Banco de México Monetary Regulation Bonds

Banco de México Monetary Regulation Bonds BANCO DE MÉXICO

TECHNICAL DESCRIPTION OF BANCO DE MÉXICO MONETARY REGULATION BONDS 1. INTRODUCTION Based on article 7 paragraph VI, 17 and 46 paragraph VI of Banco de México s Law, and articles 6, 7, and 12 of its Internal Bylaws, Banco de México has decided to issue Monetary Regulation Bonds (BREMS) in order to regulate money market liquidity and thereby facilitate monetary policy implementation. The aim of this note is to present a technical description of these securities so that financial intermediaries and the general public are more informed about them. 2. DESCRIPTION 2.1 Name Banco de México Monetary Regulation Bonds (BREMS). 2.2 Face value 100 pesos (one hundred pesos). 2.3 Term They can be issued for any term that is a multiple of 28 days. However, to date, these securities have been issued for terms of 3 years and 1 year. 2.4 Interest period The securities pay interest in pesos each month. In other words, interest is paid every 28 days or the term substituting it in the event of non-working days. 2

2.5 Interest rate For each interest rate period, the rate resulting from the following formula will be applied: [ ( ) ] where: TC J = Annual interest rate of coupon J N J = Term in days of coupon J Operator meaning multiply the factors in brackets r i = Weighted overnight rate of bank securities corresponding to day i. Banks use this rate this to rate carry banks out undertake overnight buy-sell and and repocon transactions with bank securities. The rate is calculated daily by Banco de México and published on its website: www.banxico.org.mx. In the event of a non-working day, the rate published the previous working day will be used to calculate the interest rate. If this rate cannot be calculated or published, Banco de México will request in writing two brokerage firms that the Money Market Committee of the Mexican Bankers Association (ABM, for its acronym in Spanish) to select the average overnight buy-sell and repo transaction using bank securities. Banco de México will calculate the average of the two rates obtained and the result will be published as the aforementioned substitute rate. 2.5.1 Interest payment Interest is calculated based on the number of days that have elapsed between payment dates, using years consisting of 360 days as a base, and is settled at the end of each interest period. where: I J = Interest payable at the end of period J 3

TC J = Annual coupon interest rate J VN = Nominal value of the security in pesos 2.6 Placement The securities are placed through an auction in which participants make bids for the amount they wish to acquire and the price they are willing to pay. The rules for participating in these auctions are listed in Appendix 7 of Banco de México s Circular 2019/95 for banks. The auctions currently take place every Thursday. It should be pointed out that Banco de México sometimes offers securities issued prior to their placement date in these auctions. In such cases, the auctions take place at a clean price (without accrued interest) and in order to settle them interest accrued on the current coupon must be added to the auction assignment price according to the following formula: where: I devj = Interest accrued (rounded to 12 decimals) during period J d = Days elapsed between the issuance date or last interest payment (J - 1), as appropriate, and the valuation date TC dev = Accrued annual interest rate calculated in accordance with the following formula: { ( ) } 4

2.7 Decimal precision for calculations All calculations should be done using 6 or more decimals, unless otherwise specified. 2.8 Identifying securities The ticker symbol for BREMS issuance is designed so that instruments are fungible. In other words, BREMS issued previously and BREMS issued recently may have the same ticker symbol as long as they mature on the same date. For this purpose the symbol comprises eight characters; the first two identify the security ( XA ) while the other six indicate is maturity date (year, month, day). As shown, the maturity date is key to identifying a BREM; thus, two BREMS that were issued on different dates but mature on the same day have the same ticker symbol and are indistinguishable. For example, the ticker symbol of a BREM issued on February 9, 2011 with a 3-year maturity (1092 days), maturing on February 6, 2004 would be: XA040206. 5

APPENDIX 1 BREMS VALUATION The market has different ways of quoting these securities and therefore valuing them. This appendix presents a methodology for a general price valuation of BREMS. I. GENERAL METHODOLOGY FOR VALUING BREMS The general formula for valuing BREMS is: ( ) ( ) ( ) where: P = Clean price of BREM (rounded to 5 decimals) VN = Nominal value of the security K = Number of coupons pending settlement including the current one d = Number of days elapsed on the current coupon N j = Coupon term in days j C j = Coupon j, obtained as follows: { 6

TC j = Coupon j annual interest rate [ ( ) ] [( ) ( ) ] { F j = Discount factor for cash flow j, obtained using the formula: ( ) where: R j = Expected internal rate of return for coupon j R j r j s j * N j 360 7

r j = Relevant interest rate for discounting coupon j s j = Spread associated with coupon j From formula (1) we infer that the price of BREMS is made up of three different elements: the present value of the coupons, the present value of the principal, and interest accrued on the current coupon. Similarly, each of the coupons along with the principal is discounted using a different interest rate, so it is necessary to know or to be able to forecast an interest rate for each discount factor. II. CALCULATING THE PRICE OF BREMS Below we include a formula that can be used to obtain the price of BREMS. To arrive at this formula several assumptions were made that will become clear when observing the definitions of the variables used. Furthermore, the spread concept, currently employed to consult and value other variable rate securities, is used. There are several ways of calculating the value of the previous expression; one of them is assuming that C j, r j, s j and N j are constant for j = 1,2,,K, as a result of which the equation (1) is reduced to: ( [ ] ( ) ( ) ) ( ) [ ] ( ) where: C 1 = Expected amount of current interest payment: TC 1 = Expected annual rate for the following interest payment: [( ) ( ) ] 8

r C = Weighted overnight rate published the day before the valuation date = Expected amount of interest payments 2,...,K: C VN * 28 * TC 360 TC = Expected annual rate for interest payments 2,3,,K [( ) ] R = Effective interest rate for discounting flows obtained in accordance with the following formula: [( ) ] s = Spread 9

