*The behavior of loss reserves for self-insured organizations may seem mystifying at times. This article is designed to help readers understand the key factors that influence the direction of loss reserve estimates over time. *

There are several factors that contribute to changes in loss reserve estimates over time. The most significant is often random volatility in claims experience. In fact, the influence of randomness is usually so large that no attempt is made to forecast loss reserves beyond a few months into the future. Despite the significant role randomness plays, it is possible to project loss reserves several years into the future based on a few simplifying assumptions. The resulting projection can be used to establish a benchmark around which budgeting, capital management, and program performance can be organized.

In this article, we will explore a simple model for establishing benchmark loss reserve estimates using a newly self-insured program as an example. This model is *deterministic* in the sense that it does not contemplate randomness. More sophisticated versions of the model will be discussed in future articles that incorporate elements of randomness in the form of confidence intervals.

Our model is based on assumptions in each of the five following areas.

– In a self-insured context, inflation refers to the change in the cost of claims over time. Hypothetically, this refers to the cost of**Inflation***identical*claims and does not contemplate changes in the*types*or*frequency*of claims over time (these costs are included in exposure growth, below). For simplicity, we assume that inflation applies on a policy year basis. In other words, with a 10% inflation assumption, the loss pick would increase from $1 million in the first policy year to $1.1 million in the second policy year, and so forth.**Exposure growth**– In this context, exposure growth is anything, aside from the claim inflation defined above, that leads to an increase in claim costs. This is our “catch all” category. Exposure growth may be due to an increase in the number of employees (for workers compensation), an increase in the self-insured retention, or a deterioration of the organization’s risk profile. Exposure growth can be favorable (a negative percent) or adverse (a positive percent).– A payment pattern refers to the rate at which losses are paid over time. For our purposes, we are interested in the payment pattern corresponding to an individual policy year. Payment patterns are often characterized as “fast” or “slow”, referring to the rate at which claims are paid.**Payment pattern****Initial loss pick**– In practice, an actuarial estimate of ultimate loss and expense for a policy year is commonly called a loss pick. In each of the following examples, we assume that an organization begins a newly self-insured program with a $1 million loss pick for the first policy year.**Changes in prior policy year ultimates**– In each of the following examples, we assume that there are no changes in prior policy year ultimates. This simplifying assumption is equivalent to assuming that the policy year loss picks are selected with perfect foresight. In pratice, random volatility in claims experience results in periodic revaluations of prior policy year ultimates.

Note that the assumptions for items 4 and 5 are fixed throughout this article. In this simplified environment, we will examine the influence of inflation, exposure growth, and payment pattern on loss reserve estimates.

### First Scenario: Company A

In our first example, we begin with the following assumptions for Company A:

**Inflation**– 0% per year**Exposure growth**– 0% per year**Payment pattern**– the selected payment pattern for each policy year is such that 100% of claims are paid ten years after the beginning of each policy year. This represents our “medium” speed pattern. For convenience, we present the pattern as the amounts*unpaid*^{1}at the end of each respective year. The complete pattern is illustrated in Figure 1.

Later, we will use the above assumptions to forecast Company A’s loss reserve estimates at the end of each of the next ten years. First, let’s focus on the estimates associated with just the first policy year.

The loss pick for Company A’s first policy year is $1 million. Based on our payment pattern assumption, 75% of the losses will be unpaid one year after the inception of the policy year. Therefore, at the end of year one, Company A’s loss reserve estimate is $750 thousand (75% of $1 million). Using similar logic, Company A’s loss reserve estimate at the end of year two (two years after the beginning of the first policy year) is $520 thousand. These amounts, as well as those for the next several years are illustrated in Figure 2.

Notice the similarity between the results in Figure 1 and Figure 2. In this simplified example, the loss reserves for Company A’s single policy period mirror the shape of the payment pattern.

Next, let’s look at Company A’s loss reserve estimates for multiple policy years. Here things start to get more interesting. As illustrated in Figure 3, the loss reserve balance increases rapidly at first and then stablizes at $2.520 million after nine years.

Let’s look more closely at the composition of the loss reserve estimates over time. At the end of one year, loss reserves are $750 thousand. This is the same result we observed in Figure 2, above: $750 thousand equals 75% of the $1 million loss pick for the first policy year.

At the end of two years, there are two policy years that require a total of $1.27 million of loss reserves:

- 1st Policy Year:
**$520 thousand**= $1 million x 52% unpaid loss - 2nd Policy Year:
**$750 thousand**= $1 million x 75% unpaid loss

In each subsequent year of the program, an additional policy year is added to the portfolio. After three years, there are three policy years that require a total of $1.660 million of loss reserves, and so forth.

The stabilization of the loss reserves occurs nine years after the inception of the program due to the characteristics of our selected payment pattern. It is interesting to note the similarities between the rightmost two columns in Figure 3. After nine full years, the addition of reserves from a new policy year (the tenth policy year) is exactly offset by the collective run-off of the prior nine policy years.

