SUPERIOR INSURANCE INC.
Written by
Peter Tryfos,
Schulich School of Business,
York University.

PLEASE NOTE: APPEARANCE OF TEXT IN BROWSER IS NOT OPTIMAL


Background
An automobile insurance policy is in effect three separate policies combined in one, providing coverage for third-party liability, accident benefits, and loss of or damage to the insured automobile. Insurance companies make a separate calculation of the required premium for each of the three types of coverage. The total premium of the policy is equal to the sum of the individual premiums.
Third-party liability coverage provides indemnity against liability to others due to death, bodily injury, or property damage. Accident benefits coverage is for the loss of life, ambulance, medical and hospital costs, loss of income, and rehabilitation; insured under this coverage are the occupants of the insured vehicle, the insured and members of his or her family while occupants of any other vehicle, and other persons specified in the policy. Various forms of coverage for loss of or damage to the insured vehicle are available: "comprehensive," "specified perils," "all perils," "collision/upset," each providing coverage for particular types of damages. Insurance companies generally set limits on the coverage up to which they are responsible. All coverages may be subject to specified "deductibles."
The minimum driving age in the Province is 16. A standardized automobile insurance policy currently establishes definitions and describes at length the rights and obligations of the two parties in the contract. It is a lengthy and rather complicated legal document of over sixty pages, approved by the Insurance Commissioner and used by all insurance companies.
A similar standardized, uniform, and mandatory automobile insurance policy is used in the Province of Ontario, where it is known as the Ontario Automobile Policy 1 (OAP1). Frequently asked questions and answers concerning this policy can be viewed at the web site of the Insurance Bureau of Canada, http://www.ibc.ca./english/auto.htm. The theory and practice of automobile insurance in the United States in particular and of property and liability insurance in general are described in S. S. Huebner, K. Black, Jr., and B. L. Webb, Property and Liability Insurance, 4th Ed., Prentice-Hall, 1996. The management of financial institutions in general is the subject of A. Saunders and H. Thomas, Financial Institutions Management, First Canadian Edition, Irwin, 1997. Jean Lemaire, Automobile Insurance: Actuarial Models, Kluwer-Nijhoff Publishers, 1995, gives emphasis to actuarial models and European experience. Additional information can be located by searching electronically for “automobile insurance” in library catalogues and periodical indexes.
The new legislation affects only third-party liability, and it is to third-party liability that the rest of the case is restricted. For brevity, we shall omit from now on the words “third-party” and refer more simply to “liability policy” or “liability insurance.”

The current system
Under the current system, the insurer of a liability policy will pay any amount up to the policy limit for which the law holds responsible any person who, as a result of owning, using or operating the insured vehicle with the consent of the owner, causes bodily injury or death to or damages the property of other persons. The focus of insurance is therefore the vehicle, and eligible for coverage are any losses incurred by the fault of any person operating the vehicle with the consent of the owner. Proof of liability insurance is required for the renewal of the annual vehicle license.
Liability insurance up to a limit of $200,000 on the total annual loss is compulsory. There is no deductible. The other coverages as well as additional coverage for liability insurance are optional.
Insurance companies assign policies into classes and set the class premium proportional to the past average loss per policy in that class. These classes are based on characteristics of the vehicle and of the principal and occasional drivers of the vehicle. Different insurance companies use different classification systems; the system currently used by Superior Insurance is described in Appendix A.
One company’s class, for example, may consist of all policies in which the principal driver of the vehicle is male, 40 to 50 years old, married, and drives a full-sized car more than 10 miles to work. If in the past the average annual liability loss of all policies in that class is, say, $500 and this tendency is expected to continue next year, then the annual premium of all liability policies in that class is set at $500 times a mark-up factor to enable the company to cover other expenses and make a profit. For instance, if this factor is 1.50, the annual premium for the class is 500x1.50 or $750.

