Many loss reserves estimates rely heavily on a few traditional actuarial methods. This article explores how four of the most common methods respond to changes in case reserves. This topic is of particular importance in situations involving changes to case reserve adequacy. This article will help the reader understand the potential implications such changes may have on their self-insured organization’s loss reserve estimates.
Case reserve levels for self-insured portfolios routinely fluctuate over time as payments are made, new claims are reported, and existing claims are reevaluated. When case reserves are established on a consistent basis, both in magnitude and timing, case reserve adequacy is likewise consistent. However, when changes are made that affect either the magnitude or timing of case reserves for otherwise identical claims, case reserve adequacy is also affected. Such changes often occur as the result of revisions to claim handling practices or changes in claims administrators. This article focuses on four of the most common loss reserving methods and their response to changes in case reserves, with an emphasis on changes in case reserve adequacy.
In this discussion, total loss reserves are defined as case reserves plus IBNR (Incurred but Not Reported), where case reserves are established by claims administrators and IBNR is estimated using various actuarial methods. More detailed information on reserve components can be found here.
Incurred Development Method
The incurred development method is one of the most commonly favored approaches for estimating loss reserves. This method produces estimates of total loss reserves based on three primary inputs: paid loss (cumulative basis), case reserves, and incurred loss development assumptions. In the following discussion, the development assumptions appear in the form of age-to-ultimate loss development factors (ATUs).
In this method, IBNR and total loss reserves are calculated using the following formulas:
IBNR = Paid x (ATUInc – 1) + Case Reserves x (ATUInc – 1)
Total Loss Reserves = Paid x (ATUInc – 1) + Case Reserves x (ATUInc – 1) + Case Reserves
Where ATUInc represents the age-to-ultimate development factor used to develop incurred losses (cumulative paid plus case reserves) to their ultimate value. Except for unusual situations, ATUs are always greater than or equal to one.
The formula for IBNR demonstrates that estimates of IBNR increase as case reserves increase. Specifically, IBNR increases by a factor of (ATUInc – 1) times the increase in case reserves. Consequently, estimates of total loss reserve increase by an amount larger than the increase in case reserves.
Intuitively, the positive linear relationship between IBNR and case reserves makes sense: in most instances, higher case reserves indicate the need for higher IBNR. This is because case reserves, on average, are inadequate to fund future payments. In this sense, case reserves represent a measure of exposure to potential development.
However, a contradiction arises when changes in case reserves are due to changes in case reserve adequacy. When this occurs, case reserves are no longer consistent measures of exposure to potential development. In fact, a change in case reserve adequacy implies that case reserves and IBNR should have an offsetting relationship. For example, if a change in case reserving practices results in a $1 million increase in case reserves for an otherwise unchanged claim portfolio, then IBNR should decrease by $1 million. In this example, there is no change to the underlying characteristics of the claims, only the case reserving practices. Rather than recognizing the reduced need for IBNR when case reserve adequacy is increased, the incurred loss development method indicates the need for more IBNR (equal to $1 million times (ATUInc – 1)).
To make matters worse, an increase in case reserves will result in higher indicated incurred ATUs. To the extent the higher historical development is considered in the incurred ATUs selected for the model, the discrepancy is exacerbated further.
It is clear that the incurred loss development method does not respond appropriately to changes in case reserve adequacy. Adjustment to the results or the use of other methods are important in such instances.
Paid Development Method
The paid development method produces estimates of total loss reserves based on just two inputs: paid loss (cumulative basis) and paid loss development assumptions. This method, unlike the incurred loss development method, responds to changes in case reserves with an equal and opposite change in indicated IBNR. Additionally, estimates of total loss reserves are independent of case reserves. These observations can be seen in the following formulas:
IBNR = Paid x (ATUPaid – 1) – Case Reserves
Total Loss Reserves = Paid x (ATUPaid – 1)
Where ATUPaid represents the age-to-ultimate development factor necessary to develop paid losses to their ultimate value.
