. 1
( 10)



>>

The Global
money markets
THE FRANK J. FABOZZI SERIES

Fixed Income Securities, Second Edition by Frank J. Fabozzi
Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L.
Grant and James A. Abate
Handbook of Global Fixed Income Calculations by Dragomir Krgin
Managing a Corporate Bond Portfolio by Leland E. Crabbe and Frank J. Fabozzi
Real Options and Option-Embedded Securities by William T. Moore
Capital Budgeting: Theory and Practice by Pamela P. Peterson and Frank J. Fabozzi
The Exchange-Traded Funds Manual by Gary L. Gastineau
Professional Perspectives on Fixed Income Portfolio Management, Volume 3 edited
by Frank J. Fabozzi
Investing in Emerging Fixed Income Markets edited by Frank J. Fabozzi and
Efstathia Pilarinu
Handbook of Alternative Assets by Mark J. P. Anson
The Exchange-Traded Funds Manual by Gary L. Gastineau
The Handbook of Financial Instruments edited by Frank J. Fabozzi
The Global
money markets
FRANK J. FABOZZI
STEVEN V. MANN
MOORAD CHOUDHRY




John Wiley & Sons, Inc.
FJF
To my wife, Donna,
and my children, Karly, Patricia, and Francesco

SVM
To my wife Mary and our daughters Meredith and Morgan.

MC
To Olga”like the wild cat of Scotland,
both elusive and exclusive¦

The views, thoughts and opinions expressed in this book are those of the authors in their pri-
vate capacity and should not be taken to be representative of any employing institution or
named body. The views of Moorad Choudhry are those of his in his individual capacity and
should not in any way be attributed to JPMorgan Chase Bank, or to Moorad Choudhry as a
representative, of¬cer or employee of JPMorgan Chase Bank.
While every effort has been made to ensure accuracy, no responsibility for loss occasioned to
any person acting or refraining from action as a result of any material in this book can be
accepted by the author(s), publisher or any named person or entity.
Copyright ™ 2002 by Frank J. Fabozzi. All rights reserved.
Published by John Wiley & Sons, Inc., Hoboken, New Jersey
Published simultaneously in Canada
No part of this publication may be reproduced, stored in a retrieval system, or transmitted in
any form or by any means, electronic, mechanical, photocopying, recording, scanning, or oth-
erwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright
Act, without either the prior written permission of the Publisher, or authorization through
payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rose-
wood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at
www.copyright.com. Requests to the Publisher for permission should be addressed to the Per-
missions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, 201-
748-6011, fax 201-748-6008, e-mail: permcoordinator@wiley.com.
Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best
efforts in preparing this book, they make no representations or warranties with respect to the accu-
racy or completeness of the contents of this book and speci¬cally disclaim any implied warranties
of merchantability or ¬tness for a particular purpose. No warranty may be created or extended by
sales representatives or written sales materials. The advice and strategies contained herein may not
be suitable for your situation. You should consult with a professional where appropriate. Neither
the publisher nor author shall be liable for any loss of pro¬t or any other commercial damages,
including but not limited to special, incidental, consequential, or other damages.
For general information on our other products and services, or technical support, please con-
tact our Customer Care Department within the United States at 800-762-2974, outside the
United States at 317-572-3993 or fax 317-572-4002.
Wiley also publishes its books in a variety of electronic formats. Some content that appears in
print may not be available in electronic books.
ISBN: 0-471-22093-0
Printed in the United States of America
10 9 8 7 6 5 4 3 2 1
contents



