Teng & Perkins Flashcards
Reasons for popularity of retrospective rated policies (3)
- attracts preferred customers - encourages loss control through returned premiums for good loss experience
- cash flow advantages b/c premiums are paid as losses are reported
- shifts a large portion of the risk to insured
Premium asset
= expected ultimate premium - current booked premium
OR sum of expected future retro adjustments
Formula for premium at the nth rating adjustment
premium = ( basic premium + ( capped losses * LCF ) ) * tax multiplier
First PDLD ratio using the retro formula approach
P(1) / L(1) = ( basic premium / L(1) ) * tax multiplier + cumulative loss capping ratio * LCF * tax multiplier
Approximation for loss at time n
L(n) = standard premium * ELR * % loss emerged at time n
Interpretation of the cumulative loss capping ratio and portion of losses outside bounds of retro min and max
( 1 - cumulative loss capping ratio ) % of losses developed through the nth rating adjustment are eliminated by the retro max, retro min, and per accident limits
portion of loss outside retro min and max bounds = capped losses - uncapped losses
Subsequent PDLD ratios using the retro formula approach
= change in premiums / change in losses
= incremental loss capping ratio * LCF * tax multiplier
Incremental loss capping ratio
= ( capped loss at time 2 - capped loss at time 1 ) / ( uncapped loss at time 2 - uncapped loss at time 1 )
Advantages of the retro formula approach for calculating PDLD ratios (2)
(Teng and Perkins)
- responds to changes in retro rating parameters sold
2. PDLD ratios are more stable
Disadvantages of the retro formula approach for calculating PDLD ratios (2)
(Teng and Perkins)
- potential bias exists because average retro rating parameters are used
- does not reflect changes in loss experience
Data required for the empirical approach to calculating PDLD ratios and explanation of lag (2)
- booked premium development (27 months)
- reported loss development (18 months)
annual subsequent evaluations
lag is due to delay in processing and recording retro adjustments
PDLD ratios (first and subsequent) using the empirical approach
1st PDLD ratio = cumulative booked premium / cumulative reported losses
subsequent PDLD ratios = change in booked premiums / change in reported losses
** calculate triangle of factors and select average at each retro adjustment
Reasons for an upward trend in PDLD ratios (2)
- more liberal retro rating parameters sold (more losses covered by premiums)
- improvement in loss experience (larger portion of loss w/in retro boundaries)
Reasons historical PDLD ratios may fluctuate significantly after 1st adjustment (3)
- premium or loss development on a few policies can drive total incremental development
- significant upward development in high loss layers results in no additional premium
- downward development on layers w/in loss limits can result in returned premium
> > 2 and 3 mean negative PDLD ratios are possible
How to respond if there are large fluctuations in historical PDLD ratios (2)
- average as many historical points as possible
2. use the retro formula approach
Reasons PDLD ratios calculated using the retro formula and empirical approaches could diverge (2)
- avg retro parameters are changing over time
- worse (better) than expected loss experience can cause a larger portion of loss to be outside (inside) retro/per accident bounds than predicted
Cumulative PDLD ratio
weighted average with weights = incremental % emerged
Interpretation of the cumulative PDLD (CPDLD) ratio
amount of premium insurer can expect to collect per dollar of loss yet to emerge
Reasons the CPDLD ratio is usually greater than 1 at the first adjustment (3)
- 1st retro premium includes the basic premium
- small portion of loss limited at early maturities
- LCF and tax multiplier result in more than a dollar of premium per dollar of loss
Expected future premium
expected future premium = CPDLD ratio * expected future loss
Ultimate premium
ultimate premium = expected future premium + booked premium from prior adjustments
Reasons that current booked premium may not = booked premium from prior adjustments (3)
- differences in timing of retro adjustments
- minor premium adjustments
- interim premium booking b/w regularly scheduled retro adjustments
Advantages of the PDLD method (3)
Feldblum
- easy to explain b/c it is modeled directly on retro rating formula
- emphasis on premium responsiveness parallels RBC loss-sensitive contract offset in UW risk charges and loss-sensitive contract in part 7 of schedule P
- useful when retro rating parameters adjust indications from other methods
What is covered in the basic premium (2)
- UW and acquisition expenses
2. insurance charge and excess loss charge
Description of Fitzgibbon’s method and Berry’s adjustment
plots retro premium against incurred loss (both as % of standard premium)
y = A + Bx where A = basic premium % and B = premium responsiveness
Berry adds a credibility weighting for actual experience
Problem with Fitzgibbon’s method
ignores actual experience
Teng and Perkins’ graph and Feldblum’s enhancement
Teng and Perkins - retro premium against incurred losses (both as % of standard premium) series of line segments with decreasing slope that passes through the origin*
Feldblum - removes avg basic premium so graph has an intercept at the basic premium amt
What slope represents and why line segments have decreasing slopes in Teng and Perkins/Feldblum graphs
slope = premium responsiveness
decreases over time because a larger percent of loss is excluded from rating due to loss limits and maximum premiums
