Teng & Perkins Flashcards
what does a premium asset represent (for retro-rated policies)?
(Teng/Perkins)
premium that the insurer expects to collect based on the expected ultimate loss experience, less the premium that the insurer has already booked
what is the premium asset also known as?
Teng/Perkins
earned but not reported premium (EBNR)
what are three reasons that retro policies are popular?
Teng/Perkins
- encourage loss control and loss management
- offer cash flow advantage to insureds
- shifts large portion of risk to the insured
how do retro policies encourage loss control and loss management?
(Teng/Perkins)
returns premium to the insured for good loss experience
good for insurer bc attracts preferred customers
how do retro policies offer a cash flow advantage to insureds?
(Teng/Perkins)
allow them to pay premium as losses are reported or paid
how do retro rated policies shift a large portion of risk to the insured?
(Teng/Perkins)
premium varies directly with the insured’s actual loss experience
(great for insurer due to increasing difficulty in predicting the cost of insurance)
how is “retro reserve” defined?
Teng/Perkins
difference between the premium deviation to date and the ultimate premium deviation
what is premium deviation?
Teng/Perkins
amount by which the booked premium differs from the standard premium
what is standard premium?
Teng/Perkins
manual premium adjusted for experience rating
what can the retro reserve be thought of as?
Teng/Perkins
negative equivalent of the premium asset
what is the first method that Berry and Fitzgibbon offer for calculating the retro reserve?
(Teng/Perkins)
- analyze historical relationship between LR & prem. deviation
- apply relationship to projected LR to determine projected ult. prem. deviation
- subtract prem. deviation to date from ultimate prem. deviation to produce retro reserve
what is the second method that Berry and Fitzgibbon offer for calculating the retro reserve?
(Teng/Perkins)
- estimate ult. prem using historical premium emergence pattern
- subtract current premium to get the retro reserve
what is the PDLD ratio?
Teng/Perkins
ratio of how premiums develop as losses develop
what are capped losses? (when calculating PDLD ratios for retro-rated policies?
(Teng/Perkins)
losses that contribute to additional premium
any total loss that exceeds the retro minimum and is below the maximum
what can the difference between the capped loss and uncapped loss be viewed as?
(Teng/Perkins)
portion of loss outside the boundaries of the retro min. and max.
how does the loss capping ratio change as data matures?
Teng/Perkins
decreases at data becomes more mature
why does the loss capping ratio decrease as data matures?
Teng/Perkins
increasing portion of the loss development occurs outside of loss limitations
what does the second PDLD ratio refer to?
Teng/Perkins
INCREMENTAL premiums developed between the first and second retro adjustments, divided by the INCREMENTAL losses developed between these two adjustments
(ie - chg in prem / chg in loss)
what is an advantage of using the retro formula to estimate the PDLD ratio?
(Teng/Perkins)
-responds to changes in retro params that are sold
what adjustments should be made to the PDLD ratio calculation if retro params change significantly over time?
(Teng/Perkins)
-more weight should be given to PDLD ratios derived from the formula than those derived from historical data
what is a disadvantage of using the retro formula to estimate the PDLD ratio?
(Teng/Perkins)
potential bias exists, since the formula approach uses the average params for the LCF, tax multiplier, max, min, and per accident limitation
what two types of data are needed for the empirical PDLD approach?
(Teng/Perkins)
- booked prem dev.
- reported loss dev
how should data be segregated when using the empirical PDLD approach?
(Teng/Perkins)
-segregated into homogeneous groups by size of account and type of rating plan sold
how are policies grouped over time?
Teng/Perkins
grouped based on calendar quarter in which they became effective
(policy effective quarter)
what age loss and premium is the first retro premium computation based on?
(Teng/Perkins)
- losses developed through 18 months
- premium booked through 27 months
why is a premium lag of 9 months assumed?
Teng/Perkins
it takes time to process and record adjusted premiums
when do subsequent retro adjustments occur?
Teng/Perkins
in annual intervals
e.g. losses at 30 mo., prem at 39; losses at 42 mo, prem at 51 mo.
what is the first empirical PDLD ratio defined as?
Teng/Perkins
prem booked through 27 mo divided by losses reported through 18 mo
what is the second empirical PDLD ratio?
Teng/Perkins
-change in prem / change in loss –>
prem at 39 mo - prem at 27 mo) / (loss at 30 mo - loss at 18 mo
why might historical PDLD ratios fluctuate significantly after the first retro adjustment?
(Teng/Perkins)
- prem and loss dev. on a few policies can drive total incremental dev. on quarterly data
- negative PDLD ratios are possible
how might negative PDLD ratios occur?
Teng/Perkins
-upward dev. in high loss layers (resulting in no add’l prem) AND downward dev. in layers within loss limitations (resulting in return prem)
how can we handle large fluctuation in empirical PDLD ratios?
(Teng/Perkins)
- average as many historical points as possible
- use formula approach
what are two reasons that historical and formula PDLD ratios could diverge?
