If you have ever had a conversation with a casualty actuary, you may have thought they were speaking a foreign language. We tend to throw around terms like “Bornhuetter-Ferguson Method,” “loss triangle,” or “ultimate loss” and sometimes forget that the phrases that are second nature to us are completely foreign to most. Add in the acronyms we use (IBNR, LDF, ALAE), and it’s a bit like alphabet soup.

This article will help risk management professionals from self-insured organizations navigate through our actuarial speak. We’ll cover inputs, such as loss and exposure terminology, and outputs, such as report terminology. Welcome to “How to Speak Casualty Actuary 101.”

What do casualty actuaries need to perform an actuarial study?

Let’s focus first on information that is provided to the actuary: the inputs. The cornerstone of most actuarial analyses is a loss run or claim listing, a detailed record of a company’s specific loss history. The second input is exposure data, which is used by the actuary to gauge the overall size and, therefore, the insured’s propensity for loss. The loss runs and exposure information are either provided by the client directly or by an intermediary, such as a broker.

Loss runs: Financial information

Common financial fields provided in a loss run include paid loss, case reserve, and incurred loss. For any given claim, paid loss is the amount that the claimant has received as of the evaluation date. The case reserve is the amount the claim adjuster believes is remaining to be paid on the claim as of the evaluation date. Case reserves may be adjusted over time as more information is learned about the claim or as payments are made. The combination of the paid loss and the case reserve is labeled incurred loss or reported loss.

Depending on the loss run, the paid loss, case reserve, and incurred loss may each be separated into individual components. For workers’ compensation, the loss run may include medical losses, or the portion related to medical treatments, and indemnity losses, or the portion related to the reimbursement for an employee’s lost time from work or pain and suffering. Expenses, also referred to as allocated loss adjustment expense (ALAE), are the portion related to managing the claim and are directly attributable to a specific occurrence, such as legal or investigative costs. Any expenses that cannot be tied to a specific claim, such as overhead, are deemed unallocated loss adjustment expense (ULAE). Given that ULAE isn’t attached to an individual claim, it isn’t found in a loss run.

Another field that may be separated out in a loss run is recoveries. Recoveries can include salvage, the trade-in value of an asset that has been damaged beyond further use, and subrogation, the amount an insurer recoups from a separate responsible party, such as another insurer. Gross losses describe the amount prior to the application of recoveries, and net losses are gross losses less recoveries.

All losses defined above are typically shown on an unlimited basis on the loss run. This means that they represent the full amount, from the ground up or first dollar, that has been paid or incurred. This includes dollars that the insured is responsible for paying as well as dollars that the insurer is responsible for paying. A limited loss on the other hand, is calculated from the unlimited loss and represents the amount in a specific layer. Reimbursements, the portion of the claim paid by the insurer, are sometimes listed in a loss run.

If the insured is on a loss-sensitive program, they might be solely interested in the portion of the loss that they are responsible for paying. This is referred to as the retained amount. Retention is a term that reflects the dollar amount that the insured must pay on each claim. Insurance policies can be structured with two types of retentions: deductibles and self-insured retentions. With a deductible the insurer pays all losses first and then seeks reimbursement from the insured for their portion of the loss. With a self-insured retention (SIR), the insured pays their portion of the claim and notifies the insurer when the claim is nearing the SIR. The terms retention and deductible are often used interchangeably; however, all deductibles are retentions but not all retentions are deductibles.

Loss runs: Calendar dates

A loss run also typically includes multiple calendar dates that are useful to an actuary. The date of loss, sometimes called an accident date or incident date, marks the date the accident occurred. The date of report, sometimes called a report date or notification date, marks the date the claim was reported to the insured or insurer.

These two dates help the actuary organize the data. Policies can be written on an occurrence or a report basis. For an occurrence-based policy, the policy covers claims that occurred during a certain timeframe. For a report-based or claims-made policy, the policy covers claims that were reported during a certain timeframe.

These distinctions are important, particularly for certain lines of business. Auto liability tends to be written as an occurrence-based policy while hospital professional liability is frequently written as a report-based policy. Auto liability claims, for example, are typically reported very quickly. However, hospital professional liability claims may not be known about or reported for many years after they occurred.

The length of time between date of loss and date of report is called report lag. For example, if a workers’ compensation claim occurred in 2019 but it wasn’t reported until 2022, it would have a report lag of three years. Long-tailed lines of business, such as workers’ compensation, tend to have long report lags or long times from occurrence to when all claims are fully paid and closed, or the closure date.

