Proposed Rule2023-12693
Corporate Bond Yield Curve for Determining Present Value
Primary source
Metadata and text below are from the Federal Register, a public-domain U.S. government work. Always verify the official published version before relying on it for any legal matter.
Published
June 23, 2023
Issuing agencies
Treasury DepartmentInternal Revenue Service
Abstract
This document sets forth proposed regulations specifying the methodology for constructing the corporate bond yield curve that is used to derive the interest rates used in calculating present value and making other calculations under a defined benefit plan, as well as for discounting unpaid losses and estimated salvage recoverable of insurance companies. These regulations affect participants in, beneficiaries of, employers maintaining, and administrators of certain retirement plans, as well as insurance companies.
Full Text
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<title>Federal Register, Volume 88 Issue 120 (Friday, June 23, 2023)</title>
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[Federal Register Volume 88, Number 120 (Friday, June 23, 2023)]
[Proposed Rules]
[Pages 41047-41051]
From the Federal Register Online via the Government Publishing Office [<a href="http://www.gpo.gov">www.gpo.gov</a>]
[FR Doc No: 2023-12693]
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DEPARTMENT OF THE TREASURY
Internal Revenue Service
26 CFR Part 1
[REG-124123-22]
RIN 1545-BQ57
Corporate Bond Yield Curve for Determining Present Value
AGENCY: Internal Revenue Service (IRS), Treasury.
ACTION: Notice of proposed rulemaking and notice of public hearing.
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SUMMARY: This document sets forth proposed regulations specifying the
methodology for constructing the corporate bond yield curve that is
used to derive the interest rates used in calculating present value and
making other calculations under a defined benefit plan, as well as for
discounting unpaid losses and estimated salvage recoverable of
insurance companies. These regulations affect participants in,
beneficiaries of, employers maintaining, and administrators of certain
retirement plans, as well as insurance companies.
DATES: Written or electronic comments must be received by August 22,
2023. A public hearing on this proposed regulation has been scheduled
for August 30, 2023 at 10:00 a.m. ET. Requests to speak and outlines of
topics to be discussed at the public hearing must be received by August
22, 2023. If no outlines are received by August 22, 2023, the public
hearing will be cancelled. Requests to attend the public hearing must
be received by 5:00 p.m. ET on August 28, 2023. The public hearing will
be made accessible to people with disabilities. Requests for special
assistance during the public hearing must be received by August 25,
2023.
ADDRESSES: Commenters are strongly encouraged to submit public comments
electronically via the Federal eRulemaking Portal at
<a href="http://www.regulations.gov">www.regulations.gov</a> (indicate IRS and REG-124123-22) by following the
online instructions for submitting comments. Requests for a public
hearing must be submitted as prescribed in the ``Comments and Requests
for a Public Hearing'' section. Once submitted to the Federal
eRulemaking Portal, comments cannot be edited or withdrawn. The
Department of the Treasury (Treasury Department) and the IRS will
publish for public availability any comments submitted to the IRS's
public docket. Send paper submissions to: CC:PA:LPD:PR (REG-124123-22),
room 5203, Internal Revenue Service, P.O. Box 7604, Ben Franklin
Station, Washington, DC 20044.
FOR FURTHER INFORMATION CONTACT: Concerning the regulations, Arslan
Malik or Linda S.F. Marshall at (202) 317-6700 (not a toll-free
number); concerning submissions of comments, the hearing, and/or to be
placed on the building access list to attend the hearing, Vivian Hayes
at (202) 317-5306 (not a toll-free number) or by sending an email to
<a href="/cdn-cgi/l/email-protection#f4848196989d979c9195869d9a9387b49d8687da939b82"><span class="__cf_email__" data-cfemail="97e7e2f5fbfef4fff2f6e5fef9f0e4d7fee5e4b9f0f8e1">[email protected]</span></a> (preferred).