(Teng/Perkins)
- worse (better) than expected loss experience may have caused a larger portion of the loss to be outside (inside) the boundaries of the retro max and the per accident limitation than the formula approach predicted
- average retro params may be changing over time
what is a CPDLD ratio? (calculation/formula explanation)
Teng/Perkins
average of the PDLD ratios in all subsequent retro periods (including the current adj. period), weighted by the percentage of losses to emerge in each period
what does the CPDLD ratio mean?
Teng/Perkins
tells an insurer how much prem it can expect to collect for a dollar of loss that has yet to emerge
(e.g.: if CPDLD ratio = 1.63, then each dollar of loss emerged provides insurer 1.63 prem)
why is the CPDLD ratio at the first retro adjustment normally greater than 1.0?
(Teng/Perkins)
- first retro prem computation includes basic prem
- only a small portion of loss is limited at this point
- application of loss conversion factor and tax multiplier results in more than a dollar of prem per dollar of loss
why is the CPDLD ratio less than 1.0 at subsequent adjustments?
(Teng/Perkins)
-retro max and per accident limitation limit losses
why are the current booked premiums different than the booked premium from the prior retro adjustment?
(Teng/Perkins)
- timing of retro adjustments
- minor prem. adjustments
- interim premium booking that occurs between the regularly-scheduled retro adjustments
what are three possible issues when calculating the CPDLD or PDLD ratios?
(Teng/Perkins)
- definition of loss may include LAE
- changes in mix of business by state, industry group, or geographical region may change the PDLD ratio
- collectibility of prem should be considered
how do we prevent issues from LAE being included with loss?
Teng/Perkins
-make sure data used in computing PDLD ratios is consistent with that used in the rating plan
how would we handle changes in the mix of business by state, industry group, or geographical region?
(Teng/Perkins)
-can alter average rating params sold and the underlying claim frequency and severity
what might we do when considering collectibility of premium?
Teng/Perkins
-if portion of premium asset is not secured, a provision should be made to anticipate bad debt
what are three advantages of the PDLD method?
Teng/Perkins
- modeled directly on the retro rating formula - easy to explain
- emphasis on premium sensitivity in retro formula parallels the RBC loss-sensitive contract offset in Part 7 of the Schedule P
- useful when changes in retro rating plan params distort the indications of other methods
why not estimate the accrued retro premium asset using a CL development procedure on historical triangles of either collected or billed prem?
(Teng/Perkins)
-lag in processing and recording retro prem. adj -> CL estimate is not available until at least 9 months after policy expiration, can only be updated annually after
[Fitzgibbon or PDLD methods can produce estimates sooner, and can update each quarter with new loss data]
what two parts is the retro prem composed of?
Teng/Perkins
- part covers incurred losses, LAE, state taxes, and other assessments
- other part covers company expenses (UW, acquisition), net insurance charge (results for max/min), state taxes, other state assessments
how is the part of retro prem covering losses, LAE, taxes, and state assessments expressed?
(Teng/Perkins)
loss conversion factor x limited incurred losses x tax multiplier
how is the part of retro prem covering company expenses, net insurance charge, state taxes, and other state assessments expressed?
(Teng/Perkins)
[expense provision + net insurance charge + excess loss charge] x tax multiplier
what components are included in the basic premium?
Teng/Perkins
-company expenses, net insurance charge, excess losse charge
what is the net insurance charge?
Teng/Perkins
difference between:
- expected loss to insurer caused by maximum retro premium AND
- expected gain to insurer caused by minimum retro premium
how do Fitzgibbon and Berry estimate average parameters A and B?
(Teng/Perkins)
from a historical regressions using standard loss ratios and retro adj. from mature policy years
why must we use regression to estimate A and B instead of using pricing actuarial estimates?
(Teng/Perkins)
- actuarial reserves are estimated on aggregate basis, but plan params vary from:
- -year to year (interest rates/investment income)
- -state to state (prem taxes)
- -plan to plan (smaller insured may choose lower max prem)
what are difficulties with regression?
Teng/Perkins
- regression performed on historical data may not apply to current policies due to changes in rating plan factors and aggregate loss ratios
- prem on individual plans is not a simple linear function of total incurred losses (losses are capped)
how is Fitzgibbon’s method graphically represented?
Teng/Perkins
-plots net EP (after retro adj.) against incurred losses, both as % of standard premium
what line/params does the graphical representation of Fitzgibbon’s method result in?
(Teng/Perkins)
-straight line, Y = A + B*X
where:
-A = basic premiumg percentage (net prem / standard prem)
-B = premium responsiveness
what are reasons that B != 1 when graphing Fitzgibbon’s method? [B: prem. responsiveness to loss]
(Teng/Perkins)
- loss limitations (retro max, per accident limitation)
- minimum premium exceeds basic premium
- LCF and TM are applied to incurred losses
what does “swing” of the plan mean?
