Resolution CMN No. 4624 — Amends and Consolidates Norms Regarding the Calculation Methodology for the Basic Financial Rate (TBF) and the Reference Rate (TR)

RESOLUTION No. 4,624, OF JANUARY 18, 2018

Amends and consolidates the norms relating to the calculation methodology for the Basic Financial Rate (TBF) and the Reference Rate (TR).

The Central Bank of Brazil, in accordance with Art. 9 of Law No. 4,595, of December 31, 1964, makes public that the National Monetary Council, in an extraordinary session held on January 18, 2018, based on Art. 1 of Law No. 8,177, of March 1, 1991, Art. 1 of Law No. 8,660, of May 28, 1993, and Art. 5 of Law No. 10,192, of February 14, 2001,

RESOLVES:

Art. 1 The Basic Financial Rate (TBF), referred to in Art. 5 of Law No. 10,192, of February 14, 2001, and the Reference Rate (TR), referred to in Art. 1 of Law No. 8,177, of March 1, 1991, and Art. 1 of Law No. 8,660, of May 28, 1993, shall be calculated from interest rates negotiated in the secondary market with National Treasury Bills (LTNs).

Art. 2 A database composed of all definitive operations carried out in the secondary market, registered in the Special Settlement and Custody System (Selic), with LTNs with maturity terms immediately prior to, coincident with, or immediately subsequent to a one-month term, shall be constituted on each business day.

§ 1 From the database referred to in the caput, operations that present a rate with a variation greater than 15% (fifteen percent) relative to the average rate calculated on the previous day for the respective maturity shall be excluded from each LTN maturity.

§ 2 Subject to the provisions of § 1, the remaining operations shall be subjected to statistical treatment based on the box-plot tool, such that those presenting rates:

I - higher than the rate corresponding to the third quartile plus one and a half times the interval between the first and third quartiles; and

II - lower than the rate corresponding to the first quartile minus one and a half times the interval between the first and third quartiles, are eliminated.

§ 3 For the purposes of § 2, the definition of the quartiles and their respective rates shall be based on the financial amounts of the operations.

Art. 3 For each LTN maturity that makes up the database referred to in Art. 2, the average interest rate (TM) shall be calculated, according to the following formula:

TMk = (∑ Fj x ij) / (∑ Fj)

from j=1 to m, in which:

I - Fj corresponds to the financial amount of the j-th definitive operation of the k-th LTN maturity;

II - ij corresponds to the interest rate of the j-th definitive operation of the k-th LTN maturity, expressed in annual form, with four decimal places, considering the convention of 252 business days; and

III - “m” corresponds to the number of definitive operations with the k-th LTN maturity.

§ 1 If one of the LTN maturities, after applying the statistical treatment provided for in §§ 1 and 2 of Art. 2, does not present at least six transactions in the secondary market on the day, an indicative interest rate that has broad acceptance as a price reference in the national financial market shall be used for both LTN maturities.

§ 2 In the event that there are no LTNs with a maturity term lower than or coincident with a one-month term, the Selic rate shall be used as the indicative rate for an LTN with a maturity term of one business day.

Art. 4 For each day of the month – the reference day – the Central Bank of Brazil must calculate the TBF, for a one-month period, starting on the reference day itself and ending on the day corresponding to the reference day in the following month, considering the hypothesis provided for in § 1 of Art. 5.

Sole Paragraph. When the day corresponding to the reference day in the following month does not exist, the end of the period shall be considered the first day of the second month subsequent to the reference day.

Art. 5 The TBF shall be calculated from the interest rates of the LTNs determined in accordance with Art. 3, according to the following methodology:

I - if the reference day is a business day, the TBF must be obtained by interpolation, according to the following formula:

TBFu = 100 x 0.93 × [((1 + TJANT)^(DUANT/252) × ((1+TJPOS)/(1+TJANT))^((DUTBF−DUANT)/(DUPOS−DUANT)))^(DUPOS/252) − 1] (%), in which:

a) TJANT corresponds to the interest rate of the LTN with a maturity term immediately prior to or coincident with a one-month term, if existing, or to the effective Selic rate determined on the day, expressed in annual form, according to the convention of 252 business days;

b) TJPOS corresponds to the interest rate of the LTN with a maturity term immediately subsequent to a one-month term, expressed in annual form, according to the convention of 252 business days;

c) DUTBF corresponds to the term, in business days, of the TBF;

d) DUANT corresponds to the term, in business days, of the LTN with a maturity term immediately prior to or coincident with a one-month term, if existing, or one business day; and

e) DUPOS corresponds to the term, in business days, of the LTN with a maturity term immediately subsequent to a one-month term;