The new system
Under the new system, the focus of liability insurance is not the vehicle but the licensed driver. The new liability policy will pay any amount up to the policy limit for which the insured driver is held responsible for injury or death to another person or damage to the property of other persons resulting from the operation of any vehicle. Proof of insurance coverage will be required for the renewal of the annual driving license. As with the current system, liability insurance remains compulsory with no deductible and the same limit of $200,000 on the total annual loss.
A simple example will illustrate the differences between the two systems. You live, let us suppose, in town A where you drive your own car. While visiting a friend in town B for a few days and driving the friend’s car, you collide with another car. The accident is your fault. There is damage to the other car and a passenger requires hospitalization. Under the present system the losses resulting from this accident will be covered by your friend’s insurance policy (assuming, of course, there is adequate coverage). Under the new system, you are covered while operating your friend’s car and the losses will be covered by your own policy. Many insurance companies view a claim as an indicator of the risk of a policy and of the “accident propensity” of the insured. Under the present system, therefore, the accident may not affect next year’s premium of your policy but may raise the premium of your friend’s policy. Under the new system, the accident may affect your own policy’s future premium.

The new system was and is still controversial. Of particular concern is the fact that some will be unable to drive if they cannot afford insurance.
The law creating the new system passed after many years of study, several lengthy commission reports, and much debate in the legislature and the press. The numerous arguments for and against the new system cannot be repeated here in detail. Opponents point out that the current system is being used in most states and provinces, and that the considerable experience accumulated under the current system will be lost or converted to the new system at a very high cost. Proponents, on the other hand, argue that by grouping under one policy drivers of different ages, driving experience, gender and other characteristics, the current system penalizes safe drivers, does not reveal fully the consequences of unsafe driving, and does not permit higher premiums to act as an effective deterrent to future accidents.
To a large measure, the successful passage of the legislation was due to the crusading efforts of Mr. John Able, the widely read columnist, whose scathing attacks on the complexity of the current system and slogans---"It is not cars that cause accidents, but the people who drive them" and "Cars don’t kill, drivers do"---held strong appeal with the voters.

Available data
In anticipation of the new legislation, the insurance industry invested considerable effort and expense to review and revise its records so as to convert them into a form suitable for determining the new premiums. The task of carrying out this review was assigned to the Insurance Advisory Bureau (IAB), a not-for-profit organization created by insurance companies in the Province for just this purpose.
Superior Insurance and the other companies supplied IAB with all available information concerning the liability policies in effect during one calendar year. 1995 was the selected year, because nearly all claims arising from the 1995 policies had been settled when IAB undertook the study.
It must be realized that a long time may elapse before the total loss resulting from an accident or mishap is known with certainty and the allocation of that loss to the party or parties at fault determined. The more serious the accident and injuries, the longer tends to be the period before all claims are finally settled in court or by negotiation. Also, fault may be shared: it may ultimately be decided that the accident was not the fault of one driver alone, but that one was responsible for, say, 75% of the total loss and another of the remaining 25%.
IAB studied carefully each liability claim submitted and reconstructed when necessary each accident, so as to arrive at a list showing for each licensed driver appearing in the records the total amount for which the driver was held responsible as a result of accidents that occurred in 1995 as well as relevant characteristics of the driver and vehicle. This list can be imagined as a table, the rows of which correspond to the 1995 insured drivers and the columns to driver and vehicle characteristics. The following excerpt illustrates the structure of this database:
IDNO
LOSS
GENDER
AGE
EXPER
MARSTAT
PRESID
TOWORK
MILES
CLAIMS
CITATS
SIZE
100
0.000
0
51
32
2
0
5
3
2
0
1
101
0.544
1
24
4
1
1
21
5
1
1
2
102
0.000
1
16
0
2
1
4
10
0
0
2
103
0.000
1
28
10
2
0
1
6
1
1
4
104
2.553
0
26
3
1
0
5
16
0
2
1
105
0.000
1
70
31
2
1
0
25
0
4
2
106
0.354
1
16
0
2
1
2
9
0
0
2
107
0.000
1
46
27
2
0
5
18
1
3
1
108
0.000
1
32
16
2
0
5
26
2
4
1
109
0.241
1
36
10
2
1
10
5
1
1
1

The definition of the variables is as follows:

