BPA182

Savings Protection Bonds with a biannual interest payment and

protection against inflation (BPA182)

Disclaimer: This technical note does not substitute its original version in Spanish for any legal

purpose. It is solely intended for guidance and didactic use.

TECHNICAL DESCRIPTION OF THE BONOS DE PROTECCIÓN AL AHORRO CON PAGO SEMESTRAL DE INTERÉS Y PROTECCIÓN CONTRA LA INFLACIÓN (SAVINGS PROTECTION BONDS WITH A

BIANNUAL INTEREST PAYMENT AND PROTECTION AGAINST INFLATION, BPA182) ISSUED BY THE INSTITUTO PARA LA PROTECCIÓN AL AHORRO BANCARIO (INSTITUTE FOR THE PROTECTION OF

BANK SAVINGS, IPAB)*

1. INTRODUCTION

The Instituto para la Protección al Ahorro Bancario (Institute for the Protection of Bank Savings,

IPAB), on the basis of Article 2 of the Federal Income Law for the fiscal year of 2004, decided to

issue Bonos de Protección al Ahorro con pago semestral de interés y protección contra la inflación

(Savings Protection Bonds with a biannual interest payment and protection against inflation,

BPA182). IPAB uses Banco de México as its financial agent.

The issues are made for the sole purpose of exchanging or refinancing IPAB’s financial needs to

meet its payment obligations, provide liquidity for its securities, and, in general, to improve

the terms and conditions of its financial obligations.

The purpose of this note is to present a technical description of these instruments so that public

and financial intermediaries have better information on these securities.

DESCRIPTION

2.1 Name

Bonos de Protección al Ahorro con pago semestral de interés y protección contra la inflación

(Savings Protection Bonds with a biannual interest payment and protection against inflation,

BPA182)

2.2 Face value

100 pesos (one hundred pesos)

2.3 Term

The securities can be issued for any term as long as their maturity is a multiple of 182 days. The

securities are issued at 2548-day terms (7 years).

* The present document is only a translation of the original Spanish. It has no validity for official purposes.

For any official purpose, please refer to the original document via the following link: BPA 182

2.4 Interest rate period

These periods must be the same as those of Certificados de la Tesorería de la Federación (CETES,

Treasury Bills) for of six-month maturities, or the term substituting it in the event of a holiday,

issued at the beginning of that period. The securities accrue interest in pesos.

2.5 Interest rate

The BPA182 interest rate is composed of two elements: a market reference rate determined at the

beginning of each interest period, and an option that protects the holder from the possibility of

receiving a negative real interest rate.

2.6 Reference rate

The reference rate for the BPA182 is the rate of return on CETES issued in a primary auction for

terms of 182 days, or the term substituting it in the event of a holiday, corresponding to the week

in which interest begins to accrue. In the event that no CETES are placed for the corresponding

term, the rate is based on the rate of return on CETES issued in the primary market with the

closest term to 182 days converted to the proper term.1

2.7 Protection against inflation

BPA182 offer holders an option that protects them from unexpected changes in inflation,

eliminating the possibility of a negative real interest rate. Whenever the percentage increase in the

value of an inflation-indexed Investment Unit (UDI) over the interest period is greater than

the return on 182-day CETES, the security pays the holder the reference rate, plus an

additional premium determined on the basis of the difference between the percentage increase

in the value of the UDI and the return on 182-day CETES.

1

The method for converting interest rates to different terms is presented in Appendix 3.

Where:

= Value of the UDI corresponding to the payment day of coupon J

= Value of the UDI corresponding to the first day of coupon J

= Term of coupon J in days

= Interest rate of 182-day CETES issued in the primary auction at the beginning of

coupon J

2.8 Interest payment

Interest is calculated on the basis of the number of effective days elapsed between the interest

payment dates, using 360-day years, and is paid at the end of each interest rate period, according

to the following formula:

Where:

= Interest to be paid at the end of period J

= Annual interest rate of coupon J

VN = Face value of the security in pesos

= Term of coupon J in days

2.9 Primary issuance

The securities are issued through auctions, where participants submit their bids for the amount

they desire to purchase and the price they are willing to pay. The rules to participate in these

auctions are the same as those for government securities auctions, as described in Banco de

México’s Circular 5/2012, which is addressed to credit institutions, brokerage houses, mutual

funds, pension funds and Financiera Rural.

The method for pricing BPA182 is shown in Appendix 1.

Often in the primary auctions, IPAB offers securities originally issued prior to the auction date. In

these cases, auctions are carried out at a clean price (with no accrued interest) this means that

investors who buy these securities have to add the accrued interest of the current coupon to

the allotted price resulting from the auction, according to the following formula:

Where:

= Accrued interest (rounded to 12 decimal points) during period J.

= Days accrued between the issue date or the last interest payment (J – 1),

whichever applies, and the valuation date.

A practical example is presented in Appendix 2.