II - if the reference day is a non-business day, the TBF must be obtained according to the formula presented in item I, considering the interest rates of the LTNs determined in accordance with Art. 3, for the business day immediately subsequent to the reference day; and

III - if the reference day is the last business day of the year, the TBF must be obtained according to the following formula:

TBFz = 100 x [(1 + TBFu /100)^(nz/nu) - 1] (%), in which:

a) TBFz corresponds to the TBF relative to the last business day of the year;

b) TBFu corresponds to the TBF relative to the penultimate business day of the year, calculated in accordance with item I;

c) “nz” corresponds to the number of business days included in the period from the last business day of the year, inclusive, to the corresponding day in January, exclusive; and

d) “nu” corresponds to the number of business days included in the validity period of TBFu.

§ 1 When the reference date is the first day of a month with a number of days greater than the number of days of the previous month, as many additional TBFs as is the difference between the number of days of these months must be calculated, in accordance with items I and II of the caput, valid for the periods between the first day of the current month (reference date) and the days of the current month that do not have a correspondence in the previous month.

§ 2 In the event of impossibility to estimate the TBF for a given reference date, including due to insufficient information about negotiations in the secondary market and, simultaneously, absence of the indicative prices mentioned in § 1 of Art. 3, the rate shall be determined according to the following formula:

TBFi = 100 x [(1 + TBFj /100)^(ni/nj) - 1] (%), in which:

I - TBFi corresponds to the TBF relative to the reference date;

II - TBFj corresponds to the TBF relative to the last business day for which the TBF was calculated;

III - ni corresponds to the number of business days of the validity period of TBFi; and

IV - nj corresponds to the number of business days of the validity period of TBFj.

§ 3 The TBF shall be expressed in monthly form, with four decimal places.

Art. 6 For each TBF obtained, according to the methodology described in Art. 5, the corresponding TR must be calculated, by applying a reducer “R”, according to the following formula:

TR = max { 0 ; 100 x {[ (1 + TBF/100) / R ] - 1}} (%)

§ 1 The value of the reducer “R” must be calculated for all days, including non-business days, according to the following formula:

R = (a + b x TBF/100), in which:

I - TBF corresponds to the TBF relative to the reference day;

II - “a” corresponds to 1.005; and

III - “b” corresponds to the value obtained in the table below, as a function of the TBF relative to the reference day, expressed in percentage terms per year, considering the convention of 252 business days:

TBF (% a.a.)	b
TBF greater than 16.0	0.48
TBF less than or equal to 16.0 and greater than 15.0	0.44 TBF less than or equal to 15.0 and greater than 14.0

§ 2 The Central Bank of Brazil must calculate the reducer “R” using, in the process, all decimal places of the values involved, proceeding to rounding the final value to four decimal places, using the Rounding Rules in Decimal Numbering (NBR 5891) established by the Brazilian Association of Technical Standards (ABNT).

§ 3 The values of the reducer “R” must be disclosed by the Central Bank of Brazil when the TR is disclosed.

§ 4 The TR shall be expressed in monthly form, with four decimal places.

Art. 7 The Central Bank of Brazil must disclose the TBFs and the corresponding TRs on the first business day subsequent to the reference day mentioned in the caput of Art. 4.

Sole Paragraph. If the reference day is a non-business day, the disclosure referred to in the caput must occur by the second business day subsequent to the reference day.

Art. 8 This Resolution enters into force on the date of its publication, producing effects from the calculation of the TBF and TR relative to February 1, 2018.

Art. 9 The following are repealed:

I - on the date of publication of this Resolution, § 2 of Art. 1 of Resolution No. 3,354, of March 31, 2006; and

II - on February 1, 2018, Resolutions Nos. 3,354, of March 31, 2006, 3,446, of March 5, 2007, 3,530, of January 31, 2008, and 4,240, of June 28, 2013.

Ilan Goldfajn
President of the Central Bank of Brazil

This text does not replace the published in the DOU of 1/19/2018, Section 1, p. 19/20, and rectified in the DOU of 1/25/2018, Section 1, p. 99, and in Sisbacen.