PBGC’s Valuation Methodology

Derivation of ERISA 4044 Yield Curve 

August 18, 2023 

This White Paper describes the methodology PBGC intends to use

to determine the ERISA 4044 Yield Curve assuming the proposed

rule, issued on August 18, 2023 is finalized without any changes.

Once the rule is finalized, PBGC will modify this draft, as needed. It

is being posted now to help practitioners and other interested

parties better understand how the process will work.
                             

                         

   

                                   

                         

                                    

                                 

                        

                           

                       

                                

                              

                         

                               

       

                                   

                              

                                   

                                    

                                   

                                       

                       

                           

               

       

                       

                             

                                  

                                     

                                

                                 

                                      

                             

                             

                                 

                                   

                            

                                     

                                

                         

PBGC’s benefits valuation regulation (subpart B to 29 CFR part 4044) requires the use of the 4044 yield

curve to discount expected future benefit payments when determining benefit liabilities upon plan

termination. The purpose of this paper is to describe the principles and methods that would be used to

create the 4044 yield curve beyond what was included in the preamble to PBGC’s rule on Valuation

Assumptions and Methods published in the Federal Register on August 18, 2023.

Introduction

PBGC has historically applied a consistent basis both for valuing the benefit liabilities in PBGC‐trusteed

plans and, through its benefits valuation regulation, for valuing benefit liabilities in non‐trusteed

terminating pension plans. This basis values a plan’s benefit liabilities based on the approximate cost of

purchasing group annuities from an insurance company in the private sector. PBGC currently uses a

quarterly survey1 of insurance companies’ annuity prices, administered for PBGC by the American

Council of Life Insurers (ACLI), to determine the discount rates used to value PBGC’s and terminating

pension plans’ benefit liabilities.

Once the value of a pension plan’s benefit liabilities is determined, PBGC can determine the amount of a

terminating plan’s unfunded benefit liabilities (“UBL”). This is done by subtracting the value of the

plan’s assets from the value of its benefit liabilities. Under ERISA, PBGC has a claim against the plan

sponsor and any members of its controlled group for the plan’s UBL as of the plan’s termination date.

The benefits valuation regulation is used to determine the amount of the plan’s UBL for this claim. PBGC

uses the same approach to determine the amount of the UBL for pension plans that are likely to, or have

terminated, so that PBGC can accrue these liabilities on its financial statements.

PBGC’s approach is intended to be consistent with actuarial practices of group annuity providers

(insurers) for determining benefit liabilities in settlement situations.

Group Annuity Price Principle

The fundamental principle underlying the way benefit liabilities are determined per PBGC’s benefits

valuation regulation (subpart B to 29 CFR part 4044) isthat such benefit liabilities should approximate

the fair market price of group annuities sold by private sector insurance companies. This means that the

discount rate should reflect the value of expected future benefit cash flows as well as the risk that actual

future payments differ from the expected amounts. The market cost of settling a benefit liability for

these payments is adjusted upwards by insurers to account for the risk borne by the insurer, expenses,

and a profit for taking on this risk. This profit is compensation demanded in the settlement of any risky,

irrevocable financial obligation and is therefore a reasonable part of the cost of settling pension

obligations.

PBGC’s benefit liability valuation approach also minimizes the “moral hazard” inherent in the Title IV

termination insurance program by ensuring that it is not less costly for an employer to terminate a

pension plan in a distress termination with PBGC than to terminate the plan in a standard termination in

the private sector. Marking benefit liabilities in PBGC‐trusteed plans to the annuity market matches

those benefit liabilities to the price that a plan sponsor would have to pay to settle their pension plan

obligations in the annuity market. This avoids the moral hazard mentioned above as well as overpricing

benefit liabilities when PBGC becomes trustee of a plan sponsor’s terminated pension plan.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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Structure of Rates

Insurance companies develop interest rates for pricing group annuities starting with the expected yield

in each future year on the investments they expect to make with the premium proceeds for a contract.