SUPPLEMENTARY INFORMATION:
Background
Section 412 of the Internal Revenue Code (Code) prescribes minimum
funding requirements for defined benefit pension plans. Section 430
specifies the minimum funding requirements that apply generally to
defined benefit plans that are not multiemployer plans.\1\ For a plan
subject to section 430, section 430(a) defines the minimum required
contribution for a plan year by reference to the plan's funding target
for the plan year. Under section 430(d)(1), a plan's funding target for
a plan year generally is the present value of all benefits accrued or
earned under the plan as of the first day of that plan year.
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\1\ Section 302 of the Employee Retirement Income Security Act
of 1974, Public Law 93-406, 88 Stat. 829 (1974), as amended (ERISA)
sets forth funding rules that are parallel to those in section 412
of the Code, and section 303 of ERISA sets forth additional funding
rules for defined benefit plans (other than multiemployer plans)
that are parallel to those in section 430 of the Code. Pursuant to
section 101 of Reorganization Plan No. 4 of 1978, 5 U.S.C. App., as
amended, the Secretary of the Treasury has interpretive jurisdiction
over the subject matter addressed in these regulations for purposes
of ERISA, as well as the Code. Thus, these Treasury regulations
issued under section 430 of the Code also apply for purposes of
section 303 of ERISA.
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Section 430(h)(2) provides rules regarding the interest rates to be
used under section 430. Section 430(h)(2)(B) provides that a plan's
funding target and target normal cost for a plan year are determined
using three interest rates: (1) the first segment rate, which applies
to benefits reasonably determined to be payable during the 5-year
period beginning on the valuation date; (2) the second segment rate,
which applies to benefits reasonably determined to be payable during
the next 15-year period; and (3) the third segment rate, which applies
to benefits reasonably determined to be paid after that 15-year period.
Under section 430(h)(2)(C)(i) through (iii), each of these segment
rates is determined for a month on the basis of the corporate bond
yield curve for the month, taking into account only that
[[Page 41048]]
portion of the yield curve that is based on bonds maturing during the
period for which the segment rate is used.
Section 430(h)(2)(C)(iv), which was added to the Code in 2012 by
section 40211 of the Moving Ahead for Progress in the 21st Century Act,
Public Law 112-141, 126 Stat. 405, and has been modified several times
since then (most recently in 2021 by section 80602 of the
Infrastructure Investment and Jobs Act, Pub. L. 117-58, 135 Stat. 429),
provides interest rate stabilization rules under which the segment
rates are constrained by reference to the 25-year average segment
rates. Under section 430(h)(2)(C)(iv), if a segment rate for a month is
less than the applicable minimum percentage, or more than the
applicable maximum percentage, of the average of the corresponding
segment rates for years in the 25-year period ending with September 30
of the calendar year preceding the calendar year in which the plan year
begins, then the segment rate for that month is equal to the applicable
minimum percentage or the applicable maximum percentage of the
corresponding 25-year average segment rate, whichever is closest. The
last sentence of section 430(h)(2)(C)(iv)(I) provides that any 25-year
average segment rate that is less than 5 percent is deemed to be 5
percent.
Under section 430(h)(2)(D)(i), the term ``corporate bond yield
curve'' means, with respect to any month, a yield curve prescribed by
the Secretary for the month that reflects the average, for the 24-month
period ending with the month preceding such month, of monthly yields on
investment grade corporate bonds with varying maturities and that are
in the top 3 quality levels available. Section 430(h)(2)(D)(ii) permits
a plan sponsor to elect to use the corporate bond yield curve, rather
than the segment rates, to determine the plan's minimum required
contribution. The yield curve that applies pursuant to this election is
determined without regard to 24-month averaging. This election, once
made, may be revoked only with the consent of the Secretary.
Under section 430(h)(2)(F), the Secretary is instructed to publish
for each month the corporate bond yield curve (without regard to the
24-month averaging specification), the segment rates described in
section 430(h)(2)(C), and the 25-year averages of segment rates used
under section 430(h)(4)(C)(iv). The Secretary is also instructed to
publish a description of the methodology used to determine the yield
curve and segment rates which is sufficiently detailed to enable plans
to make reasonable projections regarding the yield curve and segment
rates for future months based on the plan's projection of future
interest rates.
