Basic Ratemaking

My notes refer to the study manual BASIC RATEMAKING Fifth Edition, May 2016.

Chapter 1 Introduction

FUNDAMENTAL INSURANCE EQUATION

• Price = Cost + Profit
• Premium= Losses + LAE + UW Expenses + UW Profit

  Exposure

  The basic unit of risk underlying the insurance premium includes written, earned, unearned, and in-force exposures

• Written exposures are the total exposures arising from policies issued (i.e., underwritten or written) during a specified period of time, such as a calendar year or quarter.
• Earned exposures represent the portion of the written exposures for which coverage has already been provided as of a certain point in time.
• Unearned exposures represent the portion of the written exposures for which coverage has not yet been provided as of that point in time.
• In-force exposures are the number of insured units that are exposed to loss at a given point in time.

Premium

The amount the insured pays for insurance coverage includes written, earned, unearned, and in-force premium

• Written premium is the total premium associated with policies that were issued during a specified period.
• Earned premium represents the portion of the written premium for which coverage has already been provided as of a certain point in time.
• Unearned premium is the portion of the written premium for which coverage has yet to be provided as of a certain point in time.
• In-force premium is the full-term premium for policies that are in effect at a given point in time.

Claim

• An insurance policy entails the insured paying a premium to the insurer for coverage against specific events.
• When such an event occurs, the insured (now the claimant) files a claim. The event’s date is known as the date of loss or accident date.
• Claims unknown to the insurer at a given time are termed unreported claims or incurred but not reported (IBNR) claims
• After the report date, a claim becomes known to the company and is classified as a reported claim. It remains an open claim until settled, after which it is considered closed. However, claims can be reopened if further activity occurs post-closure.

Losses

Loss under an insurance policy is the compensation amount payable to the claimant. Loss terminology includes paid loss, case reserve, reported or case incurred loss, IBNR/IBNER reserves, and ultimate loss.

• Paid loss is amounts already disbursed to the claimant.
• Case reserve is an estimate of the amount of money required to ultimately settle the claim, it excludes any payments already made.
• Reported loss is equal to Paid loss + Case reserve
• Ultimate loss is the total required to settle the claim. Estimated Ultimate Loss equal to Reported Loss + IBNR Reserve + IBNER Reserve.

Loss Adjustment Expense (LAE)

In addition to the money paid to the claimant for compensation, loss adjustment expenses (LAE) are costs insurers incur while settling claims, divided into allocated loss adjustment expenses (ALAE) and unallocated loss adjustment expenses (ULAE):

LAE = ALAE + ULAE.

• ALAE are claim-related expenses that are directly attributable to a specific claim; for example, fees associated with outside legal counsel hired to defend a claim can be directly assigned to a specific claim.
• ULAE are claim-related expenses that cannot be directly assigned to a specific claim. For example, salaries of claims department personnel are not readily assignable to a specific claim and are categorized as ULAE.

Underwriting Expenses (UW Expenses)

In addition to loss adjustment expenses, underwriting expenses are costs insurers incur for various expenses in acquiring and servicing policies.

• Commissions and brokerage: are payments made to insurance agents or brokers for generating business.
• Other acquisition costs: are expenses beyond commissions and brokerage, such as those for media advertising and mailings to potential customers.
• General expenses: are the operational and any other miscellaneous costs. For example, upkeep for the home office.
• Taxes, licenses, and fees: are all taxes and miscellaneous fees paid by the insurer excluding federal income taxes. Premium taxes and licensing fees are examples of items included in this category.

Underwriting Profit (UW Profit)

The two primary profit sources for insurance companies are underwriting profit and investment income.

• Underwriting profit, also known as operating income, is the profit from individual policies calculated as income minus expenses, similar to profit definitions in other industries.
• Investment income is the profit from investing the funds that the insurance company holds.

Basic Insurance Ratios

A set of basic ratios to monitor and evaluate the appropriateness of an insurance company’s rates.