- narrow swing = B < 1 -> low loss limits and max. prems
- wide swing = B > 1 -> high loss limits and max prems
what type of accounts tend to have narrow/wide swing?
Teng/Perkins
- narrow: small accounts
- wide: large accounts
what is the problem with the Fitzgibbon graphical method?
Teng/Perkins
-ignores emerging experience, which may differ from what is expected in terms of premium responsiveness
how might emerging experience differ from what is expected when trying to graphically represent the Fitzgibbon method?
(Teng/Perkins)
- A and B are estimates - may vary from year to year
- prem. responsiveness may be less than expected due to large losses on individual policies
- if true B is less than estimate of B shown on graph - method will overstate retro prem
what is Berry’s solution to the problem’s with graphically representing Fitzgibbon’s method?
(Teng/Perkins)
- use a method that relies on actual experience
- begin with Fitzgibbon and then gradually give more weight to actual experience as book of business matures
how would you think of the Fitzgibbon graph?
Teng/Perkins
movement over time of reported losses, net EP, and reported loss ratio
what are two ways to interpret the Fitzgibbon graph of Y = A + B*X?
(Teng/Perkins)
- relates the ult. LR and ult. retro prem. ratio among different books of business or different years (Berry & Fitzgibbon)
- relates reported LR and net EP at different points of time for a single book of business (Teng/Perkins)
what does graphing the Teng/Perkins interpretation look like?
(Teng/Perkins)
-set of line segments with decreasing slope as we move to the right
why is the slope decreasing on the Teng/Perkins plot?
Teng/Perkins
due to loss limits and max prems
what are two general rules about the Teng/Perkins plot?
Teng/Perkins
- as a book of business matures, prem. responsiveness on loss-sensitive contracts declines
- at higher loss ratios, premium responsiveness on loss-sensitive contracts declines
why does prem. responsiveness on loss-sensitive contracts decline as a book of business matures?
(Teng/Perkins)
as policies mature, greater percentage of policies are excluded from retro rating by the max prem and by the loss limit
why does premium responsiveness decline at higher loss ratios?
(Teng/Perkins)
- overall loss ratio, not specific types of claims loss ratio
- at higher overall loss ratios, more policyholders have reached their max prems, so even a small claim will result in no add’l prem
at the first adjustment, how might actual experience differ from expected experience?
(Teng/Perkins)
- actual reported losses may differ from projected reported losses at policy inception
- relationship between reported losses and retro prem may differ from what was projected at policy inception (eg: formula gives 72% LR, actual LR is 70%)
what two assumptions underlie the PDLD method?
Teng/Perkins
1- prem responsiveness during subsequent adjustments is ind’t of the prem responsiveness during preceding adjustments
2- slope of line segment depends on the time period, not on the beginning loss ratio or beginning retro prem ratio
what does assumption #1 of the PDLD method mean for the plot? [prem responsiveness in separate periods is ind’t]
(Teng/Perkins)
-even if slope of first line segment is different from what is expected, we do NOT change our expectations for the slope of the second line
what does assumption #2 of the PDLD method mean for the plot? [slope of line segment depends on time, not LR or prem ratio]
(Teng/Perkins)
- relates to when we change from one line to another
- we move from one line segment to the next at the retro adj., regardless of where the loss ratio ended up
how do the two assumptions of the PDLD method fix the issues in Fitzgibbon’s method?
(Teng/Perkins)
- Fitzgibbon relates ult. LR to ult. retro prem ratio - if actual experience differs from expected, there’s no way to get back on track
- PDLD ratio related reported loss ratio to retro prem, ratio - if actual experience deviates from expected, next line segment begins at a starting point that corresponds to actual experience
how does the PDLD method calculate the premium asset?
Teng/Perkins
- project future loss dev. in each adj. period
- estimate future prem by the product of future loss dev. in each period and the slope of the line segment in that period
- sum these products to get premium asset
what is an implication of the Teng/Perkins plot’s first line segment passing through the origin?
(Teng/Perkins)
- combine two separate items into slope of first line segment:
- -basic prem ratio
- -true slope of first line segment (PDLD_1)
- –> cannot tell how much each item contributes to total slope of first line segment, confusing interpretations
how does the failure to distinguish the basic premium ratio from the first PDLD ratio in the first line segment of the Teng/Perkins plot make it harder to analyze changes over time?
(Teng/Perkins)
ex: if slope of first line segment has risen steadily over time, due to change in basic prem ratio, change in prem. responsiveness, or lengthening of loss reporting pattern?
how does Feldblum suggest we adjust the first line segment of the Teng/Perkins plot?
(Teng/Perkins)
-subtract the average basic prem. charge (as a ratio to standard LR) from the first CPDLD ratio
how does Feldblum’s adjustment to the Teng/Perkins plot change the plot?
(Teng/Perkins)
- plot has positive y-int.
- slope of first line would be flatter