Section 1.430(h)(2)-1 was issued in 2009 to provide rules regarding
the interest rates to be used under section 430. T.D. 9467, 74 FR
53004. Section 1.430(h)(2)-1(d) provides that the methodology for
determining the yield curve is provided in guidance that is published
in the Internal Revenue Bulletin. Notice 2007-81, 2007-2 CB 899,
describes the methodology used by the Department of the Treasury
(Treasury Department) to develop the corporate bond yield curve.
Section 1.430(h)(2)-1(d) also provides that the yield curve for each
month will be set forth in guidance published in the Internal Revenue
Bulletin. Monthly IRS notices set forth the corporate bond yield curve
for the month (without regard to the 24-month averaging specification),
the section 430 segment interest rates (before and after adjustment
pursuant to section 430(h)(3)(C)(iv)), and the 25-year average segment
rates (which are updated annually).
Section 417(e)(3) provides assumptions for determining minimum
present value for certain purposes, including the determination of a
lump-sum that is the present value of an annuity, and prescribes an
applicable interest rate for this purpose. Section 417(e)(3)(C)
provides that the term ``applicable interest rate'' means the adjusted
first, second, and third segment rates applied under rules similar to
the rules of section 430(h)(2)(C) for the month before the date of a
distribution or such other time as the Secretary may prescribe by
regulations. However, for purposes of section 417(e)(3), these rates
are determined without regard to the segment rate stabilization rules
of section 430(h)(2)(C)(iv). In addition, under section 417(e)(3)(D),
these rates are determined using the average yields for a month, rather
than the 24-month average used under section 430(h)(2)(D).
Under section 846(c), the Secretary determines the applicable
interest rate to be used by insurance companies to discount unpaid
losses on the basis of the corporate bond yield curve (as defined in
section 430(h)(2)(D)(i), determined by substituting ``60-month period''
for ``24-month period''). Under Sec. 1.832-4(c), the applicable
interest rate determined under section 846(c) is also used by insurance
companies to discount estimated salvage recoverable, unless the
Commissioner publishes applicable discount factors to be used for that
purpose.
Explanation of Provisions
These proposed regulations specify the methodology used to develop
the corporate bond yield curve. This methodology is generally the same
as the methodology set forth in Notice 2007-81 but would include two
refinements to take into account changes in the bond market since 2007.
The proposed regulations would also amend the existing regulations
under section 430(h)(2) to reflect the addition of the interest rate
stabilization rules of section 430(h)(2)(C)(iv) and to eliminate
transition rules that applied to plan years beginning before January 1,
2010.
Under these proposed regulations, as under Notice 2007-81, the
monthly corporate bond yield curve for a month is defined as the set of
spot rates at specified durations. The specified durations are at 6-
month intervals ranging from 6 months through 100 years, and the spot
rate at a duration is the yield (when compounded semiannually) for a
bond that matures at that duration with a single payment at maturity.
Each spot rate at a specified duration on the monthly corporate bond
yield curve for a month is equal to the arithmetic average for each
business day of that month of the spot rates at that duration on the
daily corporate bond yield curves.
Under these proposed regulations, as under Notice 2007-81, each
spot rate on the daily corporate bond yield curve is calculated using a
discount function, which is derived from a forward interest rate
function (that is, the projected instantaneous interest rate at each
point in time). The forward interest rate function is defined by the
selection of five coefficients of B-splines that are determined using
the bond data and taking into account certain adjustment factors.
Two of those adjustment factors, which are included in the
methodology set forth in Notice 2007-81, take into account the ratings
of the bonds used to develop the daily corporate bond yield curve. The
third adjustment factor, which was not included in the methodology set
forth in that notice, is a hump adjustment variable that peaks at 20
years maturity \2\ and serves to capture the effects of the hump in
spot rates that is often seen around 20 years maturity.
