News & Policy

I. General Description

The Pension Benefit Guaranty Corporation offers this note to explain how it selects the interest factors used to value its liabilities.

PBGC uses recent prices of group annuities to derive the interest factors that we use to calculate the present value of future benefit-payment obligations. These future benefits are obligations that we must pay to participants in the plans that we have taken over as trustee. This note provides a description of, and rationale for, the procedure that we use to derive these interest factors.

In valuing our future benefit-payment obligations, PBGC determines values that reflect current conditions in the annuity markets. To do this, we use a specific mortality table[i] and then derive a set of interest factors from the most recent available annuity prices. We determine the interest-factor set that, when combined with the specified mortality table, produces present values that most closely approximate the prices private insurers would charge to annuitize the same benefit-payment obligations.

PBGC's procedure for calculating interest-factor sets that are used for our financial statements is described below. We use a similar process to derive the interest-factor sets used to value immediate and deferred annuities for purposes of determining benefits under section 4044 of ERISA and determining PBGC's claim against employers for unfunded benefit liabilities. This note, however, focuses on the procedure that we use for our financial statements.

II. ACLI Annuity Price Survey

PBGC obtains information about the prices charged by private insurers from quarterly surveys conducted for PBGC by the American Council of Life Insurers (ACLI). The ACLI surveys gather annuity-pricing information as of March 31, June 30, September 30, and December 31 of each year. The surveys collect information on private-sector annuity prices for immediate and deferred annuities at a range of ages. These prices are net of administrative expenses. That is, the prices exclude costs for record-keeping, communication with annuitants, related corporate overhead, etc., but include profit and taxes. The annuity-price data that the survey collects are the prices that the insurers would charge, as of the quarterly survey date, for a $10/month annuity, payable in straight-life form, beginning at the ages specified.

Preserving Survey Respondents' Confidentiality

ACLI forwards the survey responses it receives[ii] to PBGC in sealed envelopes without information that identifies the respondent. The sealed envelopes contain the respondents' price quotes, to which ACLI does not have access. ACLI does not inform us how many or which annuity providers received the survey, or which companies responded. Participation in the survey is voluntary, and the number of responses ACLI receives can vary from quarter to quarter.

The survey results show annuity prices grouped by company - that is, the prices for the immediate and deferred annuities for all ages are listed separately for each company. The companies are not explicitly identified, but are named Company A, Company B, and so on. The letter codes are randomly generated by ACLI each quarter, so a given company will have different letter codes applied to it in different quarterly surveys.

III. Selecting the Interest Factor Set-General Procedure

PBGC uses a "select and ultimate" interest-factor structure, where the select factor applies for either the first 20 or 25 years after the valuation date (the "select period"), and the ultimate factor applies for all remaining years (the "ultimate period"), which is to age 120 in the current mortality table. The two interest factors and the select period constitute an interest-factor set. We currently use a version of the RP-2000 mortality table when selecting the interest-factor set because this table best reflects mortality experience in PBGC-trusteed plans. The interest-factor set is sensitive to the mortality table used. In general, if a different mortality table were used, a different interest-factor set would be obtained.

PBGC currently uses 14 annuity-price data price points for males[iii] when calculating its interest-factor sets. These prices are for: (1) immediate annuities beginning at ages 50, 55, 60, 65, 70, 75, and 80; and (2) deferred annuities that will begin at age 65 for individuals currently at ages 30, 35, 40, 45, 50, 55, and 60. , We use two consecutive ACLI surveys to derive an interest-factor set (see section IV).

Once we derive the interest-factor set, the factors for PBGC's financial statements are effective as of the last day of the quarter following the most recent ACLI survey and remain in effect until the next quarterly recalibration. Thus, for example, the interest-factor set effective from September 30 through December 30 of any given year is based on the annuity-price surveys for June 30 and March 31of the same year.

Eliminating the Effect of Outlier Responses

In examining the ACLI survey responses, PBGC first tests for companies whose responses could be considered “outliers.” We do not use the prices of “outlier” companies because we want to avoid skewing our interest-factor set when the survey prices quoted by one company are unreasonably high or low, relative to the survey prices of other responding companies. (In our experience, an outlier response is rare, occurring once every three to four years.) We use three outlier tests for a company’s survey responses, and all three tests must be met for us to consider a company an outlier. The tests are:

1. The price quotes from a particular company must be the highest (lowest) for at least all but two of the annuity-price data points used. Thus, to be considered an outlier, the company’s price quotes must be the highest (lowest) for at least 12 of the 14 male annuity-price data points.
2. For a male immediate annuity at age 65, the company’s annuity price must be at least 12.5% higher (lower) than the median of all age-65 immediate-annuity prices.
3. For a male immediate annuity at age 65, the difference between the company’s annuity price and the annuity price of the company with the second highest (lowest) price must be greater than the difference in annuity prices of the companies with the second and fourth highest (lowest) annuity prices.

