# Rate Making: How Insurance Premiums Are Set

**Rate making** (aka **insurance pricing**, also spelled *ratemaking*), is the determination of what rates, or premiums, to charge for insurance. A **rate** is the price per unit of insurance for each **exposure unit**, which is a unit of liability or property with similar characteristics. For instance, in property and casualty insurance, the exposure unit is typically equal to $100 of property value, and liability is measured in $1,000 units. Life insurance also has $1000 exposure units. The **insurance premium** is the rate multiplied by the number of units of protection purchased.

Insurance Premium = Rate × Number of Exposure Units Purchased

The difference between the selling price for insurance and the selling price for other products is that the actual cost of providing the insurance is unknown until the policy period has lapsed. Therefore, insurance rates must be based on predictions rather than actual costs. Most rates are determined by statistical analysis of past losses based on specific variables of the insured. Variables that yield the best forecasts are the criteria by which premiums are set. However, in some cases, historical analysis does not provide sufficient statistical justification for selling a rate, such as for earthquake insurance. In these cases, catastrophe modeling is sometimes used, but with less success. Actuaries set the insurance rate based on specific variables, while underwriters decide which variables apply to a specific insurance applicant.

Because an insurance company is a business, it is obvious that the rate charged must cover losses and expenses, and earn some profit. But to be competitive, insurance companies must also offer the lowest premium for a given coverage. Moreover, all states have laws that regulate what insurance companies can charge, and thus, both business and regulatory objectives must be met.

The primary purpose of ratemaking is to determine the lowest premium that meets all of the required objectives. A major part of ratemaking is identifying every characteristic that can reliably predict future losses, so that lower premiums can be charged to the low risk groups and higher premiums charged to the higher risk groups. By offering lower premiums to lower risk groups, an insurance company can attract those individuals to its own insurance, lowering its own losses and expenses, while increasing the losses and expenses for the remaining insurance companies as they retain more of the higher risk pools. This is the reason why insurance companies spend money on actuarial studies with the objective of identifying every characteristic that reliably predicts future losses.

Note that both the ratemaking and the underwriting must be accurate. If the rate is accurate for a particular class, but the underwriter assigns applicants that do not belong to that class, then that rate may be inadequate to compensate for losses. On the other hand, if the underwriting is competent, but the rate is based on an inadequate sample size or is based on variables that do not reliably predict future losses, then the insurance company may suffer significant losses.

The **pure premium**, which is determined by actuarial studies, consists of that part of the premium necessary to pay for losses and loss related expenses. **Loading** is the part of the premium necessary to cover other expenses, particularly sales expenses, and to allow for a profit. The **gross rate** is the pure premium and the loading per exposure unit and the **gross premium** is the premium charged to the insurance applicant, and is equal to the gross rate multiplied by the number of exposure units to be insured. The ratio of the loading charge over the gross rate is the **expense ratio**.

Pure Premium = Losses / Exposure Units

Example: an average loss of $1 million per year per 1000 automobiles yields the following pure premium:

Pure Premium = $1,000,000 / 1000 = $1000 per Automobile per Year

Gross Rate = Pure Premium + Load

The loading charge consists of the following:

- commissions and other acquisition expenses
- premium taxes
- general administrative expenses
- contingency allowances
- profit

Loading charges are often expressed as a proportion of premiums, since they increase proportionately with the premium, especially commissions and premium taxes. Hence, the loading charge is often referred to as an **expense ratio**. Therefore, the gross rate is expressed as a percentage increase over the pure premium:

Gross Rate | = | Pure Premium 1 – Expense Ratio |

Example: If the pure premium is $60 and the expense ratio is 40%, then:

Gross Rate = $60/(1 – 0.4) = $60/0.6 = $100

Gross Premium = Gross Rate × Number of Exposure Units

Expense Ratio = Load / Gross Rate

Other **business objectives** in setting premiums are:

- simplicity in the rate structure, so that it can be more easily understood by the customer, and sold by the agent;
- responsiveness to changing conditions and to actual losses and expenses; and
- encouraging practices among the insured that will minimize losses.

The main **regulatory objective** is to protect the customer. A corollary of this is that the insurer must maintain solvency in order to pay claims. Thus, the 3 main regulatory requirements regarding rates is that:

- they be
**fair**compared to the risk; - premiums must be
**adequate**to maintain insurer solvency; and - premium rates are
**not discriminatory**—the same rates should be charged for all members of an underwriting class with a similar risk profile.

Although competition would compel businesses to meet these objectives anyway, the states want to regulate the industry enough so that fewer insurers would go bankrupt, since many customers depend on insurance companies to avoid financial calamity.

