A14

Question 1

Define the following terms: Premium asset

Answer 1

Teng & Perkins

Premium asset – for retrospectively rated policies, this represents the premium that the insurer expects to collect based on the expected ultimate loss experience, less the premium that the insurer has already booked

Question 2

Define the following terms: Standard premium

Answer 2

Teng & Perkins

Standard premium – manual premium adjusted for experience rating

Question 3

Define the following terms: Premium deviation

Answer 3

Teng & Perkins

Premium deviation – amount by which the booked premium differs from the standard premium

Question 4

Define the following terms: Retro reserve

Answer 4

Teng & Perkins

Retro reserve – the di↵erence between the premium deviation to date and the ultimate premium deviation

Question 5

Provide three advantages of retrospectively rated policies.

Answer 5

Teng & Perkins

1. They encourage loss control and loss management by returning premium to the insured for good loss experience
2. They offer a cash flow advantage to insureds by allowing them to pay premium as losses are reported or paid
3. Since premium varies directly with the insured’s actual loss experience, it shifts a large portion of the risk to the insured

Question 6

Briefly describe two methods for calculating the retro reserve.

Answer 6

Teng & Perkins

Method 1: Analyze the historical relationship between the loss ratio and the premium deviation, and apply that relationship to the projected loss ratio to determine the pro- jected ultimate premium deviation. Then, subtract the premium deviation to date from the ultimate premium deviation to produce the retro reserve

Method 2: Estimate ultimate premium using the historical premium emergence pattern, and then subtract current premium to get the retro reserve

Question 7

Provide one advantage of using the retro formula to estimate the PDLD ratio.

Answer 7

Teng & Perkins

It responds to changes in the retro rating parameters that are sold. If retro parameters change significantly over time, more weight should be given to PDLD ratios derived from the formula than those derived from historical data

Question 8

Provide one disadvantage of using the retro formula to estimate the PDLD ratio.

Answer 8

Teng & Perkins

Potential bias exists since the formula approach uses the average parameters for the LCF, tax multiplier, maximum, minimum and per accident limitation. We should retrospectively test PDLD ratios against actual emergence to check for bias

Question 9

a) Identify two types of data needed to calculate PDLD ratios empirically.
b) Briefly explain how this data should be segregated.
c) Briefly explain any organizational differences between premiums and losses.

Answer 9

Teng & Perkins

Part a: Booked premium development -Reported loss development

Part b: Data should be segregated into homogeneous groups by size of account and type of rating plan sold

Part c: Premiums and losses should be organized into twelve month intervals. In addition, premi- ums should lag losses by nine months to account for the time it takes to process and record adjusted premiums (losses at 30 months and premiums at 39 months, losses at 42 months and premiums at 51 months, etc.)

Question 10

Explain why historical and formula PDLD ratios may diverge

Answer 10

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 maximum and the per accident limitation than the formula approach predicted. In addition, average retro parameters may be changing over time

Question 11

Explain how negative PDLD ratios can occur.

Answer 11

Teng & Perkins

Upward development in high loss layers (resulting in no additional premium) and downward development in layers within loss limitations (resulting in return premium)

Question 12

Identify three reasons why the current booked premiums may not equal the booked premium for the prior retro adjustment.

Answer 12

Teng & Perkins

1. The timing of retro adjustments
2. Minor premium adjustments
3. Interim premium booking that occurs between the regularly scheduled retro adjustments

Question 13

Fully describe why the PDLD method is preferable to using the chain-ladder method on historical premium triangles when determining the premium asset.

Answer 13

Teng & Perkins

Due to the lag in processing and recording retro premium adjustments, a chain-ladder estimate of the premium asset is not available until at least nine months after the policy expiration, and it can be updated only annually thereafter. Using the PDLD method, an initial estimate of the premium asset can be produced soon after the policy expires, using the known loss information and the relationships between incurred losses and retro premium. In addition, the premium asset estimate can be updated each quarter as new loss data becomes available

Question 14

Briefly describe how premium responsiveness changes with the following:

1. Maturity of the book
2. Loss ratio

Answer 14

Teng & Perkins

1. As a book of business matures, premium responsiveness on loss-sensitive contracts declines
2. At higher loss ratios, premium responsiveness on loss-sensitive contracts declines

Question 15

Describe two assumptions underlying the PDLD method.

Answer 15

Teng & Perkins

Assumption 1: The premium responsiveness during subsequent adjustments is independent of the premium responsiveness during preceding adjustments • The premium responsiveness is represented by the slope of the line segment in that adjustment period • Even if the slope of the line segment is different from what is expected, we do NOT change our expectations for the slope of the next line

Assumption 2: The slope of the line segment depends on the time period, not on the beginning loss ratio or the beginning retro premium ratio • Assumption relates to when we change from one line to another • For example, when moving from the first line segment to the second line segment, we change at the first retro adjustment (regardless of where the loss ratio ended up)

Question 16

One issue with the PDLD method is the failure to separate the basic premium ratio from the first PDLD ratio.

a) Fully describe two problems that arise from the failure to separate these two items.
b) Briefly describe a solution to this problem.

Answer 16

Teng & Perkins

Part a:

1. One problem with combining these items is that we cannot tell how much each item con- tributes to the total slope of the first line segment. This leads to results that are unclear and di cult to interpret. For example, we would normally interpret a CPDLD ratio of 1.492 at policy inception to the first retro adjustment to mean that each dollar of loss emerged provides the insurer one dollar and 49 cents of premium. This would be wrong because part of that 1.492 comes from the basic premium charge, which does not represent emerged losses
2. The failure to distinguish these items also makes it harder to analyze changes over time. For example, assume the slope of the first line segment has risen steadily over the past 30 years. Is this due to a change in the average basic premium ratio, a change in premium responsiveness during the first period, or a lengthening of the loss reporting pattern?

Part b: Subtract the average basic premium charge (as a ratio to the standard loss ratio) from the first CPDLD ratio

Question 17

Explain how these (underlying the PDLD method) assumptions fix the issues underlying Fitzgibbon’s method.

Answer 17

Teng & Perkins

Fitzgibbon relates the ultimate loss ratio to the ultimate retro premium ratio. If actual experience deviates from what is expected, we have no way to get back on track. On the other hand, the PDLD ratio relates the reported loss ratio to the retro premium ratio. If actual experience deviates from what is expected, the next line segment begins at a starting point that corresponds to actual experience

Question 18

What does the Insurance charge represent?

Answer 18

Teng & Perkins

The Insurance charge is the difference between the expected loss to the insurer caused by the maximum retro premium and the expected gain to the insurer caused by the minimum retro premium.