Analyzing Loss Data by Calendar Year, Accident Year, and Policy Year: Practice Questions and Solutions

This section of the study guide is intended to provide practice problems and solutions to accompany the pages of Basic Ratemaking, cited below. Students are encouraged to read these pages before attempting the problems. This study guide is entirely an independent effort by Mr. Stolyarov and is not affiliated with any organization(s) to whose textbooks it refers, nor does it represent such organization(s).

Some of the questions here ask for short written answers based on the reading. This is meant to give the student practice in answering questions of the format that will appear on Exam 5. Students are encouraged to type their own answers first and then to compare these answers with the solutions given here. Please note that the solutions provided here are not necessarily the only possible ones.

Source:
Werner, Geoff and Claudine Modlin. Basic Ratemaking. Casualty Actuarial Society. 2009. Chapter 6, pp. 89-92.

Original Problems and Solutions from The Actuary's Free Study Guide

Problem S5-38-1. An actuary is examining loss data pertaining to Accident Year 3602, as of November 1, 3604.

(a) What is the accounting period pertaining to these data?
(b) What is the valuation date pertaining to these data?
(c) There are two ways to describe these data in terms of number of months relative to Accident Year 3602. What are these two ways?

Solution S5-38-1. This question is based on the discussion in Werner and Modlin, p. 90. The following are the correct answers:

(a) The accounting period is Accident Year 3602. This is the period to which the losses pertain.

(b) The valuation date is November 1, 3604. This is the date from whose vantage point the actuary is examining the loss data. Because accident-year data can change after the end of the time period to which they refer, it is possible for data as of a later time period to be different from data as of the end of the accident year in question.

(c) The two ways to describe these data in terms of number of months relative to Accident Year 3602 are Accident Year 3602 as of 34 months and 22 months after the close of Accident Year 3602. The difference in the number of months is accounted for by the fact that the first description incorporates the months comprising the year 3602, whereas the second description excludes these months.

Problem S5-38-2. Actuary Q is analyzing two insurance policies and transactions pertaining to them. The relevant data are given below.

Policy A:

Effective date: March 1, 2030.

Date of occurrence of first loss: October 2, 2030.

Report date of first loss: November 5, 2030.

Transactions on first loss:
On November 5, 2030, a case reserve of $5460 was established on the loss. Nothing was paid yet.

On November 15, 2030, a payment of $300 was made, and the case reserve was revised to $5300.

On January 4, 2031, a payment of $800 was made, and the case reserve was revised to $4000.

On October 30, 2031, a payment of $3000 was made, and the case reserve was revised to $950.

On February 4, 2032, a payment of $670 was made, and the claim was closed.

Policy A:

Date of occurrence of second loss: January 17, 2031

Report date of second loss: March 9, 2031

Transactions on second loss: On March 9, 2031, a case reserve of $6000 was established on the loss. In addition to the case reserve, a payment of $9000 was made.

On October 9, 2031, a payment of $5000 was made, and the case reserve was revised to $2000.

On January 19, 2032, a payment of $2000 was made, and the claim was closed.

Policy B:

Effective date: May 20, 2031

Date of occurrence of loss: December 30, 2031

Report date of loss: January 4, 2032

Transactions on loss: On January 4, 2032, a case reserve of $7000 was established on the loss nothing was paid yet.

On January 5, 2033, a payment of $8000 was made, and the claim was closed.

What are the Calendar Year 2030 reported losses?

Solution S5-38-2. The Calendar Year 2030 reported losses are equal to the sum of losses paid in 2030 and the ending reserve (sum of case reserves) on December 31, 2030.

Only one loss occurred in 2030 or earlier. In 2030, a payment of $300 was made on this loss, and the year ended with a case reserve of $5300. Thus, Calendar Year 2030 reported losses are 300 + 5300 = $5600.

Problem S5-38-3. Actuary Q is analyzing two insurance policies and transactions pertaining to them. The relevant data are given below.

Policy A:

Effective date: March 1, 2030.

Date of occurrence of first loss: October 2, 2030.

Report date of first loss: November 5, 2030.

Transactions on first loss:
On November 5, 2030, a case reserve of $5460 was established on the loss. Nothing was paid yet.

On November 15, 2030, a payment of $300 was made, and the case reserve was revised to $5300.

On January 4, 2031, a payment of $800 was made, and the case reserve was revised to $4000.

On October 30, 2031, a payment of $3000 was made, and the case reserve was revised to $950.

On February 4, 2032, a payment of $670 was made, and the claim was closed.

Policy A:

Date of occurrence of second loss: January 17, 2031

Report date of second loss: March 9, 2031

Transactions on second loss: On March 9, 2031, a case reserve of $6000 was established on the loss. In addition to the case reserve, a payment of $9000 was made.

On October 9, 2031, a payment of $5000 was made, and the case reserve was revised to $2000.

On January 19, 2032, a payment of $2000 was made, and the claim was closed.

Policy B:

Effective date: May 20, 2031

Date of occurrence of loss: December 30, 2031

Report date of loss: January 4, 2032

Transactions on loss: On January 4, 2032, a case reserve of $7000 was established on the loss nothing was paid yet.

On January 5, 2033, a payment of $8000 was made, and the claim was closed.