The expected investment yields are adjusted for potential defaults and are then adjusted downwards,

which increases the price to reflect risk, expenses, and profit. The structure of the 4044 yield curve and

the process used to develop it are intended to estimate these net yields that are used to price group

annuity contracts.

The 4044 yield curve is made up of a “blended market yield curve” plus spreads developed to adjust the

market‐based curve to represent yields used by insurance companies to price group annuity contracts.

The spreads are developed using quarterly surveys of group annuity insurers. The market‐based curve as

of any measurement date is adjusted by the average spreads determined from earlier annuity price

surveys.

The blended market yield curve reflects interest rates as of the date of liability measurement, which is

important because assets invested to fund the liability are impacted by the same interest rates. The

yield spreads in the 4044 yield curve reflect the average or typical difference between market interest

rates and group annuity pricing yields during the prior year. Determining the 4044 spreads as of the

measurement date is impractical, but also less important than using the market interest rates on the

measurement date. The spreads do not affect asset values and do not vary over time as much as

interest rates do.

Blended Market Yield Curve

The 4044 yield curve is an adjusted version of the blended market yield curve. The blended market yield

curve is a combination of two‐thirds of the corporate bond spot yield curve and one‐third of the

Treasury spot yield curve. It has rates determined out to 30 years and fixed rates after 30 years. Unlike

the curves from which it is determined, 4044 rates are assumed to be constant after 30 years because

this was determined to be more consistent with group annuity pricing yields. With a normal upward

sloping yield curve, this means that these rates are lower and represent higher risk for payments made

more than 30 years in the future.1

1 The underlying yield curves have slightly different shapes up to 30 years if yields are held constant after 30 years

rather than increasing.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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Both the corporate bond and Treasury yield curves are created by the Treasury Department as of the

last day of each month and are generally available at Treasury.gov within one to two weeks after the

end of the month. The HQM curve is based on the same bond data used to develop the monthly

corporate bond yield curve provided under § 1.430(h)(2)‐1(d) for funding and other purposes, but is

based on the spot rates as of the end of month whereas the monthly § 1.430(h)(2)‐1(d) curve

represents the average of each day in the month. The TNC curve as of the end of month is used for the

Treasury rates.2

The Treasury portion of the blended market yield curve is not meant to represent insurer investment

practices. The specific 1/3 Treasury – 2/3 corporate bond rate mix creates a curve that has the highest

correlation with changes in group annuity pricing yields, based on data from 2011‐ 2020. The yield

curve of spreads is not typically flat, indicating that the shape of the typical insurance pricing curve is

different than the shape of the blended market yield curve.

The blended market yield curve more heavily weights the yields on investment grade corporate bonds

because corporate bond yields are the most important driver of group annuity prices3

. However, based

on discussions with insurers and PBGC’s own analysis, PBGC understands that insurers likely adjust the

level of the corporate spread they expect to earn based on economic conditions. In times of economic

distress, when the difference between corporate bond yields and Treasury bond yields (the corporate

bond spread) widens considerably, group annuity prices do not typically reflect the full extent of this

spread widening. This is because insurance companies may avoid investing in the highest yielding

(riskiest) bonds in any credit rating category and they may increase their assumption about how yields

will be offset by future downgrades and defaults. In these environments, the inclusion of Treasury bond

yields in the blended market yield curve will dampen the impact of this difference and allow PBGC to

estimate private‐sector group annuity pricing more accurately.

Group Annuity Market Survey

To obtain the cost of single premium group annuity contracts that would pay benefits for a terminated

plan, PBGC conducts a “double‐blind” survey of current premium rates (prices) charged by insurance

companies for single premium group annuities. Insurance companies consider such pricing information

to be confidential and will not publicly disclose it. Therefore, PBGC relies on a trade association, the

ACLI, to obtain this price information for PBGC. On a quarterly basis, ACLI sends group annuity surveys

to various insurance companies participating in the group annuity market. These insurers complete the

surveys with information as of the end of each calendar quarter and return them to ACLI. ACLI then

forwards the unopened/anonymized company‐coded responses to PBGC. Each company’s response is

2 PBGC generally uses a similar process described in this paper for determining interest rates used to value PBGC’s

financial statement liability. However, yield curves available daily from ICE Data Services LLC are used for the

blended market yield curve in the financial statement process in order to produce financial statements on time.