IDNODriver identification number
LOSSAmount of loss for which driver was held responsible in 1995 ($000)
GENDERDriver’s gender (1=male, 0=female)
AGEDriver’s age (in years)
EXPERDriver’s experience (number of years since issue of first license)
MARSTATDriver’s marital status (1=single, 2=married, 3=other)
PRESIDDriver’s place of residence (1=urban, 0=rural)
TOWORKDistance between driver’s home and workplace (in miles)
MILESMiles expected to be driven in 1995 (in 000 miles)
CLAIMSNumber of liability claims made in the 5-year period 1990-94
CITATSNumber of citations for traffic violations in the 5-year period 1990-94
SIZESize of vehicle most frequently used by driver (1=full, 2=intermediate, 3=compact, 4=small, 5=other)

It is recognized that the number of years since the issue of the first driver license may overstate experience in cases where the license was allowed to lapse for one or more years. Age, experience, marital status, place of residence, distance to workplace are as of January 1, 1995. 1995 mileage, distance to workplace, and size of vehicle are based on the driver’s declaration. Distance to workplace is listed as zero if the insured does not work or drive to work.

Following is an index (1990=100) of the cost of car repairs and the level of court awards in the period from 1991 to 1998:
Year
Index
Year
Index
1991
103
1995
114
1992
105
1996
116
1993
108
1997
119
1994
110
1998
122

Superior Insurance Inc.
Superior Insurance is the Canadian subsidiary of a large British parent company also operating in Europe and the United States. It offers several lines of insurance through independent agents including, in addition to third-party automobile liability, other types of automobile insurance as well as home, commercial, and marine insurance.
Provincial regulations require insurers to maintain an equity reserve equal to at least 10% of the total premiums earned in a year for third-party liability insurance. Because of Superior’s size and that of its parent company, this requirement can be easily adjusted upward or downward depending on the volume of 1999 premiums.
Operating expenses are expected to amount to about 34% of premiums. Premiums are invested and expected to earn on average 8% in 1999. Superior Insurance hopes to achieve in 1999 a rate of return on equity of at least 15%.

The task
Your objective is to maximize Superior’s gross profit from liability insurance in 1999. Gross profit is defined as the difference between total revenue, on the one hand, and the sum of losses and direct expenses, on the other, as explained below.
In order to be considered as a supplier of insurance, Superior must be ready to quote a premium (“to bid”) to any driver who requests it. The driver will provide the same information as in the IAB database, but as of the time of request---i.e., gender, age, experience, marital status, place of residence, and distance to work as of January 1, 1999; expected mileage in 1999, number of claims and citations in the 5-year period 1994-98, and size of the car expected to be driven most frequently in 1999. Superior does not have to reveal how the quotation was calculated, but, if its bid is accepted, it is bound to cover any losses incurred at the fault of the driver in 1999.
Several insurance companies compete in Superior’s region. All enjoy the same good reputation as Superior and the market is highly competitive. It can be assumed that each driver will request bids from all companies and purchase insurance from the lowest bidder. The following table illustrates this process.


IDNO
GENDER
AGE
EXPER
MARST
PRESID
TOWORK
MILES
CLAIMS
CITATS
SIZE
A
B
C
WBID
WCOMP
LOSS
1
1
50
31
2
1
5
5
1
1
2
1
1.2
1.17
1
1
0.591
2
0
57
34
2
0
2
21
0
3
3
1
0.8
1.08
0.8
2
0.437
3
0
34
16
2
1
3
12
2
2
3
1
0.8
1.62
0.8
2
1.086
4
0
17
1
1
0
15
1
0
0
2
1
0.8
2.07
0.8
2
1.468
5
0
27
6
1
1
5
14
1
2
1
1
0.8
1.92
0.8
2
1.248
6
1
51
32
2
1
6
20
1
3
2
1
1.2
1.14
1
1
0.558
7
0
21
3
1
1
5
12
0
1
1
1
0.8
2.01
0.8
2
1.316
8
0
45
21
2
1
11
13
2
2
1
1
0.8
1.47
0.8
2
0.723
9
0
19
3
1
1
4
5
0
0
3
1
0.8
2.01
0.8
2
1.565
10
1
17
1
1
1
20
5
0
0
2
1
1.2
2.07
1
1
1.775