Calculating the Interest-Factor Set

After eliminating the price quotes from any outlier companies, PBGC averages the price quotes of the remaining companies for each of the 14 male annuity-price data points.

We then select the interest-factor set using a two-step process:

1. The first step relies on the most recent ACLI price survey. PBGC selects the interest-factor set that results in calculated annuity values (the present value of future benefits) that best match the 14 averaged annuity-price quotes from the companies responding to that survey. To determine which interest-factor set gives this best match, we calculate an annuity value for each of the 14 annuities using our specified mortality table and thousands of interest-factor sets.
2. The second step relies on the survey previous to the most recent. The same calculations are used for this second step as in the first step, but with constraints on the select period and the ultimate interest factor. These constraints are described in Section IV.

In both the first and second steps, we first use a select period of 20 years and a low ultimate interest factor, and test for the best select-interest factor by increasing a low initial select-factor value by one basis point (one one-hundredth of one percent) for each new run until the select-interest factor reaches an upper limit. (Using lower and upper limits, set by PBGC based on our experience, avoids the need for thousands more unnecessary runs that would not change the results.)

Example – Assume the first test begins with a select-interest factor of 3.0% for the first 20 years and an ultimate-interest factor of 3.0% (3.00, 20, 3.00).

• Additional iterations are performed using the same ultimate interest factor and select period ((3.01, 20, 3.00), (3.02, 20, 3.00), . . .).
• Then the ultimate interest factor is increased by one basis point, and the process is repeated for all possible select-interest factors.
• This process repeats until the PBGC-chosen upper bound on the ultimate factor is reached – say, 7%.
• Finally, the entire process repeats, using a 25-year select period. (Note that tested interest-factor sets include those where the ultimate factor is greater than the select factor.)
• From all these iterations using different select and ultimate interest factors and two select periods, the interest-factor set is determined by the process discussed next.

For each interest-factor set, we calculate the annuity value of the 14 immediate and deferred male annuities at the ages mentioned in Section II. We also calculate the error – that is, the percentage difference between the calculated value and the average of the surveyed annuity prices. To determine the best fit between the calculated values and average of the survey prices, we use the interest-factor set that gives the smallest "key mean error sum." The "key mean error sum" is the sum of the "absolute value of the mean error" ("|ME|") and the "mean absolute error" ("MAE").
For PBGC’s procedure, the key mean error sum equals:

• the absolute value of one-fourteenth of the sum of the 14 individual errors, plus
• one-fourteenth of the sum of the absolute values of the 14 individual errors.

Why Use the Key Mean Error Sum?

It is not appropriate to use the interest-factor set that has only the smallest absolute value of the mean error because the mean error ignores the possibility of having large errors with different signs that "cancel each other out." If the interest-factor set results in a large error for one of the data points, then PBGC will overestimate (or underestimate if the error is negative) the present value of future benefits for plans that have many participants clustered around that age. Thus, it is important that the interest-factor set give the best fit over all 14 data points.

The absolute value of the mean error shows which interest-factor set gives the best result, on average, while the mean absolute error penalizes those interest-factor sets where there are large errors at certain ages. By selecting the interest-factor set with the smallest sum of these two error measures — that is, the smallest key mean error sum — we ensure that we select the set that will provide the most accurate estimated annuity values regardless of the age distribution of participants in the plans that we trustee.

Example (3 iterations) - This simplified example illustrates our procedure for determining the key mean error sum.

Assume there are only five annuity-price data points (immediate annuities beginning at ages represented by 1, 2, 3, 4, and 5). PBGC's procedure calculates and compares the key mean error sums of thousands of interest-factor sets. In this example, we limit the number of iterations to three. Three separate interest-factor sets are used to generate the respective illustrated iterations. Using these interest-factor sets and the specified mortality table, we calculate annuity values for each of the five data points and compare those calculated results with the averaged annuity prices quoted by companies responding to the ACLI survey. The steps used to calculate the key mean error sum are shown below for each iteration.