The HQM and TNC curves are used for 4044 purposes because they are publicly accessible at no cost. The use of

different yield curve information does not result in meaningful differences in liability measurement because both

blended market yield curves are adjusted to represent group annuity prices.

3

See NAIC Special Markets Report as of the end of 2021 for breakdown of life insurance company investment

allocation.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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identified only by a company‐code letter, which changes quarterly, so PBGC does not know the identity

of the companies who respond to the survey.

Insurers price group annuities by analyzing participant demographics and making assumptions about

variables such as yield on investments, mortality rates and retirement age. PBGC requests that the

premium rate (price) information on the surveys exclude the insurers’ administrative expenses because

PBGC has its own expense assumption. The premium rates provided on the surveys 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 requested ages. More detail on the survey contents in discussed in the

“Composite Premium” section below.

Because the ACLI survey is double‐blind (PBGC does not know the identity of the survey respondents,

and ACLI does not see the prices contained in the responses), PBGC cannot independently verify the

accuracy of the information it obtains. However certain tests are used to eliminate “outliers” which may

skew the results as described below. PBGC also checks the outcome of its process against both publicly

available and fee‐based surveys that collect group annuity pricing yields, as described below in Review

of Yield Curve Rates.

Determination of Spreads

The 4044 yield curve is derived from the group annuity survey information. Because PBGC does not

have access to the component assumptions the insurance companies use in pricing, PBGC uses an

iterative process to determine the yield curve that best fits the survey information based on a mortality

assumption assumed to be used by the insurance companies in the sample prices.4 Once this yield curve

is determined, the spreads between this group annuity pricing yield curve and the blended market yield

curve on the survey date are calculated for each year on the curve. Spreads are updated each quarter

and averaged over four quarterly surveys to smooth out random variation and any impact of seasonality

in pricing. The average spreads are used to adjust the blended market yield curves as of future valuation

dates in the applicable quarter.

4 Currently the Pri‐2012 Total Dataset with separate employee and nondisabled‐annuitant rates together with the

latest mortality improvement scale as issued by the Society of Actuaries. PBGC understands this to be

representative of the mortality assumption used in the premium information provided by insurers in response to

the quarterly survey.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

Page 4
                             

                         

   

                                 

                                      

   

       

     

   

   

     

   

   

     

   

   

     

   

   

                                

                                 

                                  

                           

                                

                                 

                                 

                                 

     

         

                       

                                

                        

                            

                                 

                       

   

                                

                                   

The chart below shows which surveys are averaged to develop the spreads and which spreads are used

to determine which 4044 yield curves. See the appendix for a full example of how the 4044 yield curve

is determined.

Valuation

Date

Blended

Market

Yield Curve

Applicable

Spreads

Surveys Averaged to Develop Spreads

01/31/2023 01/31/2023 Q1 2023 09/30/2022 06/30/2022 03/31/2022 12/31/2021

02/28/2023 02/28/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

03/31/2023 03/31/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

04/30/2023 04/30/2023 Q2 2023 12/31/2022 09/30/2022 06/30/2022 03/31/2022

05/31/2023 05/31/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

06/30/2023 06/30/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

07/31/2023 07/31/2023 Q3 2023 03/31/2023 12/31/2022 09/30/2022 06/30/2022

08/31/2023 08/31/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

09/30/2023 09/30/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

10/31/2023 10/31/2023 Q4 2023 06/30/2023 03/31/2023 12/31/2022 09/30/2022

11/30/2023 11/30/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

12/31/2023 12/31/2023 ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐ same as above ‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐

Changes in spreads from quarter to quarter are likely impacted most by supply and demand factors. It

isn’t practical to receive and process surveys quickly enough to use the pricing discount rates from a

survey for liability measurement on the date of the survey. That means that unusual conditions in the

group annuity market on any particular measurement date won’t be represented in benefit liability

measurements as of that date. PBGC averages spreads over four quarters to minimize the impact of

unusual conditions in the group annuity market on one date on the liability measurement as of another

date. In addition, because there may be some seasonality to the supply and demand factors, using

spreads from four quarterly surveys ensures that all parts of the year are represented in the average

spread every quarter.

