Introduction

The Actuarial Standards Board provided a revised Actuarial Standard of Practice No. 4 (ASOP 4) entitled “measuring pension obligations and determining pension plan costs or contributions”, effective for pension funding valuations with measurement dates on or after February 15, 2023. As indicated on its website, the Actuarial Standards Board (ASB) “sets standards for appropriate actuarial practice in the United States through the development and promulgation of Actuarial Standards of Practice (ASOPs). These ASOPs describe the procedures an actuary should follow when performing actuarial services and identify what the actuary should disclose when communicating the results of those services.”

This is the fourth article in a series regarding public pension funding policies. As with the previous articles, this article explores various methods of amortizing liabilities. Section 3.14 of ASOP 4 addresses the amortization method used. According to the ASOP, for purposes of that section, “the actuary should assume that all assumptions will be realized.”

The series of articles we have written has dealt with deviations from expectations and how the different amortization methods react to volatility in investment markets. Although not required by the revised ASOP 4, the conclusions drawn regarding the effectiveness of the various amortization methods are very different when you assume that all assumptions will be realized compared to the conclusions from an analysis based on the possibility of deviations from expectations. It is important to understand how methods will react when actual results differ from expected. However, it is important to understand the disclosure requirements required by ASOP 4 regarding amortization methods.

Refresher on amortization methods

Typically, actuarially calculated contribution rates are comprised of two pieces. The first is the service cost, the cost of benefits earned during the year, and the second is an amortization of the difference between the current funded status of the plan and the target funded status. The target funded status is usually 100%, the point where the actuarial value of assets is equal to the total pension liability.

Plan sponsors use a variety of methods to determine the amortization amount for the net pension liability. Our articles have examined the following methods, with amortization periods varying from 10 years to 30 years.

• Layered method, where an additional layer of amortization is calculated each year based on the experience or assumption changes made that year. In our analysis, the first layer is set to the current unfunded liability, also known as the net pension liability, or the difference between the actuarial value of assets and the total pension liability.
• Rolling method, where the amortization is reset annually based upon the entire net pension liability. The amortization period remains constant, resulting in a consistent percentage of the net pension liability paid each year.
• Aggregate cost method, which considers the entire actuarial present value of benefits. The difference between the actuarial present value of benefits and the actuarial value of assets is divided by the actuarial present value of future salaries for members as of the valuation date to calculate the contribution rate. This contribution rate is then applied to current salaries. The employer contribution portion takes into account the portion paid by the present value of future employee contributions.

ASOP 4 Section 3.14 amortization method

Here is the relevant passage from the revised ASOP 4:

“When selecting an amortization method, the actuary should select an amortization method that is expected to produce total amortization payments that are expected to fully amortize the unfunded actuarial accrued liability within a reasonable time period or reduce the unfunded actuarial accrued liability by a reasonable amount within a sufficiently short period.”

“The actuary should assess whether the unfunded actuarial accrued liability is expected to be fully amortized.”

“For purposes of this section, the actuary should assume that all assumptions will be realized and actuarially determined contributions will be made when due.”

The unfunded actuarial accrued liability (UAAL) is the difference between the actuarial accrued liability (AAL), or total pension liability using the terminology of Governmental Accounting Standards Board (GASB) Statements No. 67 and 68, and the actuarial value of assets.

There are two criteria in the first paragraph above. Plans must meet at least one of these criteria.

1. An amortization method that is expected to produce total amortization payments that are expected to fully amortize the UAAL within a reasonable time period, or
2. An amortization method that reduces the UAAL by a reasonable amount within a sufficiently short period.

When a layered amortization is used, if all assumptions are precisely met, the UAAL will be fully amortized after the time period equal to the length of the longest layer. If this is considered a reasonable time period, the first criterion will be met.

When a rolling amortization method is used with a target of 100% funding, the UAAL approaches zero but is never fully paid if assumptions are precisely met. This means that the current assets, plus contributions toward the UAAL, will not be sufficient to pay all future benefits for current employees if all assumptions are realized. It is clear that, if all assumptions are realized, rolling amortization methods are not expected to “fully amortize the UAAL within a reasonable time period.” Because a rolling amortization period does not meet that criterion, the method selected should be one that reduces the UAAL by a “reasonable amount within a sufficiently short period.”

