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3 Reasons For Increased Popularity of Retro Rated Policies
- 1. Policy returns premium to the insured for good loss experience
- 2. Cash flow advantages since premiums are paid as losses are reported or paid
- 3. Cost of insurance is harder to predict than in the past
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2 Methods of Calculating PDLD Ratios
- 1. Empirical Approach: use historical premium and loss development data
- 2. Formula Approach: use retro rating plan parameters
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Retro Premium Formula
- Pn = [BP + (CLn * LCF)] * TM where
- 1. Pn = Premium at nth retro adjustment
- 2. BP = Basic Premium
- 3. LCF = Loss Conversion Factor
- 4. TM = Tax Multiplier
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PDLD Ratio for 1st Retro Adjustment
- 1. P1 / L1 = [BP + (CL1 * LCF)] * TM / L1 or
- 2. P1 / L1 = [(BP / L1) * TM] + [(CL1 / L1) * LCF * TM]
- 3. Or Approximately,
- [(BP * TM) / (SP * ELR * %Loss1)] = [(CL1 / L1) * LCF * TM]
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PDLD Ratio for 2nd Retro Adjustment
- PDLD2 =
- 1. = (P2 - P1) / (L2 - L1)
- 2. = [(CL2 - CL1) / (L2 - L1)] * LCF * TM
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Loss Capping Ratio
- 1. Defi nition: ratio of capped losses to uncapped losses
- 2. Formula 1: CL1 / L1
- 3. Formula 2: LR * (1 - χ - LER), where
- a) LR = uncapped loss ratio and
- b) χ = Table M charge at max - Table M charge at min
- 4. Usually decreases as the data becomes more mature
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Reasons Slope is Not 1 in Fitzgibbon's Method
- 1. Some losses exceed loss limit, reducing slope
- 2. In some plans, minimum premium exceeds basic premium
- 3. A loss conversion factor (LCF) and a tax multiplier (TM) are applied to the incurred losses in the retro rating formula, thereby changing the slope of the line segment
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Teng & Perkins Assumptions
- 1. The premium responsiveness during subsequent adjustments is independent of the premium responsiveness during previous adjustments
- 2. The slope of the line segment depends on the time period, not on the beginning loss ratio or the beginning retro premium ratios
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3 Advantages of the PDLD Method (Feldblum)
- 1. Modeled directly on retro formula, so it is easily explained
- 2. Emphasis on the premiums sensitivity in the retro rating formula parallels the RBC loss sensitive contract o ffset in the underwriting risk charges and Part 7 of Schedule P
- 3. May prove useful when changes in the retro rating plan parameters distort the indications of other methods
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Reasons For a Change in The Slopes of Line Segments
- 1. Change in the average basic premium ratio (i.e., Change in the y-intercept)
- 2. Change in premium responsiveness (i.e., Change in the slope)
- 3. Change in the length of the loss reporting pattern (i.e., Change in the length of the line segment)
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Advantage/Disadvantage of Using Retro Formula to Estimate PDLD Ratio
- 1. Advantage: Responds to changes in retro rating parameters that are sold, whereas the PDLD ratios derived from the historic data may not be indicative of the future PDLD ratios
- 2. Disadvantage: Possible source of bias is the use of average parameters for the LCF, TM, max, min, and per accident limitation
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2 Facets of Underwriting Risk
- 1. Written Premium Risk: risk that future premiums will prove inadequate to cover the future losses and expenses
- 2. Reserving Risk: risk that the reserves held for accidents that have already occurred may prove inadequate
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3 Reasons PDLD1 Usually Greater Than Unity
- 1. Basic premium is included in the fi rst retro premium computation
- 2. Only a small portion of loss is limited by the retro max and per accident limit at this maturity
- 3. Application of the loss conversion factor and tax multiplier results in more than a dollar of premium per dollar of loss
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