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\2\ The hump adjustment variable is a mathematical function that
is a cubic spline in the interval from 10 years maturity through 30
years maturity made up of two polynomials with a smooth junction at
20 years maturity.
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These proposed regulations generally adopt the specification for
the bond data set for a month in Notice 2007-81 but
[[Page 41049]]
modify an exclusion from that bond data set. Under Notice 2007-81 and
the proposed regulations, subject to certain exclusions, the bonds that
are used to construct the daily corporate bond yield curve for a
business day are bonds with the following characteristics: (1)
maturities longer than a \1/2\ year,\3\ (2) at least two payment dates,
(3) designated as corporate, (4) high quality ratings (that is, AAA,
AA, or A) as of that business day from the nationally recognized
statistical rating organizations,\4\ (5) at least $250 million in par
amount outstanding on at least one day during the month, (6) payment of
fixed nominal semiannual coupons and the principal amount at maturity,
and (7) maturity not later than 30 years after that day.
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\3\ Under Notice 2007-81 and the proposed regulations, the data
for durations equal to or below \1/2\ year that is used to construct
the daily corporate bond yield curve consists of AA financial and AA
nonfinancial commercial paper rates, as reported by the Federal
Reserve Board.
\4\ Although section 939A(b) of the Dodd-Frank Wall Street
Reform and Consumer Protection Act, Public Law 111-203, 124 Stat.
1376, generally prohibits federal agencies from issuing regulations
that apply a standard that is based on credit ratings from
statistical rating organizations, this prohibition does not apply to
the construction of the daily corporate bond yield curve because the
use of those credit ratings is required by section 430(h)(2)(D) of
the Code.
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Under Notice 2007-81 and these proposed regulations, the following
categories of bonds are excluded from the bond data set: (1) bonds not
denominated in U.S. dollars, (2) bonds not issued by U.S. corporations,
(3) bonds that are capital securities (sometimes referred to as hybrid
preferred stock), (4) bonds having variable coupon rates, (5)
convertible bonds, (6) bonds issued by a government-sponsored
enterprise (such as the Federal National Mortgage Association), (7)
asset-backed bonds, (8) putable bonds, (9) bonds with sinking funds,
and (10) bonds with a par amount outstanding below $250 million for the
day for which the daily yield curve is constructed.
Notice 2007-81 also excluded callable bonds (unless the call
feature is make-whole) from the bond data set used to construct the
daily corporate bond yield curve. The proposed regulations generally
retain this exclusion but narrow it. Under the proposed regulations,
this exclusion does not apply if the call feature is exercisable only
during the last year before maturity. This type of call feature has
recently become more widely used, and the inclusion of bonds with this
feature in the data set will result in a significantly larger pool of
bonds that more accurately reflects the market for high quality
corporate bonds.
Proposed Applicability Date
The rules in the proposed regulations are proposed to apply for
months that begin more than 15 days after the date final regulations
specifying the methodology for constructing the corporate bond yield
curve are published in the Federal Register.
Statement of Availability of IRS Documents
IRS Revenue Rulings, Revenue Procedures, and Notices cited in this
document are published in the Internal Revenue Bulletin (or Cumulative
Bulletin) and are available from the Superintendent of Documents, U.S.
Government Printing Office, Washington, DC 20402, or by visiting the
IRS website at <a href="http://www.irs.gov">www.irs.gov</a>.
Special Analyses
Regulatory Planning and Review (Executive Orders 12866 and 13563)
These regulations are not subject to review under section 6(b) of
Executive Order 12866 pursuant to the Memorandum of Agreement (April
11, 2018) between the Treasury Department and the Office of Management
and Budget regarding review of tax regulations.