It is assumed that there are three companies in the region (labeled A, B, and C) and ten drivers who obtain quotations from all three companies. The driver and vehicle characteristics in the columns GENDER to SIZE are known to all companies. Company A bids a flat annual premium of $1,000; B’s premium quotation is $1,200 for male or $800 for female drivers, while C’s premium is arrived at by the formula
Premium = (2.1) - (0.03)(Years of Experience)
The winning bid (the lowest of the bids by A, B and C) and the winning company are shown under the labels WBID and WCOMP, respectively. LOSS is the amount by which the driver is held responsible in 1999.
It can be verified that A’s bid is accepted by 3, B’s by 7, and C’s by 0 drivers. In this illustration, the 1999 premium revenue, total loss, and operating profit of the three companies are as follows:

COMPANY
NAME
DRIVERS
PR.REVENUE
LOSS
OP. PROFIT
1
A
3
3
2.924
-0.704
2
B
7
5.6
7.844
-3.700
3
C
0
0
0
0

The operating profit is defined as

(Operating Profit) = (Premium Revenue) + (Investment Revenue) - (Total Losses) - (Operating Expenses) = (0.74) (Premium Revenue) - (Total Losses)

In order to determine Superior’s bid for a driver with given characteristics, you may need the assistance of IAB. When IAB was formed, the participating companies agreed on the rules by which data could be retrieved and the fees to be paid. As one of the participating companies, Superior is entitled to a simple random sample of records from the IAB database at a cost of $20 per selected record (a record is one row of data in the IAB database).
Thus, Superior’s 1999 gross profit from liability insurance (the performance measure to be maximized) is
Gross Profit = (Operating profit) - ( Cost of IAB sample)



ASSIGNMENTS

The ultimate objective is to maximize Superior’s 1999 gross profit and explain to the management of this company your decisions in pursuit of this objective. In doing so, you may wish (or may be required) to consider the following intermediate steps:

1. In a report addressed to the management of Superior, state your recommendations regarding the size of the simple random sample of IAB records. Implement your recommendations by running the computer program SUPINS0.EXE according to the instructions in Appendix B.
2. Analyze the data collected in (1) so as to gather as much information as possible relevant to Superior’s task. In a report addressed to the management of Superior, describe the main findings in detail.
3. Consider how to forecast the 1999 liability loss of a driver with given values of the characteristics GENDER to SIZE. In a report addressed to the management of Superior, describe in detail the alternatives considered, the selected method, and the reasons for your selection.
4. Assume that there is only one competitor to Superior in the market for liability insurance, and that this company has announced it will charge a flat premium of $1,000 for the new standard third-party liability policy. In a report addressed to the management of Superior, explain in detail how Superior should set its premiums so as to maximize 1999 profits. Submit your “premium formula” in the manner described in Appendix C. Estimate the number of drivers to be “signed-up” in 1999, the 1999 profit, and the 1999 rate of return on equity.
5. There are several competitors in the market for liability insurance, and their premium formulas are not known at this time. In a report addressed to the management of Superior, explain in detail how the company should determine its premiums so as to maximize 1999 profits. Submit your “premium formula” in the manner described in Appendix C. Estimate the number of drivers to be “signed-up” in 1999, the 1999 profit, and the 1999 rate of return on equity.


APPENDIX A
SUPERIOR’S CURRENT CLASSIFICATION SYSTEM

The current classification criteria are the sex, age, and marital status of the principal and occasional drivers, the use to which the automobile is put, and the claim record of the insured drivers. Sixty five classes in total are used.
Thirteen sex/marital status/age/use classes (“sex/use” classes, for short) are distinguished as shown in the following table.