This stabilization of the portfolio is what many risk managers and finance professionals expect of a “mature” portfolio. However, as we will see below, a more realistic scenario that includes inflation and exposure growth does not result in a similar plateau effect.

### Second Scenario: Company B

In our second scenario, we begin with the same initial assumptions as for Company A, except for inflation. Here, we assume that inflation will increase claims costs by 4% a year.

**Inflation**– 4% per year**Exposure growth**– same as Company A (0%)**Payment pattern**– same as Company A (medium payment pattern)

As you can see in Figure 4, this seemingly modest change in assumptions has a significant effect on the loss reserves for the portfolio. Whereas our inflation assumption for Company A was 0%, we assumed 4% per year inflation for Company B. Over the ten year period, Company A’s loss reserves are forecasted to grow to $2.520 million; however, Company B’s grew to $3.324 million.

In addition to Company B’s much larger loss reserve estimate, observe that there is a much less pronounced plateau effect. In fact, between the respective ends of years nine and ten, the reserves increased by – you guessed it: 4%. In this scenario, a mature portfolio will continue to grow at the rate of inflation.

In the next scenario, we will look at the effect of exposure growth on the loss reserve estimates.

### Third Scenario: Company C

In our third scenario, we begin with the same initial assumptions as for Company B, except for exposure growth. In this scenario, we assume that, in addition to inflation, exposure growth will increase claims costs by 4% a year. On a combined basis, inflation and exposure growth will result in an increase in the annual policy year loss pick of just over 8%^{2}

**Inflation**– same as Company B (4%)**Exposure growth**– 4% per year**Payment pattern**– same as Companies A and B (medium payment pattern)

In Figure 5, the combined influence of inflation and exposure growth on reserve balances is obvious. Over the ten year period, Company C’s loss reserves are forecasted to grow to $4.409 million compared to Company B’s at $3.324 million and Company A’s at $2.520 million.

In this model, inflation and exposure growth have identical effects on the behavior of the loss reserves. For example, a scenario with 4% inflation and 0% exposure growth would be identical to one with 0% inflation and 4% exposure growth. If we desired, we could further simplify our model by combining inflation and exposure growth into one category, “loss pick growth.”

In the next two scenarios, we return to the 0% inflation and 0% exposure growth assumptions and explore how the speed of the payment pattern affects loss reserves.

### Fourth Scenario: Company D

In our fourth scenario, we begin with the same initial assumptions as for Company A, except for our choice of payment pattern:

**Inflation**– 0% per year (same as Company A)**Exposure growth**– 0% per year (same as Company A)**Payment pattern**– the selected payment pattern for each policy year is such that 100% of claims are paid five years after the beginning of each policy year. This represents our “fast” payment pattern. The complete unpaid version of the pattern is illustrated in Figure 6.

The loss reserve estimates resulting from these assumptions are illustrated in Figure 7. The faster payment pattern results in a quicker “plateau” and a significantly decreased loss reserve forecasts compared to Company A.

As a rule, faster payment patterns imply less payments in future years, and therefore lower required reserves. In the last scenario, we will look at the effect of a slower payment pattern.

### Fifth Scenario: Company E

In our fifth scenario, we begin with the same initial assumptions as for Company A, again, except for our choice of payment pattern.

**Inflation**– 0% per year (same as Company A)**Exposure growth**– 0% per year (same as Company A)**Payment pattern**– the selected payment pattern for each policy year is such that 100% of claims are paid 20 years after the beginning of each policy year. This represents our “slow” payment pattern. The unpaid version of the pattern is illustrated in Figure 8 (with only the first ten years visible).

The loss reserve estimates resulting from these assumptions are illustrated in Figure 9. Here, a steady increase in the loss reserve balances can be observed. The plateau observed in earlier scenarios does not occur in the first ten years of the program (it would occur between years 19 and 20).

### Summary

The above scenarios help illustrate the long-term sensitivity of loss reserves to inflation, exposure growth, and payment patterns under non-random conditions. These results are provided for side-by-side comparison in Figure 10, below.

You can explore many other combinations of these variables using the Excel version of our **Reserve Balance Forecast Tool**. A screenshot of this tool appears below.

This free tool can be downloaded using the following link.

*Reserve Balance Forecast Tool – For Educational Purposes Only.xlsx*

Are you interested in a loss reserving forecast model tailored specifically to your organization’s self-insured program? Call or email us to discuss!

*Disclaimer: Information presented in this article should not be relied upon as actuarial or accounting advice, which should be provided by a credentialed actuary or accountant familiar with the details of your organization’s risk management program.*

#### Footnotes

1. *Unpaid loss* equals 100% minus the percent of loss paid-to-date.

2. The combined increase is 8.16% per year (= 1.04 x 1.04 – 1).