About the Authors vii
Acknowledgements viii

CHAPTER 1
Introduction 1

CHAPTER 2
Money Market Calculations 7

CHAPTER 3
U.S. Treasury Bills 23

CHAPTER 4
Agency Instruments 45

CHAPTER 5
Corporate Obligations: Commercial Paper and Medium-Term Notes 67

CHAPTER 6
Debt Obligations of Financial Institutions 85

CHAPTER 7
Floating-Rate Securities 101

CHAPTER 8
Repurchase and Reverse Repurchase Agreements 119

CHAPTER 9
Short-Term Mortgage-Backed Securities 151

CHAPTER 10
Short-Term Asset-Backed Securities 187


v
vi Contents



CHAPTER 11
Futures and Forward Rate Agreements 209

CHAPTER 12
Swaps and Caps/Floors 229

CHAPTER 13
Asset and Liability Management 275

CHAPTER 14
Bank Regulatory Capital 297

INDEX 315
about the authors



Frank J. Fabozzi is editor of the Journal of Portfolio Management and an
adjunct professor of ¬nance at Yale University™s School of Management. He
is a Chartered Financial Analyst and Certi¬ed Public Accountant. Dr.
Fabozzi is on the board of directors of the Guardian Life family of funds
and the BlackRock complex of funds. He earned a doctorate in economics
from the City University of New York in 1972 and in 1994 received an
honorary doctorate of Humane Letters from Nova Southeastern University.
Dr. Fabozzi is a Fellow of the International Center for Finance at Yale Uni-
versity. He is an Advisory Analyst for Global Asset Management (GAM)
with responsibilities as Consulting Director for portfolio construction, risk
control, and evaluation.

Steven V. Mann is a Professor of Finance at the Darla Moore School of
Business, University of South Carolina. He earned a doctorate in ¬nance
from the University of Nebraska in 1987. His research interests are in the
area of investments, particularly ¬xed-income securities and derivatives. He
has published over 35 articles in ¬nance journals and books. Dr. Mann is
an accomplished teacher, winning 16 awards for excellence in teaching. He
is a consultant to investment/commercial banks and has conducted more
than 60 training programs for ¬nancial institutions throughout the United
States.

Moorad Choudhry is a vice-president in structured ¬nance services with
JPMorgan Chase in London. He previously worked as a government bond
trader and money markets trader at ABN Amro Hoare Govett Sterling
Bonds Limited, and as a sterling proprietary trader at Hambros Bank Lim-
ited. Moorad is a senior Fellow at the Centre for Mathematical Trading
and Finance, City University Business School, and is also a Fellow of the
Securities Institute. He is Editor of the Journal of Bond Trading and Man-
agement, and has published widely in the ¬eld of debt capital markets,
derivatives, and yield curve analysis.




vii
acknowledgements



The authors wish to thank Dean Joel Smith and Professor Greg Niehaus for
their efforts in bringing a Bloomberg terminal to the Moore School of Busi-
ness. The following graduate students at the Moore School of Business
assisted in proofreading the book: Oscar Arostegui, Keshiv Desai, Jeffrey
Dunn, and Brandon Wilson. In addition, we want to thank Michael Ken-
ney for his assistance.




viii
1
CHAPTER

Introduction



he money market is traditionally de¬ned as the market for ¬nancial
T assets that have original maturities of one year or less. In essence, it is
the market for short-term debt instruments. Financial assets traded in
this market include such instruments as U.S. Treasury bills, commercial
paper, some medium-term notes, bankers acceptances, federal agency
discount paper, most certi¬cates of deposit, repurchase agreements,
¬‚oating-rate agreements, and federal funds. The scope of the money
market has expanded in recent years to include securitized products
such mortgage-backed and asset-backed securities with short average
lives. These securities, along with the derivative contracts associated
with them, are the subject of this book.
The workings of the money market are largely invisible to the aver-
age retail investor. The reason is that the money market is the province
of relatively large ¬nancial institutions and corporations. Namely, large
borrowers (e.g., U.S. Treasury, agencies, money center banks, etc.) seek-
ing short-term funding as well as large institutional investors with excess
cash willing to supply funds short-term. Typically, the only contact retail
investors have with the money market is through money market mutual
funds, known as unit trusts in the United Kingdom and Europe.
Money market mutual funds are mutual funds that invest only in
money market instruments. There are three types of money market funds:
(1) general money market funds, which invest in wide variety of short-term
debt products; (2) U.S. government short-term funds, which invest only in
U.S. Treasury bills or U.S. government agencies; and (3) short-term munic-
ipal funds. Money market mutual funds are a popular investment vehicle
for retail investors seeking a safe place to park excess cash. In Europe, unit
trusts are well-established investment vehicles for retail savers; a number
of these invest in short-term assets and thus are termed money market unit

1
2 THE GLOBAL MONEY MARKETS



trusts. Placing funds in a unit trust is an effective means by which smaller
investors can leverage off the market power of larger investors. In the UK
money market, unit trusts typically invest in deposits, with a relatively
small share of funds placed in money market paper such as government
bills or certi¬cates of deposit. Investors can invest in money market funds
using one-off sums or save through a regular savings plan.