Loss runs: Qualitative data

The loss run also includes fields that are not numeric. Claim status, which indicates whether a claim is closed, open, or has reopened, is a field commonly found in a loss run. In some cases, claim status may include incident only, meaning that no claim has been filed but the insured or insurer is aware of the incident. This information is important because closed claims are typically not expected to have any additional paid or incurred losses going forward (unless they reopen). In contrast, open claims will often continue to change with each evaluation until they are closed.

You will also find the line of business (LOB) or coverage field. The LOB can be as broad as workers’ compensation (WC), general liability (GL), or auto liability (AL), to name a few. Or it can be more specific, such as WC – Medical or WC – Indemnity.

There are many other fields that can be found in loss runs, including benefit state, loss description, and job code, to name a few. These additional fields may or may not be relevant, depending on the scope of the analysis.

Exposures

Another crucial piece of information that is provided to the actuary is exposures. Exposures are used to gauge how large the company is and, therefore, its propensity to loss. The most appropriate exposure measure to use will vary by coverage. For workers’ compensation, the exposure is typically payroll, head count, or employee hours; for general liability, revenue; and for auto liability, auto count or mileage.

For example, assume an actuary is reviewing auto liability exposure and notes that losses have doubled in a given year. At first glance, it may seem as if loss experience is drastically increasing. However, if the actuary is aware that the number of vehicles covered by the policy has also doubled, then that increase in losses is anticipated.

What are common results found in an actuarial study?

Two common metrics used by actuaries are frequency and severity of claims. Frequency refers to the number of claims normalized for the size of the program, calculated as claim count divided by exposure. The complement to frequency is severity, or the average cost of each claim.

When multiplied together, frequency and severity provide a loss cost (also known as pure premium or loss rate). This is the actual or expected cost of claims in a given year.

When this loss cost is used to forecast expected losses for an upcoming policy year, it’s called a loss projection or funding. Actuaries look at historical experience to predict the future. They review the recent history and, as a part of that, they develop and trend the losses. Development, described in more detail below, brings currently valued losses to ultimate. Ultimate loss is the estimated value of losses for any given year when all the claims have been reported, paid, and closed. Trend is a factor applied to the historical losses to account for changes in things such as frequency of claims, severity of claims, inflation, law changes, etc.

With these two adjustments, the historical losses are now reflected in “today’s dollars.” They are then converted to a loss cost for each year in the experience period. The actuary will review these loss costs and select a prospective loss cost based on professional judgment of how losses are expected to behave going forward.

Acronyms

Actuaries use a lot of acronyms in our presentations and reports, and we often only define them once. It’s up to you to remember what we are talking about! Below is a list of some of the most common actuarial acronyms.

Incurred but not reported (IBNR) is one of the most common acronyms you will see from a casualty actuary. In most contexts, IBNR reserves refer to future claim development. Pure IBNR reserves are related to claims that have occurred but have not yet been reported. This is especially important for occurrence-based policies and long-tailed lines of business, where pure IBNR may be considered for several years. For claim-made policies and short-tailed lines of business, there may not be a need to reserve for pure IBNR except in the most recent year.

IBNR reserves encompass more than just pure IBNR reserves. There may also be future development as a result of adverse development on currently open claims or claims that have closed but reopen on a later date.

Loss development triangles, shown in Figure 1, are one of the tools used by actuaries to determine IBNR reserves. A triangle is a method of organizing loss data by year (rows) and age in months (columns). They can be used to track historical claim development, which can in turn be used to estimate future development. Triangles can be built using paid losses, incurred losses, or reported claim counts. They can also be built using unlimited or limited data (capped at a specified amount, for example $250,000 per claim).

In Figure 1, $714 is the amount that has been paid for claims that occurred in 2020, after 12 months (i.e., at the end of 2020). Similarly, $2,200 is the amount that has been paid for claims that occurred in 2020, after 24 months (i.e., at the end of 2021).

The output of a triangle is loss development factors (LDFs), shown in Figure 2. Age-to-age factors (ATAFs), or incremental LDFs, are determined by dividing losses at a later maturity by an earlier maturity.

For example, referring to Figures 1 and 2, dividing the 2020 losses that are 24 months old ($2,200) by the 2020 losses that are 12 months old ($714) will produce a 12-24-month ATAF for the 2020 year of 3.081.

Based on these ATAFs, an actuary can look at the historical patterns to estimate future development. LDF selections are largely subjective, but actuaries look for trends and shifts in patterns to make their selections. Actuaries will often look at a variety of averages, as shown in Figure 3, to select each ATAF. At the last age, where the triangle ends, the actuary will select a tail factor. The selection of the tail factor may be based on an industry benchmark, a curve-fitting exercise, or actuarial judgment, depending on the line of business. Additional considerations include the last maturity of the last ATAF, the number of open claims, or the amount of case reserves. In Figure 3, the selected tail is 1.065.