The second criterion, reducing the UAAL by a reasonable amount within a sufficiently short period, is more subjective, but it should be clear that “negative amortization” does not meet it. Negative amortization occurs when the dollar amount of the UAAL is expected to grow even when assumptions are met, meaning that the payment towards the UAAL is less than interest growth in the UAAL. Thus, the UAAL is not reduced at all, and there is no need to determine whether it meets the threshold of a reasonable amount of reduction. Note that for the assumption set used in our analysis (7% investment rate of return, 3% payroll growth), a negative amortization will only be avoided if the amortization period is 21 years or less.

If all assumptions are met for the open group plan we studied, then a rolling amortization will result in a funded ratio approaching but never actually achieving 100%. While the dollar UAAL amount can grow for longer rolling amortization periods, both the AAL and the assets are growing and the deficit is shrinking as a percentage of the AAL. The funded ratio would only decline if actual experience were worse than assumed. Of course, if actual experience is worse than assumed, then any amortization method could result in worse funding than it would with experience that met expectations. Our analysis explores what happens when experience is not met.

Under the aggregate cost method, the contribution amounts are similar to the contribution amounts for the 10-year rolling amortization method, as unfunded plan liabilities are amortized over the working lifetime of the active members. Therefore, it meets the second criterion of reducing the UAAL by a reasonable amount within a sufficiently short period. Please note that by definition there is no UAAL per se under the aggregate cost method. For this reason, it is typical that a funded percentage under the entry age cost method is calculated for plans that use the aggregate cost method.

Our methodology

As with the second and third articles in this series, we focus on the volatility inherent in investment markets. We developed 1,000 “random walk” scenarios for the plan’s actual asset returns via stochastic projections using a random number generator.

Stochastic projections over the 40-year period were generated using a normal distribution, a 7.00% geometric average annual return, and a standard deviation of 12.00%. The equivalent average arithmetic return is 7.72%.

In our projections, other than the actual investment returns, we use the simplifying case that all assumptions are met and that there are no other actuarial experience gains or losses.

As you can see in the table in Figure 1, rolling periods of a certain length have results similar to layered methods that are five years longer, whether you are judging by either the likelihood of obtaining 100% funded status at some point in the projection horizon or by the median number of years until reaching a 100% funded status. For example, the median number of years until 100% funded status is first achieved is 16 years under both rolling-15 and layered-20 methods.

Rolling amortization periods of 20 or 30 years produce the greatest number of median years to first achieve 100% funded status and contain the lowest probability that 100% funding will be attained during the 40-year period.

Conclusions

Under the newly revised Actuarial Standard of Practice No. 4, amortization methods that feature “negative amortization” (amortization methods where the dollar amount of the unfunded actuarial accrued liability is expected to grow when assumptions are met) clearly do not meet the standard’s requirements. The ASOP 4 conclusion that methods with negative amortization are to be avoided is consistent with our findings that rolling amortization methods with long amortization periods are not 100% funded even in the median case after 40 years and often never achieve a 100% funded status over a 40-year horizon.

ASOP 4 states that “the actuary should assume that all assumptions will be realized.” This means that “rolling” methods never fully amortize the unfunded actuarial accrued liability and would not meet the first criterion above. However, it can meet the second criterion based on our analysis in reviewing results that deviate from expectations.

Rolling amortization methods with short amortization periods can actually be more reactive to experience and more likely to achieve goals, such as a 100% funded status, than layered amortization methods with long amortization periods. Rolling amortization methods with short amortization periods also result in contribution levels that are more consistently related to the current funded status of the plan, as discussed in the second article in this series.

In the words of ASOP 4, an amortization method should “reduce the unfunded actuarial accrued liability by a reasonable amount within a sufficiently short period.” When viewed through the framework of simulated returns allowed to deviate from expectations, methods with short rolling amortization periods achieve this better than methods with long, layered amortization periods.