GOVERNMENT DEVELOPMENT BONDS DENOMINATED IN UDIS
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 BONOS DE DESARROLLO DEL GOBIERNO FEDERAL
DENOMINADOS EN UNIDADES DE INVERSIÓN (FEDERAL GOVERNMENT
DEVELOPMENT BONDS DENOMINATED IN INVESTMENT
UNITS, UDIBONOS)*
1.
INTRODUCTION
The Bonos de Desarrollo del Gobierno Federal denominados en unidades de inversión
(Federal Government Development Bonds denominated in investment units, UDIBONOS)
were developed in 1996. They are investment instruments that protect the holder from
unexpected changes in the inflation rate. UDIBONOS are sold at long terms and pay
interest every six months based on a real fixed interest rate which is determined on
the issue date of each security.
2.
DESCRIPTION
2.1
Name
Bonos de Desarrollo del Gobierno Federal denominados en unidades de inversión (Federal
Government Development Bonds denominated in investment units, UDIBONOS).
2.2
Face value
100 UDIS1 (One hundred investment units).
2.3
Term
They can be issued for any term as long as this term is a multiple of 182 days.
Nevertheless, up to now these securities have been issued at terms of 3 , 5 , 1 0 , 2 0
and 3 0 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:
http://www.banxico.org.mx/sistema-financiero/material-educativo/intermedio/subastas-y-colocacion-de-valores/primarias-devalores-gubernamentales/notas-tecnicas-y-titulos-multiples/%7B63DB33B1-8AE4-4E40-68D3-82F833563599%7D.pdf
1
In 1995, Mexico introduced a price-level-adjusting unit of account called the Unidad de Inversión (UDI). An UDI is a unit of
account of real constant value (in contrast with the nominal value, the real value
eliminates the inflation effect). UDIs are numerical units of measurement for credit instruments, trading
contracts, and other financial operations. The value of the UDI changes every day and is calculated based on the information from the
previous two weeks, which is calculated and published by Banco de México in the Diario Oficial de la Federación (Official Gazette).
UDIS value can be found at http://www.banxico.org.mx/portal-inflacion/index.html
1
2.4
Interest payment period
The securities pay interest in pesos every six months; that is, every 182 days or the
equivalent period in the event of a holiday.
2.5
Interest rate
The interest rate the securities pay is fixed by the Federal Government upon issuance of
the securities and is specified to investors in the auction announcement and through its
publications in the main newspapers every time a new series is issued.
2.5.1 Interest payment
Interest is calculated given the days elapsed between payment dates, on the basis of a
360- day year, and paid at the end of each of these payment periods.
IJ
VN *
N J * TC
360
where:
IJ
= Interest to be paid at the end of period J
TC = Annual coupon interest rate
VN = Face value of the security in investment units (UDIS)
NJ
2.6
= Term in days of coupon J
Primary issuance
The securities are placed through auctions in which participants submit their bids for the
amount they desire to purchase at the price they are willing to pay denominated in UDIS.
The rules to participate in these auctions are described in Banco de México’s Circular
5/2012, which is addressed to credit institutions, brokerage houses, mutual funds,
pension funds and Financiera Rural.
Often, in the primary auctions, the federal government offers securities originally
issued prior to their auction date. In these cases, auctions are carried out at clean prices
(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 according to
the following formula:
I accJ
VN *
d * TC
360
2
where:
IaccJ =Accrued interest (rounded up to 12 decimal points and in UDIs) during
period J
d =Days elapsed between the issue date or the last interest rate period (J – 1),
whichever applies, and the valuation date
2.7
Conversion to domestic currency
For the purposes of the placement, interest payments, and amortization, the conversion
to domestic currency is made at the value of the UDI on the day that the corresponding
payments are made2.
2.8
Secondary market
Today, it is possible to carry out outright sale and repo transactions as well as securities
lending transactions with these securities, they 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 yield to maturity.
However, the current market convention is to quote them by their yield to maturity.
Appendix 1 describes the methodology used as a market convention to calculate the price
and yield to maturity of UDIBONOS. Appendix 2 shows a practical example of how to
calculate the price using an expected yield to maturity.
2.9
Securities Identification
Because each issue of these securities has a different fixed real interest rate from the
date of issuance until maturity, UDIBONOS are not fungible unless they pay exactly the
same interest rate. For this reason, the issuance identification code is made up of
eight characters. The first identifies the security (“S”), second blank space and the
remaining six, to indicate its maturity date (year, month, day).
Example of an identification code for a UDIBONO issued on January 18, 2001, at a term
of 10 years (3,640 days) and maturing on January 6, 2011:
S 110106
2
UDIS value can be found at:
http://www.banxico.org.mx/portal-inflacion/index.html
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APPENDIX 1
UDIBONOS VALUATION
There are several ways to quote and valuing these securities in the market. This
appendix shows a general methodology for pricing UDIBONOS.
I.
GENERAL METHODOLOGY FOR VALUING UDIBONOS
The general formula for valuing UDIBONOS is the following:
P
 C
K
j 1
j
* Fj
  F
K

