Adj Prem 1A 55, ,300 2B 100, ,000 3C 10, , , ,500 Off-balance factor = 165,700/159,500 = Proposed base rate = 100 (1.0389) (1.05) = $109.08

89 Exam 5, Question 34 a. LAS(500k) = E[x^500k] = Total Losses (0-500k) Occurrences LAS(250k) = E[x^250k] = Total Losses (0-250k) Occurrences LAS(500k) = 500, ,000, ,500, * 500,000 = 44,000, LAS(500k) = 176,000 LAS(250k) = 500, ,000, * 250,000 = 34,000, LAS(250k) = 136,000 ILF (500k) = LAS(500k) = LAS(250k) b. Two issues with using empirical data 1. Data may be censored by policy limits and therefore you would have a downward bias 2. Data may be too recent and you may not have closed all losses, you may have to develop losses to ultimate.

90 Exam 5, Question 34 a. See previous b. Two issues with using empirical data 1. Credibility - Data could be sparse for large losses, which makes the ILFs susceptible to random fluctuations and therefore unreliable 2. Ground-up loss data may not be available, especially for first party coverages where small losses under the policy deductible are not reported.

91 Exam 5, Question 35 a. If the average insurance to value (ITV) in the insurers book of business is less than that assumed in the rate calculations, rates are inadequate. If ITV > than assumed, rates too high overall. b. 1. If a new system or tool is developed to estimate replacement cost, ITV can change. 2. If the company initiates a marketing campaign encouraging customers to raise ITV, overall ITV can change.

92 a. cv F = coinsurance deficiency cv = 350,000 (.8) = 280,000 F = 275,000 Coinsurance deficiency = $5,000 b. CAR = F = 275,000 =.9821 cv 280,000 Exam 5, Question 36 c. Maximum penalty occurs when Loss = F So indemnity is.9821 (275,000) = 270, , , = $ d. 300,000 (.9821) = 294,630 No coinsurance penalty, since L > cv 300,000 > 280,000

93 Exam 5, Question More accurate indications - Since hurricane losses are very different from nonhurricane losses, separating the two allows more accurate indications and more accurate rates. 2. Apply appropriate classification - Some classification factors are not applicable to hurricane; for example, hurricane risk potential does not vary by fire protection code. Separating hurricane from non-hurricane component allows appropriate classification factors to be applied.

94 Exam 5, Question 38 a. Summary-based statistical plans summarize the data by line of business, by class, by state, and by coverage to satisfy regulatory requirements. While the transactionbased statistical plans contain detailed transaction level records which include the amount of premiums and substantial information on risk characteristics to support the insurer s business need for data. b. Transaction-based statistical plans Because this plan contains the detailed information on premiums and risk characteristics which can better serve the insurer s needs for pricing analysis.

95 Exam 5, Question Schedule Rating Based on the characteristics of loss exposures of insured, underwriters assign debit or credit for the policy. Actual experience is not considered. 2. Experience Rating Based on insured s experience, underwriters adjust the premium to be charged. Large risks that have more credible experience get more credibility towards their experience whereas small risks get less credibility towards their experience.

96 Exam 5, Question 40 a. An insured may have had bad loss experience in the past and the underwriter may only accept the risk using retrospective rating. b. If an insured has good loss experience or better than average loss experience, it will be reflected in their premium using retro rating.

97 Exam 5, Question 41 a. Company subject BL losses &ALAE = (Prem/Ops Manual prem) x (Expected BL Loss & ALAE ratio) X (Policy Adjustment Factor) x (Detrend factor) = $200k (.7) (.9) (.95) = $119.7k AER = actual experience ratio = Reported+ Expected unreported loss + ALAE Limited by BL & MSL Company subject BL losses & ALAE = $115k + $35k $119.7k = b. (credit)/debit = (AER-EER) * Z EER = Expected experience ratio, Z = credibility EER = ( ) (.45).85 =.213 < Max debit = +50% experience debit = 21.3

98 a. Exam 5, Question 42 Profitability At no exposures, we have no premiums and only fixed expenses. Profitability increases with sales until reaching a point where no more profitable risks can be written. As unprofitable risks are written, profitability declines. Exposures b. Adjust prices to follow the market and maintain market share. May have losses in the soft market, but larger profits in the hard market. c. The maintain market share strategy tries to stop at a fixed point on the curve, even as the curve itself moves downward. The idea is to not move backwards on the curve. Then when the hard market comes the company is near the top of the curve as the whole curve moves up due to increased prices.

99 Exam 5, Question 43 Traditional techniques only consider a single period. By doing so, they fail to consider differences in persistency amongst different risks. Persistency can have a significant impact due to loss and expense differences between new and renewal business. The asset share pricing model accounts for this by introducing multiple periods, persistency, and different assumptions for new and renewal business.

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101 Exam 5, Question 44 Prem PV (loss) Fixed Variable Persisty (cumulative) 1 x x 1 2 X x 0.6 Profit Discount PV (profit) 1 (x x) x 1 1 (0.9x 1120)/1 2 (x x) x (0.95x 1010) x 0.6/ x 1671 PV (prem) 1 X 2 0.6x / x return of equity = 1.418x 1671 = 0.06/2 x = x Indicated rate relativity = =

102 Exam 5, Question 45 (1) (2) (3) (4) Avg Net Grd-up Claim Claim Size Cost Grd-up Claim Size Interval Annual Probability of Claim in Interval ,000 18, , , , , > 600, , , When Grd-up Claim>Deductible, Net Claim Cost = Grdup Claim Cost - Deductible Note: (3) When Grd-up Claim > 600,000, the net claim costs are capped at Maximum Benefit $500,000 Annual Net Claim Cost = 300,000 * ,000 * = 140 Monthly Net Claim Cost = 140/12 Monthly Healthcare Rate = 140/12 * (1 + 20%) % = 18.82

103 Expected Claim Size in Interval Exam 5, Question 45 Accumulated Loss in layer Accumulate Prob k k 600k Over 600k Losses Excess of deductible = ,000 x = = 170 Losses Excess of Maximum Benefit = = 30 Therefore Losses in layer 100, ,000 = = 140 PMPM = 140 = Premium= (11.67) x = Answer *Assuming maximum benefit of $500,000 in excess of $100,000 deductible

104 Exam 5, Question E[X^ 500,000] E[X^ 100,000] = Expected cost. E[X^ 500,000] = 18,000 (0.0396) + 400,000 (0.0003) + 600,000 (0.0001) = E[X^ 100,000] = 18,000 (0.0396) + 100,000 (0.0004) = Expected cost = = 140 R = 140 *(1+.20) =