• Frequency: \(\text{Frequency} = \frac{ \text{# of Claims}}{\text{# of Exposures}}\).
  • Help measure the effectiveness of specific underwriting actions.
  • For example, if the number of claims is 100,000 and the number of earned exposures is 2,000,000, then the frequency is 5% (= 100,000 / 2,000,000).
• Severity: \(\text{average cost of claims} =\text{Severity} = \frac{\text{Losses}}{\text{# of Claims}}\).
  • \[\text{Paid Severity} = \frac{\text{Paid Losses}}{\text{# of Claims Closed}}\]
  • \[\text{Reported Severity} = \frac{\text{Reported Losses}}{\text{# of Claims Reported}}\]
  • Additionally, ALAE may be included or excluded from the numerator.
  • Help measure the loss trends.
  • For example, if the total loss dollars are $300,000,000 and the number of claims is 100,000, then the severity is $3,000 (= $300,000,000 / 100,000).
• Pure Premium (or Loss Cost): \(\text{average loss per exposure } =\text{Pure Premium} = \frac{\text{Losses}}{\text{# of Exposures}} = \text{Frequency} X \text{times Severity}\)
  • Typically, reported losses (or ultimate losses) and earned exposures are used.
  • The reported losses may or may not include ALAE and/or ULAE.
  • Help measure the overall loss cost trends.
  • For example, if total loss dollars are $300,000,000 and the number of exposures is 2,000,000, then the pure premium is $150 (= $300,000,000 / 2,000,000 = 5.0% x $3,000).
• Average Premium: \(\text{Average Premium} = \frac{\text{Premuim}}{\text{# Of Expesures}}\)
  • It is important that the premium and the exposures be on the same basis (e.g., written, earned, or in-force).
  • Changes in average premium may indicate
    • Rate change
    • Change in the mix of business, e.g. deductible shift, insured limit shift, risk shifts, and etc.
  • For example, if the total premium is $400,000,000 and the total exposures are 2,000,000, then the average
• Loss Ratio: \(\text{Loss Ratio} = \frac{\text{Losses}}{\text{Premium}} = \frac{\text{Pure premium}}{\text{Average Premium}}\).
  • Typically, the ratio uses total reported losses and total earned premiums; however, other variations are common. Companies may include LAE in the calculation of loss ratios (commonly referred to as loss and LAE ratios).
  • Help measure the adequacy of the rates
  • For example, if the total loss dollars are $300,000,000 and the total premium is $400,000,000, then the loss ratio is 75% (= $300,000,000 / $400,000,000).
• Loss Adjustment Expense Ratio (LAE Ratio): \({\text{LAERatio}} = \frac{\text{Loss Adjustment Expenses}}{\text{Losses}}\)
  • The loss adjustment expenses include both allocated and unallocated loss adjustment expenses. Companies may differ as to whether paid or reported (incurred) figures are used.
  • Companies monitor this ratio over time to determine if costs associated with claim settlement procedures are stable or not. A company may compare its ratio to those of other companies as a benchmark for its claims settlement procedures.

• Underwriting Expense Ratio: \(\text{UW Expense Ratio} = \frac {\text{UW Expense}}{\text{Premium}}\)

• Operating Expense Ratio: \(\text{OER} = \text{UW Expense Ratio} + \frac {\text{LAE}} {\text{Earned Premium}}\)
  • The OER is used to monitor operational expenditures and is key to determining overall profitability.
• Combined Ratio: \(\text{Combined Ratio} = \text{Loss ratio} + \frac{\text{LAE}}{\text{Earned Premium}} + \frac{\text{Underwriting Expenses}}{\text{Written Premium}}\)
  • In calculating the combined ratio, the loss ratio should not include LAE or it will be double counted.
  • some companies may compare underwriting expenses incurred throughout the policy to earned premiums rather than to written premiums. In this case, the companies may choose to define combined ratio as \(\text{Combined Ratio} = \text{Loss Ratio} + \text{OER}\)
• Retention Ratio: \(\text{Retention Ratio} = \frac{\text{# of Policies Renewed}}{\text{# of potential Renewal Policies}}\).
  • Retention ratios and changes in the retention ratios are monitored closely by product management and marketing departments
  • Retention ratios are used to gauge the competitiveness of rates and are very closely examined following rate changes or major changes in service
  • If 100,000 policies are invited to renew in a particular month and 85,000 of the insureds choose to renew, then the retention ratio is 85% (= 85,000 / 100,000).
• Close Ratio: \(\text{Closs ratio} = \frac{\text{# of Accepted Quotes}}{\text{# of Quotes}}\).
  • a prospective insured may receive multiple quotes and companies may count that as one quote or may consider each quote separately.
  • Close ratios and changes in the close ratios are monitored closely by product management and marketing departments.
  • Closed ratios are used to determine the competitiveness of rates for new business.
  • If the company provides 300,000 quotes in a particular month and generates 60,000 new policies from those quotes, then the close ratio is 20% (= 60,000 / 300,000).