2.10 Secondary market

Today, it is possible to carry out outright sale and repo transactions as well as securities’ lending

transactions. BPATs can also be used as underlying assets in derivative markets (futures and

options), although up to now they have never been used as such. Direct sales can be made

by quoting either their price or their “sobretasa” (spread in percentage points associated to coupon

interest rate). In fact, the actual market convention is to quote them through their “sobretasa”.

Appendix 1 describes the market convention method for calculating a BPA182’s price and for

determining the “sobretasa”. Appendix 2 shows an example of how to calculate these instruments’

price using a “sobretasa”.

2.11 Securities identification

The BPA182 series identification is designed to be fungible. This means that previously and

recently issued BPAT182s can have the same code as long as they have the same maturity

date. Identification codes have eight characters. The first two identify the security (“IS”), and the

remaining six characters indicate the security’s maturity date (year, month, day). The relevant

number to identify a BPA182 is the maturity date. This means that two BPA182s issued on different

dates but maturing on the same date will have the same identification code and therefore cannot

be distinguished from each other.

Example of BPA182 series issued on September 22, 2005 for a 7-year term (2548 days) and

maturing September 13, 2012: IS120913.

2.12 Fiscal regime

BPA182s’ fiscal regime is outlined in the Ley del Impuesto sobre la renta (Income Tax Law) and in

the current applicable regulations issued by the Secretaría de Hacienda y Crédito Público (Ministry

of Finance, SHCP).

APPENDIX 1

BPA182 VALUATION

There are several ways to quote and value these securities in the market. This appendix shows

a general methodology for pricing BPA182.

I. GENERAL METHODOLOGY FOR VALUING BPA182

The general formula for valuing BPA182s is the following:

Where:

= BPA182 clean price (rounded to 5 decimal points)

(1)

= Face value of the security

= Number of coupons to be paid, (including the current one)

= Number of elapsed days for the current coupon

= Term in days of coupon j

= Coupon j, which is calculated as follows:

= Annual interest rate of coupon j

Where:

= Value of the UDI corresponding to the payment day of coupon j

(2)

= Value of the UDI corresponding to the first day of coupon j

= Interest rate of 182-day CETES issued via primary auction at the beginning of

coupon j

= Discount factor for cash flow j. Calculated according to the following formula:

Where:

= Expected internal rate of return for coupon j

= Relevant interest rate for discounting coupon j

= “Sobretasa” (spread associated to coupon j’s interest rate)

Rewriting (2) yields:

Where:

By substituting (4) in (1):

(4)

(5)

Notice that in the previous equation, when j = 1, the values of N1, TC1, r1, and s1 a r e known (they

correspond to the values for the first coupon). Thus, to solve equation (1), the values of Nj, TCj, rj,

and s j must be estimated, for j = 2, 3,…, K. A simple estimation is to assign “fixed” values to N,

TC, r. Assuming that the rate for future coupons and the rate for discounting cash flows are

the same (TC = r), equation (1) simplifies to:

(6)

4

4 0

4

0 4

APPENDIX 2

A PRACTICAL EXAMPLE

1. On September 25, 2005 the Institute for the Protection of Bank Savings issues BPA182s with

the following characteristics:

Face value: 100 pesos

Issue date: September 22, 2005

Maturity date: September 13, 2012

Days to maturity: 2548 days

Coupon: 8.79%

Term of the coupon: 182 days

2. On October 12, 2005 the IPAB decides to auction BPA182s issued on September 22, 2005. The

payment date for the auction results is October 13. On this date, the securities will still

have

2,527 days to mature, and 21 days will have elapsed for the first coupon. The securities will be

auctioned the same way they were issued; i.e., at a clean price (without accrued interest) .

Therefore, the accrued interest of the first coupon will have to be added to the allotment price

in order to calculate the payment.

For example, assume that an investor wants to participate in an auction of these securities. The

investor has an expected rate of 8.89% and a “sobretasa” of 0.21%. In order to find the

corresponding clean price, equation (6) from Appendix 1 is applied.

.44383

.49439* 1

.04601

0.04601 *

1.04601

1

13

1.04601

161

182

100

13

1.04601

.44383* 21

182

P 4.44383 3.25226

1.04059

55.7260

3

.51275

P= 98.87512 rounded to 5 decimal points

The price of 98.87512 will be the bid that the investor presents for each security desired for

purchase. Assuming that the investor receives an allotment for this bid, on October 13 the investor

would have to pay the following for each security:

38787.9951275.087512.98360

0879.0*21*10087512.98

APPENDIX 3

DETERMINING THE EQUIVALENT RATE

A CETE’s implicit rate of return for a different term can be computed according to the following

formula:

Where:

= Equivalent annual interest rate

= CETES original rate of return

= CETES original term

= Term in days of the equivalent interest rate

Assume that an investor wants to know the equivalent 182-days rate for a 91-day term CETE where

the rate of return is 8.89%. According to the previous formula: