Ø The Insurance Pricing Dilemma
· How does an insurer determine the price of its product?
Ø A Bucket of Premium
· To understand how much money is sufficient to an insurer for its needs, we may think of that money as filling a bucket, with all required payments to be made by taking money from the bucket.
· The money in the insurer’s bucket is the sum of the pure premium and expenses, including development factors, trend factors, acquisition costs, administrative expenses, and profit.
· See page 3 for the definitions of pure premium, development factors, trend factors, acquisition costs, commission, administrative expenses and profit.
· Allocation of premium can be seen by the following example:
Pure Premium $0.57
Development Factors $0.04
Trend Factors $0.03
Acquisition Costs $0.15
Administrative Expenses $0.19
Profit $0.02
Total $1.00
· The list of expenses is far from complete: premium also needs to be allocated for its reinsurance expenses, unallocated loss adjustment expenses, and taxes, including premium tax, corporate income tax, and license or other fees.
· Regardless of obligations and needs, the money in the bucket must include provision for the insurer’s profit. The industry as a whole has often sacrificed this element of its pricing to competitive pressures.
Ø The Importance of Profit
· An underwriter is an investor of shareholder capital. If the shareholders are to receive a return on their capital – value for their investment – then the premium the underwriter charges for exposing the shareholders’ capital to risk must include some allowance for profit.
· Definition of Underwriting Profit (or loss) arises out of insurance operations. It is the amount by which earned premium exceed (or fall short of) the cost of incurred claims and expenses.
· Definition of Investment Income is income the insurer earns from investing money that the insurer earns from investing money that the insurer has received as premium but not yet earned, as well as money it has set aside as a reserve to pay claims.
· Investment income has often been used to offset underwriting losses and produce an overall profit for an insurer. However, investment income cannot sustain an insurer’s profitability indefinitely.
· Decisions that underwriters make about price bear strongly on the financial strength of the insurer, so the price that underwriters charge for insurance coverage is critical.
Ø The Role of the Actuary
· The price of insurance is based on historical data about incurred losses. Statistical techniques are applied to this data to develop a forecast of the rates needed to provide sufficient premium for future losses.
· Definition – An actuary is a professional skilled in the application of mathematics to financial problems. An actuary applies specialized knowledge of math of finance, statistics, and risk theory to problems faced by insurance companies, pension plans, government regulators, social programs, and individuals.
· The price of insurance reflects the work of actuaries and underwriters in two related but distinct exercises: ratemaking, done by actuaries, and rating, done by underwriters.
· Definition – a rate is the price of a unit of insurance for the policy period (usually one year)
· Definition – a premium is the total cost of the insurance. It is derived by multiplying the rate of insurance by the amount of insurance.
Ø The Ratemaking Process
· Ratemaking by actuaries produces the rates that underwriters then modify according to the insurer’s underwriting philosophy, the competition in the marketplace, and the characteristics of each risk.
· The price is set for its services before it knows the cost of those services.
· The ratemaking is prospective rather than retrospective: It must use yesterday’s statistics to calculate today’s premiums to pay tomorrow’s losses.
· The major components of any rate are: the anticipated cost of settling claims, the acquisition costs of the business, such as commissions; and the cost of administering the process, including taxes levied on the premiums.
· The cost of settling claims (the loss ratio) varies from one type of insurance to another; from one location to another; and on the basis of various risk factors. Acquisition costs (sales expenses) vary according to the distribution method.
· A rate will be adequate when two conditions occur; the actuarial forecast of future losses based on past losses must be accurate for the population. The sample represented by the book of business written by a particular underwriter or insurer must be representative of the population.
Ø The process that actuaries, acting on behalf of insurers, use to arrive at an adequate rate for a given class of risk includes the following steps:
1. Classifying the risk based on the types of objects of insurance; the hazards of exposure; or both.
- Insurer’s first step is to decide what objects of insurance it wants to cover.
- Insurer would need to decide how to subdivide each of its chosen classes.
- See the example on page 8.
- Insurer must then determine the exposures to loss that each class represents.
2. Determining the number and nature of the rating classes
- A rating class should be large enough to allow a reasonable amount of data to be collected for it. If it is too small, then the law of large numbers will not apply to the data collected for it and the rates developed from the data will lack statistical credibility.
- A rating class should reflect a reasonable level of discrimination among insureds to insure that a rate reflects the probable frequency and severity of loss that will be experienced by insureds in that class. See example on page 9.
3. Selecting the proper measure of exposure.
- The proper measure of exposure for a given class of risks is the exposure base.
- The exposure base for a given risk depends on the nature of the risk and the kinds of loss it might incur. Ideally, the exposure base will reflect the frequency and severity of loss the risk experiences. See example on page 10.
- Definition – the exposure base is the denomination in which the unit of exposure is expressed. An example of an exposure base is gross sales, which is used for some classes of liability insurance.
- Definition – the exposure unit is expressed as a specified amount of the exposure base. For example, gross sales are often expressed in units of $1,000
4. Gathering loss statistics.
- If the insurer is large enough, and depending on the line or lines of business for which statistics are being gathered, the statistics may be drawn from the insurer’s own portfolio.
- One alternative used by many insurers is to report their loss statistics to the Insurance Bureau of Canada Canada
5. Predicting future losses from the data regarding past losses.
- Predicting future losses is an application of the law of large numbers (also known as the law of averages) and the theory of probability.
- Definition – the law of large numbers is the principle that a given probability becomes more reliable the larger the number of trials or cases in the sample.
- Definition – the theory of probability concerns the likelihood of an occurrence, expressed by the ratio of the number of actual occurrences to the number of possible occurrences.
- The usefulness of the stats in predicting future loss experience depends on how much loss information is collected, when it is collected, and under what conditions it is collected.
- The size of the sample – the larger the sample, the more reliable the predictions.
- Time period over which the sample was taken – the longer the time period, the greater the reliability.
- Conditions past and future – the more stable the conditions the greater the reliability.
6. Calculating the pure premium from the predicted losses.
- The pure premium is the premium is the premium required to pay claims.
- See example on page 13.
7. Calculating the total premium
- To calculate the total premium, the insurer must add amounts to the pure premium that will provide for the additional elements.
8. Calculating the premium rate or unit cost
- The premium rate or unit cost of insurance is calculated by dividing the total premium by the exposure unit.
- See the example on page 13.
Ø Ratemaking for Different Lines of Insurance
· The premium rate is refined for each type or class of risk by the same considerations that an underwriter uses to assess an individual risk of that type or class.
- In property insurance, an underwriter analyzes the COPE factors for a risk.
- In auto insurance, ratemaking as well as underwriting will be concerned with the classification and use of the vehicle, the territory in which the vehicle is based, the driver’s age and record, and the deductible levels for the proposed coverage.
- In liability insurance, an underwriter will be interested in the nature and extent of the potential liability that might arise from the occupancy or type of operation that a risk represents. Ratemaking will also include allowances for the long-tail problem arising from losses incurred during the policy period but not discovered and reported until later, and also arising from the uncertainty about when claims will be settled and for how much.
Ø Ratemaking Summarized
- Work through the example on page 15-16
Ø Rating: The Ratemaking Process Applied
- Definition – Rating is the process by which underwriters apply the rates developed by actuaries to the information that underwriters have gathered to determine premium for individual risks.
- Insurance is a pooling device. The manual rate developed by actuaries for a particular class represents the price that is deemed to be appropriate for the “average” risk in that class.
- The job of rating for the underwriter is essentially to determine whether the particular risk is better or worse than the “average” risk in the class and by how much, and then modify the manual rate to reflect how the particular risk compares to the average risk. There are two basic approaches to this job: class rating and schedule rating.
Ø Class Rating
· Computers are programmed to carry out the rating function automatically for certain classes of insurance; auto insurance for example.
· Class rating is used when statistics can be gathered on a large number of risks that share common characteristics.
· The record of losses for the period under review can be subdivided into categories such as territory, type of unit insured, and value of the unit insured.
· The advantage of having industry-wide statistics (from IBC) is that the statistics will have enough credibility to provide a reasonably accurate basis for estimating future claims costs.
· Class rating virtually eliminates the element of judgment in rating and streamlines the policy-issuing process, thus reducing production costs.
Ø Schedule Rating
· Some classes of business are individually rated because of their complexity and the need for underwriting judgment.
· Schedule rating is used when the body of statistical data is too fragmented to permit class rating.
· Rates are based on a schedule or manual that lists a multitude of characteristics identified by underwriters over a period of many decades as important factors in measuring the degree of risk.
· The process of schedule rating involves the fixing of a base rate or key rate. Once these rates are determined, debits and credits are applied based on factors that make the risk either better or worse than the average risk of its type.
· Over several hundred years, underwriters have gained enough experience to attach a monetary value to each risk factor.
· Rates for schedule-rated risks are modified from time to time based on statistical exhibits that contain cells broad enough in scope to produce a credible indication of future claims costs. See example on bottom of page 19.
Ø The Role of the Underwriter
· The degree of flexibility available to the underwriter in rating a risk varies by type of insurance and size of the risk.
· The reliance upon past loss information to predict future losses inevitably entails assumptions based on judgment.
· Neither ratemaking nor rating is purely a science. Rather, ratemaking and rating are both art and science. It takes practical experience and theoretical knowledge to do either one well.
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