Classification by sex, marital status, age, and use
Principal driver’sUse
Sex Marital status Age A B C D
Male Single 16-18 10 10 10 10
19-20 11 11 11 11
21-22 12 12 12 12
23-24 13 13 13 13
25-29 04 04 04 07
30+ 01 02 03 07
Married 16-20 08 08 08 08
21-24 09 09 09 09
25+ 01 02 03 07
Female Single or 16-20 18 18 18 18
married 21-24 19 19 19 19
25+ 01 02 03 07

The description of the four use categories A, B, C, and D shown above is as follows:

A. Pleasure only; no drive to work.
B. Pleasure only; drive to work less than 10 miles one way.
C. Pleasure only; drive to work over 10 miles one way.
D. Used for business purposes.

Policies are also classified according to the claim record under the policy, as follows:

ClassClaim Record
5 Five years or more claim-free experience
3 Three or four years of claim-free experience
2 Two years claim-free experience
1 One year claim-free experience
0 At least one claim in the year prior to the effective date of the policy

The claim record code is applied as a suffix to the sex/use code to form a three-digit code; for example, 043 signifies policies falling into sex/use class 04 and claim record class 3. There are thus 13x5 or 65 classes in total.

APPENDIX B
INSTRUCTIONS FOR RUNNING SUPINS0

The program SUPINS0 simulates the selection of a simple random sample of IAB records. The following instructions are for running SUPINS0 on the SSB server. SUPINS0 is a DOS, not a Windows, program. You may run SUPINS0 once only.

1. Log in normally, do not start Windows. If currently running Windows, exit that program.
2. At the DOS prompt, enter supins0 and press the Enter key. Next, enter your password, exactly as authorized. If the password is not entered correctly, the program terminates; restart the program and enter the correct password.
3. The program will then request that you insert a formatted clear HD diskette in Drive A. The simple random sample of IAB records will be stored on this diskette. Guard and preserve this master diskette because it cannot be replaced without delay or penalty.
4. Next, enter the desired size of the random sample (1 to 20000). Be aware that a sample of 1000 records occupies about 50 KB, one of 10000 500 KB, and one of 20000 about 1 MB.
5. After hitting Enter, the program will begin storing the sampled records on the diskette. Wait for the countdown to reach 0 and the message that the requested data are in the file a:\supins.dat.
6. Remove your diskette and log out.

Following is a sample conversation with the program SUPINS0. User input is underlined.

Enter your password:ohmymy(Enter)
Insert a formatted diskette in Drive A. Press ESC
to abort, any other key to continue…
(Enter)
Enter the number of drivers for which
you wish to have data ( 1 to 20000): 500(Enter)
Processing the requested data…Please wait for the countdown to 0.
0

The requested data are in the file a:\supins.dat.

The ASCII (text) file supins.dat on the diskette has the format shown in p. 3: the rows correspond to the selected drivers and the columns to the variables IDNO to SIZE in the same order as the list in p. 3 of this handout. The file can be read by any spreadsheet or statistical program.


APPENDIX C
SUPERIOR INSURANCE CASE --- SUMMARY OF DECISIONS FORM



STUDENT/GROUP NAME:_________________ PASSWORD:________________



1. Size of sample of IAB records:_____________


2. Specify precisely method for calculating premium quotation (bid) under Assignment 4 (see instructions and examples on back):















3. Specify precisely method for calculating premium quotation (bid) under Assignment 5 (see instructions and examples on back):

APPENDIX C
SUPERIOR INSURANCE CASE --- SUMMARY OF DECISIONS FORM, CONTINUED
INSTRUCTIONS AND EXAMPLES FOR SPECIFYING PREMIUM QUOTATION (BID)


Preserve the names and units of the case variables (for example, LOSS is measured in $000). Define first any new variables and state their units. The premium quotation must be denoted by PREM and expressed in $000.

Example 1: Flat premium of $750:
PREM=0.75

Example 2: Premium is $1200 for men and $800 for women drivers:
if GENDER=1 then PREM=1.2
else PREM=0.8

Example 3: Premium a given function of years of experience:
PREM= 2.1-0.03*EXPER

Example 4: Similar to Example 3, but with adjustment for marital status:
M1=1 if MARST=1; else M1=0 (single)
M2=1 if MARST=2; else M2=0 (married)

PREM=2 - 0.04*EXPER + 0.1*M1 - 0.1*M2