d 
* VN   
 C1 N 

1 

(1)
where:
P
= “Clean” UDIBONOS price (rounded to 5 decimal places)
VN = Face value of the security
K =
d
Number of coupons to be paid (including the current one)
= Number of days elapsed
N j = Term in days of coupon j
C j = Coupon j, which is calculated as follows:
C j  VN *
N j * TC
360
TC = Annual interest rate of the coupon
4
F j = Discount factor for cash flow j, calculated according to the
following formula:
Fj 
1
N 

1  r j * j 
360 

j
d
N1
r j = Relevant interest rate for discounting coupon j
In formula (1), the price of the UDIBONO is comprised of three different
elements: the present value of the coupons, the present value of the
principal, and the accrued interest rate on the current coupon. Thus, each
of the coupons, as well as the principal, are discounted at a different interest
rates, making it necessary to know or estimate an interest rate for each
discount factor.
II.
DETERMINATION OF A
YIELD TO MATURITY.
UDIBONOS CLEAN PRICE THROUGH THE
There are many markets that quote securities with UDIBONOS features
according to their yield to maturity. UDIBONO’s yield to maturity can be
defined as the yield an investor would obtain by holding the security
until maturity. To determine the price of a UDIBONO, once its yield to
maturity is known, all the security’s cash flows (coupons and principal) must
be discounted at the same interest rate rj .
By knowing the security’s yield to maturity, general formula (1) can be
enormously simplified, because the interest rates rj to discount the
different present values of the cash flows become the same for all the
discount factors. Thus, once the yield to maturity is known and assuming
that the term in days of all the coupons is the same, the general formula can
be expressed as follows:



1
VN
C C1 

K 1 
K 1

R



R

1

R
1

R


P
d 

 1


 182 


1

R





d
C
182



(2)
5
Where:
C  VN *
182 * TC
360
R r
182
360
r= Annual yield to maturity
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APPENDIX 2
A PRACTICAL EXAMPLE
1.
On January 18, 2001, the federal government issues UDIBONOS with the
following characteristics:
Face value:
Issue date:
Maturity date:
Days to maturity:
Coupon:
Coupon term:
2.
100 UDIs
January 18, 2001
January 6, 2011
3640 days
8%
182 days
On February 6, 2001, the federal government auctions UDIBONOS originally
issued on January 18, 2001. The payment date from the auction’s result is
February 8, 2001. On this date, the securities will still have 3619 days to mature
and 21 days will already have elapsed for the first coupon payment period. The
security is auctioned the same way it was issued; that is, at a “clean price”
(not including accrued interest), Therefore, the accrued interest for the first
coupon will have to be added to the allotment price in order to calculate the
results’ payments.
For example, let us assume that an investor wants to participate in an auction of these
securities by submitting a bid equivalent to an annual yield of 8.25% in UDIS, in order to
find the corresponding clean price, (2) from Appendix 1 is applied.



1
1
100 


 4.04444  4.04444 * 

19 
0.04170 0.041701.04170   1.0417019 
21


P  100 * 
 4.04444 *
161/ 182

182
1.04170




4.04444  52.35690441  46.00694233
P
 0.466667
1.0368084
= 98.30596 UDIS
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The price 98.30596 will be the bid the investor presents for each security that he desires to
buy. Supposing that he relieves an allocation to such posture, the 8th of February the investor
will have to pay for each title:
 21 * 0.08 
98.30596  I dev  98.30596  100
  98.77262 UDIS
 360 
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