Regulatory Flexibility Act (5 U.S.C. Chapter 6)
It is hereby certified that this rule will not have a significant
economic impact on a substantial number of small entities. The vast
majority of plan sponsors of defined benefit plans that are subject to
section 430 choose to use the segment rates under section 430(h)(2)(C),
rather than the corporate bond yield curve under section 430(h)(2)(D),
to determine minimum required contributions. Furthermore, most of the
plan sponsors who choose to use the corporate bond yield curve for this
purpose are not small employers. Therefore, the methodology set forth
in the proposed regulations for constructing the corporate bond yield
curve will not have a significant effect on minimum required
contributions for small employers. In addition, the insurance companies
that are required to use a modified version of the corporate bond yield
curve to discount unpaid losses are typically not small employers.
Accordingly, a regulatory flexibility analysis under the Regulatory
Flexibility Act is not required.
Pursuant to section 7805(f) of the Code, these proposed regulations
will be submitted to the Chief Counsel for Advocacy of the Small
Business Administration for comment on their impact on small business.
Comments and Requests for a Public Hearing
Before these proposed amendments to the regulation are adopted as a
final regulation, consideration will be given to comments regarding the
notice of proposed rulemaking that are submitted timely to the IRS as
prescribed in the preamble under the ADDRESSES section. The Treasury
Department and the IRS request comments on all aspects of the proposed
regulation. All comments will be made available at <a href="http://www.regulations.gov">www.regulations.gov</a>.
Once submitted to the Federal eRulemaking Portal, comments cannot be
edited or withdrawn.
A public hearing has been scheduled for August 30, 2023 beginning
at 10 a.m. ET in the Auditorium of the Internal Revenue Building, 1111
Constitution Avenue NW, Washington, DC. Due to building security
procedures, visitors must enter at the Constitution Avenue entrance. In
addition, all visitors must present photo identification to enter the
building. Because of access restrictions, visitors will not be admitted
beyond the immediate entrance area more than 30 minutes before the
hearing starts. Participants may alternatively attend the public
hearing by telephone.
The rules of 26 CFR 601.601(a)(3) apply to the hearing. Persons who
wish to present oral comments must submit an outline of the topics to
be addressed and the time to be devoted to each topic by August 22,
2023 as prescribed in the preamble under the ADDRESSES section. A
period of 10 minutes will be allocated to each person for making
comments. An agenda showing the scheduling of the speakers will be
prepared after the deadline for receiving outlines has passed. Copies
of the agenda will be available free of charge at the hearing. If no
outline of the topics to be discussed at the hearing is received by
August 22, 2023, the public hearing will be cancelled. If the public
hearing is cancelled, a notice of cancellation of the public hearing
will be published in the Federal Register.
Individuals who want to testify in person at the public hearing
must send an email to <a href="/cdn-cgi/l/email-protection#8afaffe8e6e3e9e2efebf8e3e4edf9cae3f8f9a4ede5fc"><span class="__cf_email__" data-cfemail="3f4f4a5d53565c575a5e4d5651584c7f564d4c11585049">[email protected]</span></a> to have your name added to
the building access list. The subject line of the email must contain
the regulation number REG-124123-22 and the language TESTIFY In Person.
For example, the subject line may say: Request to TESTIFY In Person at
Hearing for REG-124123-22.
Individuals who want to testify by telephone at the public hearing
must
[[Page 41050]]
send an email to <a href="/cdn-cgi/l/email-protection#067673646a6f656e6367746f686175466f747528616970"><span class="__cf_email__" data-cfemail="1e6e6b7c72777d767b7f6c7770796d5e776c6d30797168">[email protected]</span></a> to receive the telephone number
and access code for the hearing. The subject line of the email must
contain the regulation number REG-124123-22 and the language TESTIFY
Telephonically. For example, the subject line may say: Request to
TESTIFY Telephonically at Hearing for REG-124123-22.