Processing and Analyzing Survey Information

PBGC’s principle of aligning benefit liability measurements with group annuity premiums requires

matching prices in actual transactions that take place in the market to the greatest extent possible.

Using actual transactions to calibrate PBGC’s assumptions would present significant practical challenges.

Finding the transactions to observe would be difficult given industry practices. Also, even if transactions

could be found to observe, it would be extremely difficult to translate the transaction data into useable

information ‐‐ for example, because the mortality assumption may be customized for each transaction.

Competitive Bidding

There are two effects from competition that are desirable to capture. First, typically, insurers enter the

bidding for a case with an initial bid (single sum dollar amount) using so called “sheet rates” or

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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“off‐the‐shelf” pricing. Later, in the final bid, insurers may reduce their bid by anywhere from a few

percentage points to high single digit percentage points. The other effect is that the lowest bid usually

wins a case.

The group annuity survey respondents typically provide “off‐the‐shelf” premium rates. To represent the

competition that determines actual transaction prices, PBGC uses an average of the lower end of prices

from each set of surveys (as explained below). Other organizations that do similar surveys that ask

directly for interest rate information also use some portion of the lowest prices (or highest interest

rates) received for this reason. For example, the Canadian Institute of Actuaries uses the highest three

premium interest rates out of seven responses received to their quarterly survey. Consulting firms in

the U.S. distinguish between average survey rates and competitive survey rates. One firm uses the

average of the interest rates from the highest third out of a typical set of nine responses received.5

PBGC uses the lowest cost half of prices provided in the survey responses, based on the composite

premiums and size units described below. However, representing the competitive process with fewer

surveys is balanced against using enough surveys to represent a meaningful portion of the market. In

addition, an approach that does not use only the lowest survey response recognizes that not every

insurer bids on every case, that some cases will be settled with higher prices due to the complexity of

the plan provisions and that the lowest bidder does not always win the business.

Composite Premiums

Survey respondents are asked to provide 28 sample premium rates through the survey, 14 male and 14

female.6 The sample premium rates provided by each insurer are weighted based on the demographic

profile of a typical pension plan population. For example, the deferred‐to‐age 65 premium rate for a

30‐year‐old has a smaller weighting than an immediate premium rate for a 65‐year‐old since the

deferred‐ to‐age 65 premium rate would be associated with a smaller liability in a typical pension

population.7 A composite premium is determined for each survey respondent by adding up the

weighted premium rates received through the survey. The primary purpose for the weightings and the

resulting composite premiums is to better represent the bidding process and enable the other

procedures described below.

Size Units

To ensure that the responses included in the average group annuity prices represent a material portion

of the market, the size of the group annuity business for each insurer is determined. The amount of

group annuity business won in the prior four quarters, the total amount of group annuity business on

the books and the capacity for taking on new business in the upcoming quarter are used to assign

respondents a numerical size rating (size units) from 1 – 15. The lowest half of survey premium rates is

determined using these size units. The size units for all insurers (excluding outliers) are summed and the

5 These survey practices for other organizations were in use in mid‐2021.

6 PBGC requests prices for immediate annuities for males and for females beginning at ages 50, 55, 60, 65, 70, 75,

and 80, and deferred annuities beginning at age 65 for individuals currently at ages 30, 35, 40, 45, 50, 55, and 60. 7 PBGC uses data from Form 5500 filings for plans used in the Projections Report modeling to determine these

weightings.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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lowest half of composite premium rate information described above is determined based on these units.

In the example below, the lowest three composite premiums and 3/15 of the fourth lowest composite

premium will be included in the lowest half cost average. This approach ensures that the information

included in the lowest half average represents a significant portion of the market.