THE MONEY MARKET
The money market is a market in which the cash requirements of market
participants who are long cash are met along with the requirements of
those that are short cash. This is identical to any ¬nancial market; the
distinguishing factor of the money market is that it provides for only
short-term cash requirements. The market will always, without fail, be
required because the needs of long cash and short cash market partici-
pants are never completely synchronized. The participants in the market
are many and varied, and large numbers of them are both borrowers
and lenders at the same time. They include:

– the sovereign authority, including the central government (“Treasury”),
as well as government agencies and the central bank or reserve bank;
– ¬nancial institutions such as the large integrated investment banks,
commercial banks, mortgage institutions, insurance companies, and
¬nance companies;
– corporations of all types;
– individual private investors, such as high net-worth individuals and
small savers;
– intermediaries such as money brokers, banking institutions, etc.;
– infrastructure of the marketplace, such as derivatives exchanges.

A money market exists in virtually every country in the world, and all
such markets exhibit the characteristics we describe in this book to some
extent. For instance, they provide a means by which the con¬‚icting needs
of borrowers and lenders can achieve equilibrium, they act as a conduit
for ¬nancing of all maturities between one day and one year, and they can
be accessed by individuals, corporations, and governments alike.
In addition to national domestic markets, there is the international
cross-border market illustrated by the trade in Eurocurrencies.1 Of


1
A Eurocurrency is a currency that is traded outside of its national border, and can
be any currency rather than just a European one.
3
Introduction



course, there are distinctions between individual country markets, and
¬nancial market culture will differ. For instance, the prevailing ¬nancial
culture in the United States and United Kingdom is based on a second-
ary market in tradable ¬nancial assets, so we have a developed and liq-
uid bond and equity market in these economies. While such an
arrangement also exists in virtually all other countries, the culture in
certain economies such as Japan and (to a lesser extent) Germany is
based more on banking relationships, with banks providing a large pro-
portion of corporate ¬nance. The differences across countries are not
touched upon in this book; rather, it is the similarities in the type of
instruments used that is highlighted.
In developed economies, the money market is large and liquid.
Exhibit 1.1 illustrates the market growth in the United States during the
1990s. Exhibit 1.2 illustrates the breakdown of the United Kingdom
money market by different types of instrument, each of which we cover
in detail in this book.



OVERVIEW OF THE BOOK
In Chapter 2 we cover money market calculations. The intent of this
chapter is to introduce some of the fundamental money market calcula-
tions and conventions that will be used throughout this book, including
day count conventions, as well as the basic formulae for price and yield.
It is essential to understand these calculations since some market instru-
ments are interest bearing while others are discount instruments. More-
over, some instruments calculate interest based on a 360-day year and
some money market securities use a 365-day year.

EXHIBIT 1.1 US Money Market Volumes, $ Billion at Year-End

Instrument 1990 1995 1999

Treasury bills 527 748 723
Federal agency securities 435 845 1,284
Commercial paper 561 675 1,213
Bankers™ acceptances 55 29 21
Fed funds borrowers and repo 409 569 762
Eurodollar borrowings 37 94 167
CDs (min size $100,000) 432 345 634

Source: Federal Reserve Bulletin, 2000, 2001
4 THE GLOBAL MONEY MARKETS



EXHIBIT 1.2 Composition of Sterling Money Markets,
£ Billion Volume Outstanding




* Includes Treasury bills, sell/buy-backs and local authority bills
Source: Bank of England Quarterly Bulletin, Autumn 2001

Chapters 3 and 4 cover short-term debt instruments issued by some
of the largest borrowers in the world”the U.S. Treasury and U.S. fed-
eral agencies. U.S. Treasury bills are considered among the safest and
most liquid securities in the money market. Treasury bill yields serve as
benchmark short-term interest rates for markets around the world.
Agency securities are not typically backed by the full faith and credit of
the U.S. government, as is the case with Treasury bills. However, short-
term agency securities are considered safer than other money market
instruments except U.S. Treasury bills.
Another large borrower of short-term funds is a corporation using
instruments such as commercial paper or short-term medium term
notes. These instruments are the subject of Chapter 5. Commercial
paper is a short-term unsecured promissory note that is issued in the
open market and represents the obligation of the issuing corporation.
An important innovation in this market is asset-backed commercial
paper. Asset-backed commercial paper is commercial paper issued by
either corporations or large ¬nancial institutions through a bankruptcy-
remote special purpose corporation and is usually issued to ¬nance the
purchase of receivables and other similar assets. In contrast, a medium-
5
Introduction