What are the Calendar Year 2031 reported losses?

Solution S5-38-3. The Calendar Year 2031 reported losses are equal to the sum of losses paid in 2031 and the ending reserve (sum of case reserves) on December 31, 2031, minus the beginning reserve in 2031 ($5300).

All three of the losses occurred either before or during 2031. But the loss on Policy B was not reported in 2031, so no payments or reserves were made.

The first loss on policy A had payments of $800 and $3000 made on it, and had an ending case reserve of $950. This means that this loss's contribution to CY 2031 reported losses is 800 + 3000 + 950 = $4750.

The second loss on policy A had payments of $9000 and $5000 made on it, and had an ending case reserve of $2000. This means that this loss's contribution to CY 2031 reported losses is 9000 + 5000 + 2000 = $16000.

Thus the total CY 2031 reported losses are 4750 + 16000 - 5300 = $15,450.

Problem S5-38-4. Actuary Q is analyzing two insurance policies and transactions pertaining to them. The relevant data are given below.

Policy A:

Effective date: March 1, 2030.

Date of occurrence of first loss: October 2, 2030.

Report date of first loss: November 5, 2030.

Transactions on first loss:
On November 5, 2030, a case reserve of $5460 was established on the loss. Nothing was paid yet.

On November 15, 2030, a payment of $300 was made, and the case reserve was revised to $5300.

On January 4, 2031, a payment of $800 was made, and the case reserve was revised to $4000.

On October 30, 2031, a payment of $3000 was made, and the case reserve was revised to $950.

On February 4, 2032, a payment of $670 was made, and the claim was closed.

Policy A:

Date of occurrence of second loss: January 17, 2031

Report date of second loss: March 9, 2031

Transactions on second loss: On March 9, 2031, a case reserve of $6000 was established on the loss. In addition to the case reserve, a payment of $9000 was made.

On October 9, 2031, a payment of $5000 was made, and the case reserve was revised to $2000.

On January 19, 2032, a payment of $2000 was made, and the claim was closed.

Policy B:

Effective date: May 20, 2031

Date of occurrence of loss: December 30, 2031

Report date of loss: January 4, 2032

Transactions on loss: On January 4, 2032, a case reserve of $7000 was established on the loss nothing was paid yet.

On January 5, 2033, a payment of $8000 was made, and the claim was closed.

What are the Accident Year 2031 reported losses, as of December 31, 2032?

Solution S5-38-4. Accident year considers when a loss occurred, irrespective of when it was reported or paid. The two losses that occurred in 2031 are the second loss on Policy A and the loss on Policy B. Thus, Accident Year 2031 reported losses, as of December 31, 2032, are the cumulative amounts paid for these two losses through December 31, 2032, plus the case reserve on these claims. Only the Policy B loss was open on December 31, 2032, with a case reserve of $7000. Nothing was paid on that loss yet. The second loss on Policy A was closed, and had cumulative payments of 9000 + 5000 + 2000 = $16000 on it. Thus, the Accident Year 2031 reported losses, as of December 31, 2032, are 7000 + 16000 = $23,000.

Problem S5-38-5. Actuary Q is analyzing two insurance policies and transactions pertaining to them. The relevant data are given below.

Policy A:

Effective date: March 1, 2030.

Date of occurrence of first loss: October 2, 2030.

Report date of first loss: November 5, 2030.

Transactions on first loss:
On November 5, 2030, a case reserve of $5460 was established on the loss. Nothing was paid yet.

On November 15, 2030, a payment of $300 was made, and the case reserve was revised to $5300.

On January 4, 2031, a payment of $800 was made, and the case reserve was revised to $4000.

On October 30, 2031, a payment of $3000 was made, and the case reserve was revised to $950.

On February 4, 2032, a payment of $670 was made, and the claim was closed.

Policy A:

Date of occurrence of second loss: January 17, 2031

Report date of second loss: March 9, 2031

Transactions on second loss: On March 9, 2031, a case reserve of $6000 was established on the loss. In addition to the case reserve, a payment of $9000 was made.

On October 9, 2031, a payment of $5000 was made, and the case reserve was revised to $2000.

On January 19, 2032, a payment of $2000 was made, and the claim was closed.

Policy B:

Effective date: May 20, 2031

Date of occurrence of loss: December 30, 2031

Report date of loss: January 4, 2032

Transactions on loss: On January 4, 2032, a case reserve of $7000 was established on the loss nothing was paid yet.

On January 5, 2033, a payment of $8000 was made, and the claim was closed.

What are the Policy Year 2030 reported losses, as of December 31, 2032?

Solution S5-38-5. Policy year considers when the policies in question were written. Policy A was written in 2030, whereas Policy B was written in 2031. Thus, only Policy A data - for both losses - applies to Policy Year 2030. By December 31, 2032, both claims on Policy A were closed, so the case reserve estimate for them is $0. The cumulative payments on the first claim were 300 + 800 + 3000 + 670 = $4770.

The cumulative payments on the second claim were 9000 + 5000 + 2000 = $16000.

The total Policy Year 2030 reported losses, as of December 31, 2032, are therefore 4770 + 16000 = $20,770.

See other sections of The Actuary's Free Study Guide for Exam 5.