Insurer

Composite

Premium Size Units

Size Units

Included in Lowest

Half Average

#1 $1,560 9 9

#2 $1,580 15 15

#3 $1,620 3 3

#4 $1,660 15 3

#5 $1,820 9 0

#6 $1,860 9 0

Total 60 30

The average net premium based on the above table is $1,586 [((9 x $1,560) + (15 x $1,580) + (3 x $1,620)

+ (3 x 1,660))/30].

Minimum Representation

PBGC believes that the validity of the survey process is compromised if the portion of the group annuity

market represented is too small. Therefore, a minimum of 15 size units will be used to determine the

average premium rates even if that represents more than half of the size units in the survey.

Outlier Responses

PBGC excludes premium rate information that is not representative of the market for settling pension

liabilities through group annuities. For example, this could happen due to an insurer inadvertently

providing information as of the wrong date or misunderstanding PBGC’s survey instructions. Outlier

responses could also be due to the wide range of practice regarding “off‐the‐shelf” prices and expense

loads or the niche markets that individual insurers may target. PBGC believes that these types of

responses are most likely to be received from insurers that are responding for the first time to the

survey. A question on the survey allows PBGC to identify respondents that have participated in the

survey in the last year.

PBGC identifies outlier premium rate information based on the composite premium described above. In

the event one or more responses from new participating insurers are significantly different from other

responses, the new responses will be compared to a benchmark that is not impacted by those new

responses. Composite premiums that are more than 15% higher or lower than the average composite

premium for respondents that have participated in the past year are considered outliers and excluded.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

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Immediate only responses

Because benefit liabilities measured based on Section 4044 represent the settlement of liabilities for a

full plan population, interest rates used to price plan terminations, rather than retiree only buyouts, are

most relevant. PBGC does receive survey responses that only provide premium rates for immediate

contracts, with no information for deferred contracts. To minimize the impact of retiree buyout pricing,

survey responses that do not include information for deferred contracts are only used if there are not

enough full survey responses (immediate and deferred contracts).

Review of Yield Curve Rates

PBGC uses several sources to benchmark the 4044 interest rates that result from the process described

above to ensure that it is a good representation of the group annuity market. These sources include

informal surveys by group annuity brokers, indexes prepared by consulting firms showing annuity pricing

relative to pension accounting liability measurement, and a commercial group annuity survey pricing

service.

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

Page 8
                             

                         

   

                               

                                         

                     

         

   

      

     

   

   

   

   

         

   

   

  

  

  

  

  

     

     

     

  

  

  

  

   

Appendix

The following example illustrates how the 4044 yield curve would have been developed for a valuation

date on the last day of June 2022 had the yield curve approach been in effect at that time and assuming

the second quarter spreads for 2022 were as shown in column D.

Time to

Maturity

(A)

June 30, 2022

Nominal TNC

Treasury Yield Curve

(B)

June 30, 2022

HQM Bond

Yield Curve

(C)

Blended Market

Yield Curve 1

/3 (A) + 2/3 (B)

(D)

Second

Quarter 2022

Spreads

(E)

Applicable 4044

Yield Curve

(C)+(D)

0.5 2.91% 2.84% 2.86% 0.27% 3.13%

1.0 2.90% 3.17% 3.08% 0.27% 3.35%

1.5 2.90% 3.45% 3.27% 0.26% 3.53%

2.0 2.92% 3.65% 3.41% 0.26% 3.67%

2.5 2.95% 3.79% 3.51% 0.26% 3.77%

. . . . . .

. . . . . .

. . . . . .

28.0 3.19% 4.84% 4.29%  ‐0.02% 4.27%

28.5 3.18% 4.84% 4.29%  ‐0.02% 4.27%

29.0 3.17% 4.84% 4.28%  ‐0.02% 4.26%

29.5 3.17% 4.83% 4.28%  ‐0.03% 4.25%

30.0 and

beyond 3.18% 4.83% 4.28%  ‐0.03% 4.25%

This White Paper represents PBGC’s proposed approach for determining the ERISA 4044 Yield Curve consistent

with the methodology described in PBGC’s proposed rule titled, Valuation Assumptions and Methods.

Page 9