term note is a corporate debt instrument with the unique characteristic
that notes are offered continuously to investors by an agent of the
issuer. The maturities of medium-term notes range from 9 months to 30
years or longer. Our focus will be on medium-term notes with original
maturities of one year or less.
The largest group of players in the global money markets are ¬nan-
cial institutions that include depository institutions, investment banks,
and insurance companies. These institutions are simultaneously the big-
gest investors in and issuers of money market instruments. There are
specialized instruments that are unique to this group of borrowers
which include certi¬cates of deposits, bankers acceptances, federal
funds, and funding agreements. Chapter 6 details these instruments.
Chapter 7 describes short-term ¬‚oating-rate securities. The term
“¬‚oating-rate security” covers several different types of instruments
with one common feature: the security™s coupon rate will vary over the
life of the instrument. Approximately, 10% of publicly traded debt
issued worldwide possesses a ¬‚oating coupon. Floating-rate securities
are the investment of choice for ¬nancial institutions whose funding
costs are based on a short-term ¬‚oating rate.
One of the largest segments of the global money markets is the mar-
ket for repurchase agreements. The repurchase agreement on one hand
is an ef¬cient mechanism used by security dealers to ¬nance bond posi-
tions, and on the other a relatively safe investment opportunity for
investors such as money market funds and corporations. In Chapter 8,
we review repurchase agreements as well as their major uses.
Chapters 9 and 10 cover short-term mortgage-backed and asset-
backed securities. Mortgage-backed securities are securities backed by a
pool of mortgage loans. The pool of loans is referred to as the collateral.
While residential mortgages are by far the largest type of asset that has
been securitized, other assets such as consumer loans, business loans
and receivables have also been securitized. Securities backed by collat-
eral other the mortgage loans are called asset-backed securities. The
largest sectors of the asset-backed securities market in the United States
are securities backed by credit card receivables, auto loans, home equity
loans, manufactured housing loans, and student loans.
Derivatives are ¬nancial instruments that derive their value from
some underlying price, index, or interest rate. Money market practitioners
use derivatives to control their exposure to risk by taking positions to
either diminish or enhance this exposure. In Chapters 11 and 12, we
describe these derivative instruments and how they are employed to create
advantageous risk and return patterns. Chapter 11 describes forward con-
tracts, futures contracts, and forward rate agreements. Chapter focuses on
swap contracts and caps/¬‚oors.
6 THE GLOBAL MONEY MARKETS



The activity of ¬nancial institutions in the money market involves an
activity known as asset and liability management. Asset and liability
management is the term covering tools and techniques used by ¬nancial
institutions to manage various types of risk while achieving its pro¬t
objectives by holding the optimal combination of assets and liabilities.
We introduce the fundamental principles of asset and liability manage-
ment in Chapter 13. An appreciation of these concepts and tools is essen-
tial to an understanding of the functioning of the global money markets.
The ¬nal chapter of the book, Chapter 14, describes bank regula-
tory capital issues. As noted, the primary players in the global money
markets are large ¬nancial institutions, in particular depository institu-
tions. These entities are subject to risk-based capital requirement. The
asset allocation decisions by managers of depository institutions are
largely in¬‚uenced by how much capital they are compelled to hold and
the capital costs incurred. As a result, these money market participants
must risk-based capital issues regardless of the products they trade or
else they will not fully understand the cost of their own capital or the
return on its use.
2
CHAPTER

Money Market Calculations



he intent of this chapter is to introduce some of the fundamental
T money market calculations that will be used throughout this book.
We will cover such topics as day count conventions, as well as the basic
formulas for price and yield.



DAY COUNT CONVENTIONS
To those unfamiliar with the workings of ¬nancial markets, it may come
as a shock that there is no widespread agreement as to how many days
there are in a year. The procedures used for calculating the number of
days between two dates (e.g., the number of days between the settle-
ment date and the maturity date) are called day count conventions. Day
count conventions vary across different types of securities and across
countries. In this section, we will introduce the day count conventions
relevant to the money markets.