CHAPTER 2 RATING MANUALS

For most lines of business, the following information is necessary to calculate the premium for a given risk:

• Rules
• Rate pages (i.e., base rates, rating tables, and fees)
• Rating algorithm
• Underwriting guidelines Generally speaking, the first three items are found in a company’s rating manual, and the underwriting guidelines are maintained in a separate proprietary underwriting manual.

  Rules

• Typically contains qualitative information that is needed to understand and apply the quantitative rating algorithms
• To be an aid in calculating premium

  RATEPAGES

• The rate pages generally contain the numerical inputs (e.g., base rates, rating tables, and fees) needed to calculate the premium
• Base Risk
  • A specific risk pre A specific risk pre–defined by the insurer – Represents a set of risk characteristics that are most common or target market.
• Base Rate
  • The rate applied to the base risk
  • Not the average rate
  • The rate for risks other than base risk is determined by modifying the base rate by a series of multipliers or addends or some unique mathematical expression.

  • Rating Algorithms

• describes in detail how to combine the various components in the rules and rate pages to calculate the overall premium charged for any risk that is not specifically pre-printed in a rate table.
• May include:
  • The order in which rating variables should be considered
  • Multiplicative or additive
  • Maximum and minimum premium

Underwriting Guidelines

• Underwriting guidelines may be used to specify – Decisions to accept, decline, or refer (to senior underwriter) risks – Company Placement
  • Tier placement – Schedule rating credits/debits

HOMEOWNERS RATING MANUAL EXAMPLE Check page 17 for homeowners rating manual example.

CHAPTER 3 RATEMAKING DATA

Data is used by actuaries for many purposes including ratemaking.

Internal Data

• Risk information including exposures, premiums, claim counts, and losses
• Accounting Information including Underwriting expense, ULAE

Risk Data

• Policy Database
  • Policy Identifier
  • Risk Identifier (one policy may have multiple risks, e.g. two cars, two locations of insured)
  • Relevant Dates (original effective date, original expiration date, date of amendment)
  • Premium
  • Exposure
  • Characteristic
• Claim Database
  • Policy Identifier
  • Risk Identifier
  • Claim Identifier
  • Claimant Identifier
  • Event Identifier
  • Relevant Loss Dates (Report data, data of loss payment, date of reserve change, data of claim status change)
  • Claim Status (open, closed, reopen, reclosed)
  • Paid Loss
  • Case Reserve
  • ALAE (ULAE is handled elsewhere)
  • Salvage & Subrogation
  • Type of Injury
  • Cause of Loss

Accounting Information

• Underwriting Expenses
  • Expenses incurred in the acquisition and servicing of the policies, including general expenses, other acquisition expenses, commissions and brokerage, taxes, licenses, and fees
• ULAE

Data Aggregation

• Calendar year
  • Consider all premium and loss transactions that occur during the 12-month calendar year
  • All premiums and exposures are fixed at the end of the CY
  • CY data is available quickly once the CY ends
  • Main disadvantage of CY is the mismatch in timing between premiums and losses. For example, premium earned during CY come from policies in force during that year, and losses may include payments and reserve changes on claims from policies issued years ago.
• Accident year
  • Considers losses for accidents that have occurred during a 12-month period, regardless of the policy-issued date
  • Premium and exposure are defined as the same as CY aggregation
  • Reported losses consist of loss payments made plus case reserves only for those claims that occurred during that year
  • Reported losses can and often do change at the end of AY
    • Additional Claims are reported and paid
    • Reserves are changed
  • Future development on those known losses needs to be estimated
  • Better match of premium and losses than CY
    • Losses on accidents occurring during the year are compared to premiums earned on policies during the same year
• Policy Year
  • Considers all premium and loss transactions on policies that were effective during a 12-month period
  • Premiums and exposures are not fixed until after the expiration date
  • Reported losses for PY consist of payments made plus case reserves only for those claims covered by policies effective during the year
  • Reported losses can and often do change at the end of AY
    • Additional claims are reported and paid
    • Reserves are changed
  • Best Match between losses and premium
    • Losses on policies effective during the year are compared with premiums earned on those same policies
  • Data takes longer to develop than both CY and AY
    • For a product with an annual policy term, premiums are not fully earned until 24 months after the start of the policy year.
• Report year
  • Considers losses for accidents that are reported during a 12-month period, regardless of when the claim occurred
  • Premium and exposures are defined as the same as CY aggregation
  • Reported losses consist of loss payments made plus case reserves only for those claims that are reported during that year
  • Reported losses can and often do change at the end of AY
    • Additional claims are reported and paid
    • Reserves are changed