The main problem that many insurers face in setting fair and adequate premiums is that actual losses and expenses are not known when the premium is collected, since the premium pays for insurance coverage in the immediate future. Only after the premium period has elapsed, will the insurer know what its true costs are. Larger insurance companies have actuarial departments that maintain their own databases to estimate frequency and the dollar amount of losses for each underwriting class, but smaller companies rely on advisory organizations or actuarial consulting firms for loss information.

An **advisory organization **(formally called a **rating bureau**) is a company that collects loss information to sell to insurance companies. The 2 major advisory organizations for property and casualty insurance companies in the United States are the **Insurance Services Office** (**ISO**) and the **American Association of Insurance Services** (AAIS). The **National Council of Compensation Insurance** (NCCI) provides rating plans and loss date for workers compensation. Although the suggestion of rates to charge is generally against antitrust laws, rating bureaus are exempt under the *McCarran-Ferguson Act of 1945*, which states that federal antitrust laws only apply to the extent that insurance is not regulated by state law. Nonetheless, advisory organizations do not suggest what rates to charge, but only sell the loss data, letting the companies determine what rates to charge. Life insurance companies do not use advisory organizations, since they rely on actuarial tables.

## Rate Making for Property and Liability Insurance

Rates for most insurance is determined by a class rating or an individual rating. Individual rating includes judgment rating and merit rating. Merit rating can be further classified as schedule rating, experience rating, and retrospective rating. Individual rates depend on the individual whereas class rates depends on the underwriting class of the insured. Individual rates are often calculated as a modification of a base class rate.

All insurance rates could be class rates, where the insurance company simply adjusts the premium to reflect the losses of the entire class. However, some insurance companies will identify lower risk groups within the class, then offer them lower premiums to grab market share. This, in turn, raises losses for the insurance company offering a class rating, forcing it to subdivide its own class, and offering different premiums that reflect the losses within those subgroups, eventually leading, with enough refinement of the subgroups, to individual rates. However, class rates remain for those risk groups that are more homogeneous, without identifiable subgroups of lower or higher risk.

### Class Ratings

**Class rating** is used when the factors causing losses can either be easily quantified or there are reliable statistics that can predict future losses. These rates are published in a manual, and so the class rating method is sometimes called a **manual rating**. The class is defined through statistical studies as a group with specific characteristics that reliably predict the insured losses of that group. A class rating must be applied to a rate class that is large enough to reliably forecast losses through statistical analysis but small enough to maintain homogeneity so that the premium covers the loss exposure and is competitive for each member of the class.

Class ratings are often used in pricing insurance products — mostly life insurance and product and liability insurance — sold to the consumer because there are copious statistics and a large enough population of similar situations that make class ratings effective. It also allows agents to give an insurance quote quickly.

There are 2 methods to determine a class rated premium or to adjust it.

In the **pure premium method**, the pure premium is 1^{st} calculated by summing the losses and loss-adjusted expenses over a given period, and dividing that by the number of exposure units. Then the loading charge is added to the pure premium to determine the gross premium that is charged to the customer.

Pure Premium | = | Actual Losses + Loss-Adjusted Expenses Number of Exposure Units |

Gross Premium = Pure Premium + Load

The **loss ratio method** is used more to adjust the premium based on the actual loss experience rather than setting the premium. The **loss ratio** is the sum of losses and loss-adjusted expenses over the premiums charged.

If the actual loss ratio differs from the expected loss ratio, then the premium is adjusted according to the following formula:

Rate Change | = | Actual Loss Ratio - Expected Loss Ratio Expected Loss Ratio |

### Individual Ratings

Individual ratings are used when many factors are used to predict the losses and those factors vary considerably among individuals. Additionally, individuals can exercise loss control measures that will reduce losses, so those individuals will pay a lower premium.

**Judgment ratings** are used when the factors that determine potential losses are varied and cannot easily be quantified. Because of the complexity of these factors, there are no statistics that can reliably assess the probability and quantity of future losses. Hence, an underwriter must evaluate each exposure individually, and use intuition based on past experience. This rating method is predominant in determining rates for ocean marine insurance, for instance.

#### Merit Ratings

A **merit rating** is based on a class rating, but the premium is adjusted according to the individual customer, depending on the actual losses of that customer. Merit ratings often determine the premiums for commercial insurance and for car insurance, and, in most of these cases, the customer has some control over losses—hence, the name. Merit ratings are used when a class rating can give a good approximation, but the factors are diverse enough to yield a greater spread of losses than if the composition of the class were more uniform. Thus, merit ratings are used to vary the premium from what the class rating would yield based on individual factors or actual losses experienced by the customer. Merit ratings are determined by 3 benefits: schedule rating, experience rating, and retrospective rating.