Day Count Basis
The day count basis speci¬es the convention used to determine the num-
ber of days in a month and in a year. According to the Securities Indus-
try Association Standard Securities Calculation Methods book, Volume
2, the notation used to identify the day count basis is:1

(number of days in a month)/(number of days in a year)


1
See, Jan Mayle, Standard Securities Calculation Methods, Volume 2 (New York;
Securities Industry Association, 1994).

7
8 THE GLOBAL MONEY MARKETS



Although there are numerous day count conventions used in the
¬xed-income markets around the world, there are three basic types.2 All
day count conventions used worldwide are variations of these three
types. The ¬rst type speci¬es that each month has the actual number of
calendar days in that month and each year has the actual number of cal-
endar days in that year or in a coupon period (e.g., Actual/Actual). The
second type speci¬es that each month has the actual number of calendar
days in that month but restricts the number of days in each year to a
certain number of days regardless of the actual number of days in that
year (e.g., Actual/360). Finally, the third types restricts both the number
of days in a month and in a year to a certain number of days regardless
of the actual number of days in that month/year (e.g., 30/360). Below
we will de¬ne and illustrate the three types of day count conventions.

Actual/Actual
Treasury notes, bonds and STRIPS use an Actual/Actual (in period) day
count convention. When calculating the number of days between two
dates, the Actual/Actual day count convention uses the actual number of
calendar days as the name implies. Let™s illustrate the Actual/Actual day
count convention with a 3.625% coupon, 2-year U.S. Treasury note with
a maturity date of August 31, 2003. The Bloomberg Security Display
(DES) screen for this security is presented in Exhibit 2.1. In the “Security
Information” box on the left-hand side of the screen, we see that the day
count is speci¬ed as “ACT/ACT.” From the “Issuance Info” box on the
right-hand side of the screen, we see that interest starts accruing on
August 31, 2001 (the issuance date) and the ¬rst coupon date is February
28, 2002. Suppose this bond is traded with a settlement date of Septem-
ber 11, 2001. How many days are there between August 31, 2001 and
September 11, 2001 using the Actual/Actual day count convention?
To answer this question, we simply count the actual number of days
between these two dates.3 To do this, we utilize Bloomberg™s DCX (Days
Between Dates) function presented in Exhibit 2.2. The function tells us
there are 11 actual days between August 31, 2001 and September 11,
2001.4 In the same manner, we can also determine the actual number of
calendar days in the full coupon period. A full 6-month coupon period can
only have 181, 182, 183 or 184 calendar days. For example, the actual
number of days between August 31, 2001 and February 28, 2002 is 184.


2
Bloomberg identifies 24 different day count conventions.
3
This is easy to accomplish using software that can convert a Gregorian date (MM/
DD/YY) into a Julian date (the number of days since some base date).
4
Note that the settlement date (September 11) is not counted.
9
Money Market Calculations



EXHIBIT 2.1 Bloomberg Security Description Screen for a
2-Year U.S. Treasury Note




Source: Bloomberg Financial Markets

EXHIBIT 2.2 Bloomberg DCX (Days Between Dates) Screen




Source: Bloomberg Financial Markets
10 THE GLOBAL MONEY MARKETS



EXHIBIT 2.3 Bloomberg Security Description Screen of a
26-Week U.S. Treasury Bill




Source: Bloomberg Financial Markets

Actual/360
Actual/360 is the second type of day count convention. Speci¬cally,
Actual/360 speci¬es that each month has the same number of days as
indicated by the calendar. However, each year is assumed to have 360
days regardless of the actual number of days in a year. Actual/360 is the
day count convention used in U.S. money markets. Let™s illustrate the
Actual/360 day count with a 26-week U.S. Treasury bill which matures
on March 7, 2002. The Bloomberg Security Display (DES) screen for this
security is presented in Exhibit 2.3. From the “Security Information” box
on the left-hand side of the screen, we see that the day count is speci¬ed
as “ACT/360.” Suppose this Treasury bill is purchased with a settlement
date on September 11, 2001 at a price of 98.466. How many days does
this bill have until maturity using the Actual/360 day count convention?
Once again, the question is easily answered using Bloomberg™s DCX
(Days Between Dates) function and specifying the two dates of interest.
This screen is presented in Exhibit 2.4. We see that with a settlement date
of September 11, 2001 there are 177 calendar days until maturity on
March 7, 2002. This can be con¬rmed by examining the Bloomberg™s YA
(Yield Analysis) screen in Exhibit 2.5. We see that with a settlement date of
September 11, 2001 this Treasury bill has 177 days to maturity. This infor-
mation is located just above the “Price” box in the center of the screen.
11
Money Market Calculations