Individuals who want to attend the public hearing in person without
testifying must also send an email to <a href="/cdn-cgi/l/email-protection#1a6a6f78767379727f7b6873747d695a736869347d756c"><span class="__cf_email__" data-cfemail="671712050b0e040f0206150e090014270e151449000811">[email protected]</span></a> to have
your name added to the building access list. The subject line of the
email must contain the regulation number REG-124123-22 and the language
ATTEND In Person. For example, the subject line may say: Request to
ATTEND Hearing In Person for REG-124123-22. Requests to attend the
public hearing must be received by 5:00 p.m. EST on August 28, 2023.
Individuals who want to attend the public hearing by telephone
without testifying must also send an email to <a href="/cdn-cgi/l/email-protection#09797c6b65606a616c687b60676e7a49607b7a276e667f"><span class="__cf_email__" data-cfemail="58282d3a34313b303d392a31363f2b18312a2b763f372e">[email protected]</span></a> to
receive the telephone number and access code for the hearing. The
subject line of the email must contain the regulation number REG-
124123-22 and the language ATTEND Hearing Telephonically. For example,
the subject line may say: Request to ATTEND Hearing Telephonically for
REG-124123-22. Requests to attend the public hearing must be received
by 5:00 p.m. EST on August 28, 2023.
Hearings will be made accessible to people with disabilities. To
request special assistance during a hearing please contact the
Publications and Regulations Branch of the Office of Associate Chief
Counsel (Procedure and Administration) by sending an email to
<a href="/cdn-cgi/l/email-protection#6f1f1a0d03060c070a0e1d0601081c2f061d1c41080019"><span class="__cf_email__" data-cfemail="136366717f7a707b7672617a7d7460537a61603d747c65">[email protected]</span></a> (preferred) or by telephone at (202) 317-6901
(not a toll-free number) at least August 25, 2023.
Drafting Information
The principal authors of these regulations are Arslan Malik and
Linda S.F. Marshall of the Office of Associate Chief Counsel (Employee
Benefits, Exempt Organizations, and Employment Taxes). However, other
personnel from the Treasury Department and the IRS participated in the
development of these regulations.
List of Subjects in 26 CFR Part 1
Income taxes, Reporting and recordkeeping requirements.
Proposed Amendments to the Regulations
Accordingly, the Treasury Department and the IRS propose to amend
26 CFR part 1 as follows:
PART 1--INCOME TAXES
0
Paragraph 1. The authority citation for part 1 continues to read in
part as follows:
Authority: 26 U.S.C. 7805 * * *
0
Par. 2. Amend Sec. 1.430(h)(2)-1 as follows:
0
1. Amend paragraph (a)(1) by removing the phrase ``and transition
rules'' in the last sentence.
0
2. Revise paragraph (b)(2).
0
3. Amend paragraph (c)(1) by removing the last sentence.
0
4. Amend paragraphs (c)(2)(i), (c)(2)(ii), and (c)(2)(iii) by removing
the phrase ``under the transition rule of paragraph (h)(4) of this
section'' and adding the phrase ``under the interest rate stabilization
rules in section 430(h)(2)(C)(iv)'' in its place.
0
5. Revise paragraph (d).
0
6. Remove paragraph (e)(3) and redesignate paragraph (e)(4) as
paragraph (e)(3) and paragraph (e)(5) as paragraph (e)(4).
0
7. In newly redesignated paragraph (e)(3)(ii), remove the phrase ``this
paragraph (e)(4)'' and add the phrase ``this paragraph (e)(3)'' in its
place.
0
8. Revise paragraph (h).
The revisions and additions read as follows:
Sec. 1.430(h)(2)-1 Interest rates used to determine present value.
* * * * *
(b) * * *
(2) In the case of benefits expected to be payable during the 5-
year period beginning on the valuation date for the plan year, the
interest rate used in determining the present value of the benefits
that are included in the target normal cost and the funding target for
the plan is the first segment rate with respect to the applicable
month, as described in paragraph (c)(2)(i) of this section.