Iteration 1

Age	Average Survey Price	Calculated Annuity Value	Percentage Difference (Error)
1	1000	1140	14.0%
2	1150	1245	8.3%
3	1329	1315	-1.1%
4	1511	1402	-7.2%
5	1700	1449	-14.8%

 

Total Error E -0.8% Total Abs Error TAE 45.4%

Mean Error ME -0.16% Mean Abs Error MAE 9.08%

Abs Value of ME 'ME' 0.16%

 

Key Mean Error Sum 'ME' + MAE = 0.16% + 9.08% = 9.24%

 

Iteration 2

Age	Average Survey Price	Calculated Annuity Value	Percentage Difference (Error)
1	1000	1030	3.0%
2	1150	1163	1.1%
3	1329	1331	0.2%
4	1511	1471	-2.6%
5	1700	1636	-3.8%

 

Total Error E -2.1% Total Abs Error TAE 10.7%

Mean Error ME -0.42% Mean Abs Error MAE 2.14%

Abs Value of ME 'ME' 0.42%

 

Key Mean Error Sum 'ME' + MAE = 0.42% + 2.14% = 2.56%

 

Iteration 3

Age	Average Survey Price	Calculated Annuity Value	Percentage Difference (Error)
1	1000	1090	9.0%
2	1150	1205	4.8%
3	1329	1341	0.9%
4	1511	1479	-2.1%
5	1700	1597	-6.1%

 

Total Error E 6.5% Total Abs Error TAE 22.9%

Mean Error ME 1.3% Mean Abs Error MAE 4.58%

Abs Value of ME 'ME' 1.3%

 

Key Mean Error Sum 'ME' + MAE = 1.3% + 4.58% = 5.88%

Discussion of the example

1. In the first iteration, the absolute value of the mean error is small at only 0.16%, but the individual errors (average survey prices vs. calculated annuity values at each age) are large, so the key mean error sum is large.
2. The second iteration shows a slightly larger absolute mean error, at 0.42%, but none of the individual errors is large, so the key mean error sum is small.
3. The third iteration, with the largest absolute mean error of 1.3%, also has small individual errors.

IV. Selecting the Interest-Factor Set — Combing the two most-recent surveys

The procedure described above describes how the interest-factor set is determined from the most recent quarterly ACLI survey. PBGC uses the two most recent quarterly surveys, in combination, to determine each quarter’s interest-factor set. In the discussion and example below, assume that we are calculating the interest-factor set that will be in effect from September 30 through December 30 of the current year.

There are three steps in determining this interest-factor set. These steps are:

1. determine the interest-factor set based on the June 30 ACLI survey (as described in the previous section);
2. determine the interest-factor set based on the March 31 ACLI survey, with the constraints that:
   1. the select period for the March-based set match the select period for the June-based set, and
   2. the ultimate interest factor for the March-based set be within 25 basis points of the ultimate interest factor determined for the June-based interest-factor set; and
3. average the two select interest factors and, separately, the two ultimate interest factors determined for June 30 and March 31

Note the constraints — that the select period for the March result matches that for the June result, and that the March ultimate factor is within 25 basis points of the June ultimate factor. These constraints model the assumption that the two ACLI surveys, only three months apart, will reflect similar views of the extremely long-term (beyond 20 or 25 years) interest environment.
It is unlikely that the March interest-factor set determined by this procedure would be the best fit of the March survey data were the constraints not imposed. This is especially true since we started testing for the interest-factor set fit using single basis-point increments. However, the key mean error sum for the constrained March 31 best fit has always been close to the key mean error sum for the un-constrained best fit.

Example - demonstrates the 3-step process:

1. Assume that the interest-factor set for the June 30 ACLI survey is:
   Select int. factor: 6.08% Select period: 25 years Ultimate int. factor: 5.91%
2. The constrained March 31 interest-factor set will be the best fit of the March 31 ACLI survey data, such that the select period is 25 years and the ultimate interest factor lies between 5.66% and 6.16%. Assume that such constrained March 31 interest-factor set is:
   Select-int. factor: 6.56% Select period: 25 years Ultimate-int. factor: 6.11%
3. The two select factors and two ultimate factors are now averaged.
   1. Averaged select interest factor is 6.32% ( [ 6.08% + 6.56% ] / 2) and
   2. Averaged ultimate interest factor is 6.01% ( [5.91% + 6.11% ] / 2).

V. Conclusions and Questions

Comments and questions can be directed to: Marc Ness in the Policy, Research and Analysis Department at 202-326-4000, ext 3227.