Each of the selected ATAFs are multiplied together to determine cumulative LDFs. For example, the tail factor of 1.065 multiplied by the 108-120-month ATAF of 1.006 equals 1.072. This is called the 108-ultimate factor and would be applied to losses that are 108 months from inception.

Because these LDFs are applied to losses (see the next section for a description of the Loss Development Method), we want to match the characteristics of those losses. For example, it’s not appropriate to apply unlimited LDFs to losses limited to $250,000 per claim. It will overstate the future development on those losses. Additionally, it is not appropriate to apply incurred LDFs to paid losses or to apply LDFs for 12 months of age to losses that are 10 months old.

LDFs have another application, which is to determine how much loss is expected to be paid or incurred at a certain age by looking at 1 / LDF. For example, in Figure 3, the cumulative LDF at 12 months is 3.222, so we would expect 31% of ultimate losses to be paid after 12 months (1 / 3.222).

Actuarial methodologies

There are a variety of actuarial methods that an actuary may review when selecting ultimate losses. In this paper we’ll focus on three commonly used methods: Expected Loss Rate (ELR), Loss Development, and Bornhuetter-Ferguson (B-F).

The Expected Loss Rate (ELR) Method examines a longer-term history to give an expectation of future losses. This method is based solely on current exposures and historical loss data, so if actual loss experience for a less mature year deviates from prior years, this method may not be a good representation of future development.

On the flip side, the Loss Development Method considers losses to date multiplied by the applicable LDF to estimate ultimate losses. Because this method fully contemplates losses to date, the absence or presence of large losses early on can have a large and often misleading impact.

Because the ELR Method ignores the losses to date and the Loss Development Method fully considers them, a blend of these two methods can often provide a more stable result. One method that marries the two concepts is called the Bornhuetter-Ferguson (B-F) Method.¹ The B-F Method takes a base expectation (called the a priori) and estimates what is left to be paid or incurred from the ultimate. It then adds the actual losses to that estimate. Oftentimes, the a priori is the result from ELR Method because it is unbiased to current loss experience.

Here’s a non-actuarial example of how these three methods work together: Let’s say your favorite basketball team typically gets 80 points in a game. After the first half, they have scored 60 points. The Expected Loss Rate Method would assume that they would score 20 points in the second half, adding up to the 80 total points. The Loss Development Method would assume that they would score 60 points in the second half, adding up to 120 total points (60 times 2). The B-F Method would assume that, because, on average, they score 40 points in the second half (half of their total score of 80), they will score a total of 100 points (expectation of 40, plus the first half score of 60).

Because there is no clear-cut answer as to when each method should be used, it is important to enlist the expertise of an experienced, unbiased actuary to weigh the merits and faults of each.

Summary

While this paper is not an all-inclusive guide to what might come out of your actuary’s mouth or from a report, it will still serve as a resource for when you can’t quite translate the results. Keep this handy for the next time you review an actuarial report, and you’ll be speaking casualty actuary in no time!

¹ Bonus fact: Ron Bornhuetter and Ron Ferguson are the two actuaries who introduced the method in their 1972 paper titled “The Actuary and IBNR.”

Glossary of terms

For easy access, here is a compiled list of casualty actuarial terms:

Accident Date. See Date of Loss.

Age-to-Age Factors (ATAFs). See Loss Development Factors.

Allocated Loss Adjustment Expense (ALAE). The portion of a loss that is related to expenses that can be tied to the specific claim, such as legal.

Bornhuetter-Ferguson (B-F) Method. A method of estimating ultimate losses that considers losses to date but assumes future development will revert to the longer-term history.

Case Reserve. The amount the claim adjuster believes is remaining to be paid on the claim. This value is static and may be adjusted over time as more information is learned about the claim.

Claim Listing. See Loss Run.

Claim Status. An indication of whether a claim is closed, open, or reopened, or in some cases an incident only.

Claim-Made Policy. See Report-Based Policy.

Closure Date. The date when the claim adjuster believes all losses on a claim have been paid and no further activity or observation is required.

Coverage. See Line of Business.

Date of Loss (aka Accident Date or Incident Date). The date the accident occurred, which resulted in a claim being filed.

Date of Report (aka Report Date or Notification Date). The date the claim was reported to the insured or insurer.

Deductible. A retention structure in which the insurer pays all losses first and then seeks reimbursement from the insured for their portion of the loss.

Expected Loss Rate (ELR) Method. A method of estimating ultimate losses that examines a longer-term history to give an expectation of future losses.