* * * * *
(d) Monthly corporate bond yield curve--(1) In general--(i)
Construction of monthly corporate bond yield curve. For purposes of
this section, the monthly corporate bond yield curve for a month is
defined as the set of spot rates at specified durations. The specified
durations are at 6-month intervals ranging from 6 months through 100
years and the spot rate at a duration is the yield (when compounded
semiannually) for a bond that matures at that duration with a single
payment at maturity. The monthly corporate bond yield curve is
constructed as the average of the spot rates from the set of daily
corporate bond yield curves as specified in paragraph (d)(1)(ii) of
this section. Each daily corporate bond yield curve is constructed
using the methodology set forth in paragraph (d)(2) of this section
based on the data described in paragraph (d)(3) of this section. Note 1
to paragraph (d)(1) of this section, the yield curve for each month
will be published in the Internal Revenue Bulletin. See Sec.
601.601(d) of this chapter.
(ii) Monthly corporate bond yield curve constructed through
averaging. Each spot rate at a specified duration on the monthly
corporate bond yield curve for a month is equal to the arithmetic
average, for each business day of that month, of the spot rates at that
duration on the daily corporate bond yield curves.
(2) Construction of the daily corporate bond yield curve--(i) In
general--(A) Calculation of spot rates. Each spot rate at duration t on
a daily corporate bond yield curve is calculated from the discount
function described in paragraph (d)(2)(i)(B) of this section and the
hump adjustment variable described in paragraph (d)(2)(iii)(D) of this
section.
(B) Derivation of discount function. The discount function for a
day at duration t is derived from the forward interest rate function as
described in paragraph (d)(2)(ii) of this section (denoted f(z)) using
the following equation:
[GRAPHIC] [TIFF OMITTED] TP23JN23.005
(ii) Determination of forward interest rates--(A) In general. The
forward interest rate function used to derive the discount function is
determined as a series of cubic polynomials (referred to as a cubic
spline) that have a smooth junction at specified knot points
(maturities of 0, 1.5, 3, 7, 15, and 30 years). The requirement that
the polynomials have a smooth junction at a knot point is satisfied if
the two polynomials that are meeting at the knot have the same value,
the same derivative, and the same second derivative at that knot point.
(B) Constraints on the forward interest function. The following
three constraints are placed on the forward interest rate function--
(1) The second derivative of the function is set to zero at
maturity zero.
(2) The value of the forward interest rate function at and after 30
years is constrained to equal its average value from 15 to 30 years.
(3) The derivative of the forward interest rate function is set to
zero at maturity 30 years.
(iii) Parameters for daily bond price model--(A) B-spline
coefficients. The
[[Page 41051]]
assumed cubic spline for the forward interest rate function can be
described as a linear combination of B-splines, with five parameters,
which are determined taking into account the two coefficients for the
bond-quality adjustment variables described in paragraphs
(d)(2)(iii)(B) and (C) of this section and the coefficient for the hump
adjustment variable described in paragraph (d)(2)(iii)(D) of this
section. The five parameters and three coefficients are determined
using the bond data weighted as described in paragraph (d)(2)(iv) of
this section. After this weighting of the bond data, the five
parameters and three coefficients are chosen to minimize the sum of the
squared differences between the bid price for each of the bonds (or ask
price for commercial paper) and the price estimated for each of those
bonds determined using the specified parameters and coefficients, and
taking into account the bond's coupon rate, number of years until
maturity, and rating.
(B) Adjustment factor for share of bonds that are AA-rated. The
first adjustment variable is based on the proportion of bonds that are
rated AA within the universe of bonds in the data set that are rated AA
or AAA, weighted by par value. In the case of an AAA-rated bond the
adjustment variable described in this paragraph (d)(2)(iii)(B) is equal
to the product of the proportion described in the preceding sentence
and the number of years until maturity for the bond. In the case of an
AA-rated bond the adjustment variable described in this paragraph
(d)(2)(iii)(B) is equal to the product of (1- that proportion) and the
number of years until maturity for the bond. In the case of an A-rated
bond, the adjustment variable described in this paragraph
(d)(2)(iii)(B) is set to 0.