APPENDIX 2 PRACTICAL EXAMPLE On June 1, 2000, Banco de México issues BREMS with the following characteristics: Face value: 100 pesos Issuance date: June 1, 2000 Maturity date: May 29, 2003 Term: 1092 days Coupon term: 28 days On June 7 th 2000, Banco de México decides to auction BREMS issued on June 1, 2000. The settlement date is June 7. On that date the securities will still have 1086 days to maturity, the term of the first coupon payment is 28 days, and 6 days have elapsed as of the first coupon. Assume an investor has assigned these securities in the auction with a clean price bid (not including accrued interest) of $99.88084 for $400'000,000.00. To calculate settlement, interest accrued on the first coupon must be added to the clean price as follows. 1. Calculating the interest accrued on a current coupon Assume that: Date Day i Weighted overnight rate published by Banco de México r i Thurs, June 1, 2000 1 16.98 % Fri, June 2, 2000 2 17.00% Sat, June 3, 2000 3 17.00 % Sun, June 4, 2000 4 17.00 % Mon, June 5, 2000 5 16.95 % Tues, June 6, 2000 6 17.07 % Accrued interest on the current coupon would therefore be: 10

{( ) ( ) ( ) ( ) ( ) ( ) } = 17.02% Thus, on June 7, the investor would have to pay $99.88084 for each security at the clean price plus $0.283666666667 of interest accrued on the current coupon, or 100.164506666667. 2. Calculating the number of securities assigned and the final settlement amount The number of securities assigned will be calculated as follows: ( ) The amount to be settled will be calculated as follows: 3'993,430 securities * $99.88084 $0.283666666667 $399'999,945.86 3. Calculating the price of a BREM based on a spread Assume that on June 7, 2000, an investor wants to know the price associated with a BREM with the abovementioned characteristics and a 0.05% spread. I) To calculate the amount of the current interest payment, we write: [( ) ( ) ] with r = 17.07% thus, 11

[( ) ( ) ] C 1 100 *.1716 28 360 1.334666666667 To calculate the expected amount of subsequent interest payments, C VN * TC 28 360 [( ) ] Then, C 100 *.1718 28 360 1.336222222222 The effective interest rate for discounting the flows is as follows: [( ) ] [( ) ] 1.34 % Substituting C 1, TC 1, TC dev, C and TC in (3) gives us: [ ] ( ) { ( ) Therefore, the clean price is $99.88594. ( ) } 4. Calculating interest for a full period Assume the following rates are observed during the June 1-29, 2000 period: 12

Date Day Weighted bank overnight rate published by Banco de México i Thurs, June 1, 2000 1 16.98 % Fri, June 2, 2000 2 17.00 % Sat, June 3, 2000 3 17.00% Sun, June 4, 2000 4 17.00% Mon, June 5, 2000 5 16.95 % Tues, June 6, 2000 6 17.07 % Wed, June 7, 2000 7 17.10% Thurs, June 8, 2000 8 17.35% Fri, June 9, 2000 9 17.44% Sat, June 10, 2000 10 17.44% Sun, June 11, 2000 11 17.44% Mon, June 12, 2000 12 17.64% Tues, June 13, 2000 13 17.60% Wed, June 14, 2000 14 17.54% Thurs, June 15, 2000 15 17.20% Fri, June 16, 2000 16 17.02% Sat, June 17, 2000 17 17.02% Sun, June 18, 2000 18 17.02% Mon, June 19, 2000 19 16.99% Tues, June 20, 2000 20 16.87% Wed, June 21, 2000 21 16.93% Thurs, June 22, 2000 22 16.96% Fri, June 23, 2000 23 16.81% Sat, June 24, 2000 24 16.81% Sun, June 25, 2000 25 16.81% Mon, June 26, 2000 26 17.01% Tues, June 27, 2000 27 17.04% Wed, June 28, 2000 28 17.11% Based on this information, the first coupon pays an interest of: TC {( ) ( ) ( ) ( ) } 17.22 % r i On June 29, 2000, the interest paid associated with the first payment on the coupon of security 1 is as follows: 13

Interest on first coupon VN * TC 1 * N 360 100 *.1722 * 28 360 $1.339333333333 If an investor has 4'000,000 securities, their face value amounts to $400'000,000.00 and he will therefore receive: 4'000,000 * 1.339333333333 $ 5'357,333.33 of interest on the first coupon. 14