EXHIBIT 2.4 Bloomberg DCX (Days Between Dates) Screen




Source: Bloomberg Financial Markets

EXHIBIT 2.5 Bloomberg Yield Analysis for a 26-Week U.S. Treasury Bill




Source: Bloomberg Financial Markets
12 THE GLOBAL MONEY MARKETS



When computing the number of days between two dates, Actual/360
and Actual/Actual will give the same answer. What then is the impor-
tance of the 360-day year in the Actual/360 day count? The difference is
apparent when we want to compare, say, the yield on 26-week Treasury
bill with a coupon Treasury which has six months remaining to maturity.
U.S. Treasury bills, like many money market instruments, are discount
instruments. As such, their yields are quoted on a bank discount basis
which determine the bill™s price (which we explain in detail in Chapter
3). The quoted yield on a bank discount basis for a Treasury bill is not
directly comparable to the yield on a coupon Treasury using an Actual/
Actual day count for two reasons. First, the Treasury bill™s yield is based
on a face-value investment rather than on the price. Second, the Treasury
bill yield is annualized according to a 360-day year while a coupon Trea-
sury™s yield is annualized using the actual number of days in a calendar
year (365 or 366). These factors make it dif¬cult to compare Treasury
bill yields with yields on Treasury notes and bonds. We demonstrate how
these yields can be adjusted to make them comparable shortly.
Another variant of this second day count type is the Actual/365. Actual/
365 speci¬es that each month has the same number of days as indicated by
the calendar and each year is assumed to have 365 days regardless of the
actual number of days in a year. Actual/365 does not consider the extra day
in a leap year. This day count convention is used in the UK money markets.

30/360
The 30/360 day count is the most prominent example of the third type of
day count convention which restricts both the number of days in a
month and in a year to a certain number of days regardless of the actual
number of days in that month/year. With the 30/360 day count all
months are assumed to have 30 days and all years are assumed to have
360 days. The number of days between two dates using a 30/360 day
will usually differ from the actual number of days between the two dates.
To determine the number of days between two dates, we will adopt
the following notation:
Y1 = year of the earlier date
M1 = month of the earlier date
D1 = day of the earlier date
Y2 = year of the later date
M2 = month of the later date
D2 = day of the later date

Since the 30/360 day count assumes that all months have 30 days,
some adjustments must be made for months having 31 days and Febru-
13
Money Market Calculations



ary which has 28 days (29 days in a leap year). The following adjust-
ments accomplish this task:5

1. If the bond follows the End-of-Month rule6 and D2 is the last day of
February (the 28th in a non-leap year and the 29th in a leap year) and
D1 is the last day of February, change D2 to 30.
2. If the bond follows the End-of-Month rule and D1 is the last day of
February, change D1 to 30.
3. If D2 is 31 and D1 is 30 or 31, change D2 to 30.
4. If D1 is 31, change D1 to 30.

Once these adjustments are made, the formula for calculating the
number of days between two dates is as follows:

Number of days = [(Y2 ’ Y1) — 360] + [(M2 ’ M1) — 30] + (D2 ’ D1)

To illustrate the 30/360 day count convention, let™s use a 4% coupon
bond which matures on August 15, 2003, issued by Fannie Mae. The
Bloomberg Security Description (DES) screen for this bond is presented in
Exhibit 2.6. We see that in the “Security Information” box that the bond
has a 30/360 day count. Suppose the bond is purchased with a settlement
date of September 11, 2001. We see from the lower left-hand corner of
the screen that the ¬rst coupon date is February 15, 2002 and the ¬rst
interest accrual date is August 27, 2001. How many days have elapsed in
the ¬rst coupon period from August 27, 2001 until the settlement date of
September 11, 2001 using the 30/360 day count convention?
Referring back to the 30/360 day count rule, we see that adjust-
ments 1 through 4 do not apply in this example so no adjustments to
D1 and D2 are required. Accordingly, in this example,
Y1 = 2001
M1 = 8
D1 = 27
Y2 = 2001
M2 = 9
D2 = 11

Inserting these numbers into the formula, we ¬nd that the number
of days between these two dates is 14, which is calculated as follows:


5
See, Mayle, Standard Securities Calculation Methods, Volume 2.
6
This is the standard convention for bonds in the U.S. and it states that if a bond™s
maturity date falls on the last day of the month so do the bond™s coupon payments.
14 THE GLOBAL MONEY MARKETS



Number of days = [ ( 2000 “ 2000 ) — 360 ] + [ ( 9 “ 8 ) — 30 ] + ( 11 “ 27 )
= 0 + 30 + ( “ 16 ) = 14

To check this, let™s employ Bloomberg™s DCX (Days Between Dates)
function presented in Exhibit 2.7. The function tells us there are 14 days
between August 27, 2001 and September 11, 2001 using a 30/360 day
count. Note that the actual number of days between these two dates is 15.