Expenses. See Allocated Loss Adjustment Expense.

Exposures. A value used to gauge the size of a company and, therefore, its propensity to loss. (Typically payroll for workers’ compensation, revenue for general liability, and auto count or mileage for auto liability).

Frequency. The number of claims, normalized for the size of the program. Calculated as claim count divided by exposure.

Funding. See Loss Projection.

Gross Losses. Loss amount prior to the application of recoveries.

Incident Date. See Date of Loss.

Incident Only. A claim status indicating that no claim has been filed but the insured is aware of the incident.

Incurred But Not Reported (IBNR). An overarching term that refers to future claim development. “Pure” IBNR refers to claims that have occurred but have not yet been reported. Beyond “pure” IBNR, the overarching term IBNR also includes future development on currently open claims, or further development on claims that have closed but will reopen on a later date.

Incurred Loss (aka Reported Loss). The combination of the paid loss and the case reserve. In the context of an insurer’s loss experience, the term incurred loss can also be interchangeable with the term ultimate loss.

Indemnity Loss. The portion of a loss that is awarded for pain and suffering as well as lost time from work.

Limited Losses. The loss amount in a specific layer. This value is calculated from unlimited losses.

Line of Business (LOB) aka Coverage. The type of claims insured under a given policy, such as workers’ compensation (WC), general liability (GL), or auto liability (AL).

Long-Tailed. A term referring to lines of business that tend to have a long report lag, or a long time from occurrence to when all claims are fully paid and closed.

Loss Cost (aka Pure Premium or Loss Rate). The actual or expected cost of claims in a given year. Calculated as the product of frequency and severity.

Loss Development Factors (LDFs). The output of a loss development triangle. These factors can be incremental, also known as Age-to-Age Factors (ATAFs), or cumulative. Incremental factors are used to develop losses from one age of development to another. Cumulative factors are used to develop losses from their age of development to ultimate.

Loss Development Method. A method of estimating ultimate losses by multiplying losses to date by the applicable cumulative loss development factor.

Loss Development Triangles. See Triangles.

Loss Projection (aka Funding). The forecasted losses for an incepting policy year.

Loss Rate. See Loss Cost.

Loss Run (aka Claim Listing). A detailed record of a company’s specific loss history.

Medical Loss. The portion of a loss that is related to medical treatments.

Net Losses. Loss amount after the application of recoveries.

Notification Date. See Date of Report.

Occurrence-Based Policy. An insurance policy covering claims that occurred during a certain timeframe.

Paid Loss. The amount that has been received to date on a claim.

Pure Premium. See Loss Cost.

Recoveries. Amount recovered on a claim, such as salvage or subrogation.

Reimbursements. The portion of the claim paid by the insurer (sometimes called Deductible Reimbursements).

Report Date. See Date of Report.

Report Lag. The length of time between date of loss and date of report.

Report-Based Policy (aka Claim-Made Policy). An insurance policy covering claims that were reported during a certain timeframe.

Reported Loss. See Incurred Loss.

Retention. The dollar amount that the insured must pay on each claim. Insurance policies can be structured with two types of retentions: deductibles and self-insured retentions.

Salvage. The trade-in value of an asset that has been damaged beyond further use (e.g., a totaled automobile involved in an accident).

Self-Insured Retention (SIR). A retention structure in which the insured pays their portion of the claim and notifies the insurer when the claim is nearing the limit.

Severity. The average cost of each claim.

Subrogation. The amount an insurer recoups from a separate responsible party, such as another insurer (e.g., insurer of other involved party reimburses insurer of claimant for its portion of the cost).

Tail Factor. A cumulative LDF selection made by the actuary for the final age shown on the triangle.

Trend. A factor applied to losses in a historical year to reflect the same loss experience in “today’s dollars.” The factor may include considerations such as frequency, severity, inflation, changes in law, etc.

Triangles (aka Loss Development Triangles). A method of organizing loss data by year (rows) and age in months (columns) that can be used to track historical claim development. Triangles can be built using paid losses, incurred losses, or reported claim counts. They can also be built using unlimited or limited data (capped at a specified amount, for example $250,000 per claim).

Unallocated Loss Adjustment Expense (ULAE). Any expenses that cannot be tied to a specific claim, such as overhead.

Ultimate Losses. The estimated losses for any given year when all claims have been reported, paid, and closed. In the context of an insurer, the term ultimate loss may be interchangeable with the term incurred loss.

Unlimited Losses. The full loss amount, from the ground up or first dollar, that has been paid or incurred. This includes dollars that the insured is responsible for paying as well as dollars that the insurer is responsible for paying.