##### Schedule Ratings

**Schedule rating** uses a class rating as an average base, then the premium is adjusted according to specific details of the loss exposure. Some factors may increase the premium and some may decrease it—the final premium is determined by adding these credits and debits to the average premium for the class. For example, schedule rating is used to determine premiums for commercial property insurance, where such factors as the size and location of the building, the number of people in the building and how it is used, and how well is it maintained are considered.

##### Experience Ratings

**Experience rating** uses the actual loss amounts in previous policy periods, typically the prior 3 years, as compared to the class average to determine the premium for the next policy period. If losses were less than the class average, then the premium is lowered, and if losses were higher, then the premium is raised.

The adjustment to the premium is determined by the loss ratio method, but is multiplied by a credibility factor to determine the actual adjustment. The **credibility factor** is the reliability that the actual loss experience is predictive of future losses. In statistics, the larger the sample, the more reliable the statistics based on that sample. Hence, the credibility factor is largely determined by the size of the business—the larger the business, the greater the credibility factor, and the larger the adjustment of the premium up or down. Because the credibility factor for small businesses is small, they are not generally eligible for experience rated adjustments to their premiums.

Rate Change | = | Actual Loss Ratio - Expected Loss Ratio Expected Loss Ratio | × | Credibility Factor |

Actual Loss Ratio | 16% | |

Expected Loss Ratio | 20% | |

Credibility Factor | 0.25 | |

Rate Change | -5.0% | = (Actual Loss Ratio – Expected Loss Ratio)/Expected Loss Ratio × Credibility Factor |

To increase credibility, insurers will sometimes observe losses over several years, but taking observations over a longer period of time may be less accurate because some variables affecting losses may have changed. To improve forecasts based on longer time periods, the insurer may give greater weight to later years than earlier years, or a **trend factor** may be used, based on average claim payments, inflation, or some other factor that may affect the insurance company's exposure.

Experience rating is typically used for general liability insurance, workers compensation and group insurance. It is also extensively used for auto insurance, including personal auto insurance, because losses obviously depend on how well and how safely the insured drives.

##### Retrospective Ratings

**Retrospective rating** (a.k.a. **retro plan**) uses the actual loss experience for the period to determine the premium for that period, limited by a minimum and a maximum amount that can be charged. Part of the premium is paid at the beginning, and the other part — the **retrospective premium** — is paid at the end of the period, the amount of which is determined by the actual losses for that period. Retrospective rating is often used when schedule rating cannot accurately determine the premium and where past losses are not necessarily indicative of future losses, such as for burglary insurance. The rretrospective premium is based on a base insurance rate, modified by the actual losses in the period, a charge for the loss adjustment, and state premium taxes. Businesses often elect retro rating plans for general liability, workers compensation, and group health insurance. This is a typical formula for calculating the retrospective premium for workers compensation:

Retrospective Premium | = | [ | Basic Premium | + | ( | Ratable Losses | × | Loss Conversion Factor | ) | ] | × | Premium Tax Multiplier |

The **loss conversion factor** is expressed as a percentage of the ratable losses. This percentage is added to 1, then multiplied by the amount of losses during the retrospective period. Likewise, the **premium tax multiplier** is a percentage of the premiums charged, so the premium tax percentage is added to 1 before multiplying it by the total premium. So if loss adjustment expenses equals 10% of the losses, then the loss conversion factor = 1 + 10% = 1.1. If the premium tax is 4% of the premiums charged, then the premium tax multiplier = 1 + 4% = 1.04.

## Rate Making for Life Insurance

Rate making for life insurance is much simpler, since there are mortality tables that tabulate the number of deaths for each age, which includes a population of many people. Age is the most important factor in determining life expectancy, but there are other well known factors that have a significant effect, such as the sex of the individual and smoking. Thus, an actuary can reasonably estimate the average age of death for a group of 25-year old males, who don't smoke.

The simplest case is determining the net single premium, which is the premium that would need to be charged to cover the death claim, but does not cover expenses or profit. Although most people don't pay a single premium because of the cost, all life insurance premiums are based on it. Annual level premiums can easily be calculated from the net single premium. The **net single premium** is simply the present value of the death benefit. The net single premium is less than the death benefit because interest can be earned on the premium until the death benefit is paid. The **gross premium** for life insurance includes the premium to cover the death claim plus all expenses, a reserve for contingencies, and profit.