The relationship between case reserves and IBNR in this method is appropriate for situations involving changes in case reserve adequacy. However, in general, this method tends to produce less stable and less accurate results than the incurred development method, thereby limiting its usefulness. The paid development method tends to underperform the incurred development method for the following two reasons:
- Utilization of Case Reserve Data – the paid development method does not use case reserves in estimates of total loss reserves. Case reserves are estimates of future payments made by claims administrators and are therefore highly correlated with total loss reserve needs. The incurred development method uses case reserves directly in estimates of total loss reserves as well as indirectly in loss development pattern assumptions.
- Speed of Development Pattern – paid losses develop more slowly than incurred losses. The “slower” payment pattern has numerically higher ATUs, especially for less mature claims portfolios. These higher ATUs can result in leveraged and unstable indications of total loss reserves that are very sensitive to payment activity.
For the above reasons, actuaries tend to favor the incurred loss development method to the paid development method when assigning weights between the two. In instances of changes in case reserve adequacy, it is rarely reasonable to simply ignore the incurred development method in favor of the paid development method.
Incurred Bornhuetter-Ferguson Method
There are two versions of the very popular Bornhuetter-Ferguson (B-F) method: the incurred B-F method and the paid B-F method. Each of these methods rely on the user to provide an a priori estimate of ultimate loss. Conceptually, this is the amount the user would have expected in the absence of actual loss experience. In the incurred B-F method, IBNR and total loss reserves are calculated using the following formulas:
IBNR = (1 – % Incurred to Date) x a priori Expected Ultimate Loss
Total Loss Reserves = (1 – % Incurred to Date) x a priori Expected Ultimate Loss + Case Reserves
The estimates produced by the incurred B-F method incorporate the actual claims experience and the appropriate portion of the a priori expected ultimate loss, where the “appropriate portion” is determined by the incurred loss development assumptions.
The incurred B-F method tends to be highly favored by actuaries, particularly for less mature claims portfolios. However, the a priori expected ultimate loss is a critical and influential assumption in the method. To the extent that this assumption is based on results of the development methods, the aforementioned weaknesses are introduced into the B-F estimates. In one sense, the incurred B-F method simply transfers the onus of an accurate estimate of IBNR to the a priori expected ultimate loss assumption.
The incurred B-F method responds to changes in case reserves on a dollar-for-dollar basis in estimates of total loss reserves. As discussed earlier, this is not an appropriate response in situations involving changes in case reserve adequacy.
Paid Bornhuetter-Ferguson Method
The paid B-F method is similar to the Incurred B-F version, except that paid losses are used in place of incurred losses. IBNR and total loss reserves are calculated using the following formulas:
IBNR = (1 – % Paid to Date) x a priori Expected Ultimate Loss – Case Reserves
Total Loss Reserves = (1 – % Paid to Date) x a priori Expected Ultimate Loss
The paid B-F method shares the following characteristics with the paid development method:
- changes in case reserves are exactly offset in estimates of IBNR, and
- estimates of total loss reserves are independent of case reserves.
Again, these are desirable characteristics in situations involving changes in case reserve adequacy.
The usefulness of the paid B-F method is highly dependent on the accuracy of the a priori expected ultimate loss estimate, particularly for less mature portfolios. This dependency is more significant than that described for the incurred B-F method due to differences between paid and incurred development patterns. This method also shares the disadvantages of the paid development method described above.
Summary
In situations involving changes in case reserve adequacy, it is important to give close attention to the methods used to estimate loss reserves. Absent any adjustments, the incurred development method and the incurred B-F method will respond to case reserve strengthening by overstating total loss reserve needs. The paid development method and the paid B-F method are not directly affected by changes in case reserves, but tend to produce less reliable and less stable estimates.
The table below summarizes how each of the four methods described above respond to a $1 increase in case reserves.
There are actuarial methods specifically designed to contemplate changes in case reserve adequacy; however, these methods are more complicated and less commonly utilized. It is important to advise actuaries and auditors of any changes in claim handling practices that may affect loss reserves so that they may incorporate alternative methods or make the appropriate adjustments to more common methods. It is particularly important to advise auditors of changes in practices before they occur.
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.