(C) Adjustment factor for share of bonds that are A-rated. The
second adjustment variable is based on the proportion of bonds rated A
within the universe of bonds in the data set, weighted by par value. In
the case of an AAA-rated bond or an AA-rated bond, the adjustment
variable described in this paragraph (d)(2)(iii)(C) is equal to the
product of the proportion described in the preceding sentence and the
number of years until maturity for the bond. In the case of an A-rated
bond the adjustment variable described in this paragraph (d)(2)(iii)(C)
is equal to the product of (1- that proportion) and the number of years
until maturity for the bond.
(D) Hump adjustment variable. The hump adjustment variable is a
mathematical function that is a cubic spline in the interval from 10
years maturity through 30 years maturity made up of two polynomials
with a smooth junction (as described in paragraph (d)(2)(ii)(A) of this
section) at 20 years maturity. The spline rises from zero at 10 years
maturity to 1.0 at 20 years maturity, then falls back down to zero at
30 years maturity. The hump adjustment variable is zero for maturities
less than 10 years and maturities greater than 30 years.
(iv) Weighting of bond data. The bond data are weighted in two
steps. First, equal weights are assigned to the commercial paper rates
at the short end of the curve, and the par amounts outstanding of all
the bonds are rescaled so that their sum equals the sum of the weights
for commercial paper. Then, the squared price difference for each bond
is multiplied by the bond's rescaled par amount outstanding, and the
squared difference for each commercial paper rate is multiplied by the
commercial paper weight. In the second stage, applicable for bonds with
duration greater than 1, the weighted squared price difference for each
bond from the first stage is divided by the bond's duration.
(3) Data used--(i) In general. Except as otherwise provided in this
paragraph (d)(3), the bonds that are used to construct the daily
corporate bond yield curve for a business day are bonds with maturities
longer than a \1/2\ year, with at least two payment dates, and that:
(A) Are designated as corporate;
(B) Have high quality ratings (AAA, AA, or A) as of that business
day from the nationally recognized statistical rating organizations;
(C) Have at least $250 million in par amount outstanding on at
least one day during the month;
(D) Pay fixed nominal semiannual coupons and the principal amount
at maturity; and
(E) Mature not later than 30 years after that business day.
(ii) Excluded bonds. The following types of bonds are not used to
construct the daily corporate bond yield curve for a date:
(A) Bonds not denominated in U.S. dollars;
(B) Bonds not issued by U.S. corporations;
(C) Bonds that are capital securities (sometimes referred to as
hybrid preferred stock);
(D) Bonds having variable coupon rates;
(E) Convertible bonds;
(F) Bonds issued by a government-sponsored enterprise (such as the
Federal National Mortgage Association);
(G) Asset-backed bonds;
(H) Callable bonds unless the call feature is make-whole or the
call feature is exercisable only during the last year before maturity;
(I) Putable bonds;
(J) Bonds with sinking funds; and
(K) Bonds with a par amount outstanding below $250 million for the
day for which the daily yield curve is constructed.
(iii) Durations equal to or below a \1/2\ year. The data for
durations equal to or below a \1/2\ year that is used to construct the
daily corporate bond yield curve consists of AA financial and AA
nonfinancial commercial paper rates, as reported by the Federal Reserve
Board.
* * * * *
(h) Applicability date of regulations. This section applies to
months that begin more than 15 days after the date final regulations
issued pursuant to these proposed regulations are published in the
Federal Register. For rules that apply for earlier periods, see Sec.
1.430(h)(2)-1, as it appeared in the April 1, 2022, edition of 26 CFR
part 1.
Douglas W. O'Donnell,
Deputy Commissioner for Services and Enforcement.
[FR Doc. 2023-12693 Filed 6-22-23; 8:45 am]
BILLING CODE 4830-01-P
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</html>Indexed from Federal Register on June 23, 2023.
This is legal information, not legal advice. Laws vary by jurisdiction and change frequently. Always verify current law with official sources and consult a licensed attorney in your jurisdiction for advice on your specific situation.