DISCOUNT INSTRUMENTS
Many money market instruments are discount securities (e.g. U.S. Trea-
sury bills, agency discount notes, and commercial paper). Unlike bonds
that pay coupon interest, discount securities are like zero-coupon bonds
in that they are sold at a discount from their face value and are
redeemed for full face value at maturity. Further, most discount securi-
ties use an ACT/360 day count convention. In this section, we discuss
how yields on discount securities are quoted, how discount securities
are priced, and how the yields on discount securities can be adjusted so
that they can be compared to the yields on interest-bearing securities.

EXHIBIT 2.6 Bloomberg Security Description Screen for a
Fannie Mae 2-Year Benchmark Note




Source: Bloomberg Financial Markets
15
Money Market Calculations



EXHIBIT 2.7 Bloomberg DCX (Days Between Dates) Screen




Source: Bloomberg Financial Markets

Yield on a Bank Discount Basis
The convention for quoting bids and offers is different for discount
securities from that of coupon-paying bonds. Prices of discount securi-
ties are quoted in a special way. Bids and offers of these securities are
quoted on a bank discount basis, not on a price basis. The yield on a
bank discount basis is computed as follows:

D 360
Y d = ---- — ---------
- -
F t

where

Yd = annualized yield on a bank discount basis (expressed as a
decimal)
D = dollar discount, which is equal to the difference between
the face value and the price
F = face value
t = actual number of days remaining to maturity

As an example, suppose a Treasury bill with 91 days to maturity
and a face value of $100 trading at a price of $98.5846. The dollar dis-
count, D, is computed as follows:
16 THE GLOBAL MONEY MARKETS



D = $100 ’ $98.5846 = $1.4054

Therefore, the annualized yield on a bank discount basis (expressed as a
decimal)

$1.4054 360
Y d = -------------------- — --------- = 5.56%
- -
$100 91

Given the yield on a bank discount basis, the price of a Treasury bill is
found by ¬rst solving the formula for the dollar discount (D) as follows:

D = Yd — F — (t/360)

The price is then

price = F ’ D

As an example, suppose a 91-day bill with a face value of $100 has
a yield on bank discount basis of 5.56%, D is equal to

D = 0.0556 — $100 — 91/360 = $1.4054

Therefore,

price = $100 ’ $1.4054 = $98.5946

As noted earlier, the quoted yield on a bank discount basis is not a
meaningful measure of the potential return from holding a discount instru-
ment for two reasons. First, the measure is based on a face-value investment
rather than on the actual dollar amount invested. Second, the yield is annu-
alized according to a 360-day rather than a 365-day year, making it dif¬cult
to compare discount yields with the yields on Treasury notes and bonds that
pay interest on a Actual/Actual basis. The use of 360 days for a year is a
common money market convention. Despite its shortcomings as a measure
of return, this is the method that dealers have adopted to quote discount
notes like Treasury bills. Many dealer quote sheets and some other reporting
services provide two other yield measures that attempt to make the quoted
yield comparable to that for a coupon bond and interest-bearing money
market instruments”the CD equivalent yield and the bond equivalent yield.

CD Equivalent Yield
The CD equivalent yield (also called the money market equivalent yield)
makes the quoted yield on a bank discount basis more comparable to
17
Money Market Calculations



yield quotations on other money market instruments that pay interest
on a 360-day basis. It does this by taking into consideration the price of
the discount security (i.e., the amount invested) rather than its face
value. The formula for the CD equivalent yield is

360Y d
CD equivalent yield = -----------------------------
360 “ t ( Y d )

To illustrate the calculation of the CD equivalent, suppose a 91-day
Treasury bill has a yield on a bank discount basis is 5.56%. The CD
equivalent yield is computed as follows:

360 ( 0.0556 )
CD equivalent yield = --------------------------------------------- = 0.05639 = 5.639%
-
360 “ 91 ( 0.0556 )


Bond-Equivalent Yield
The measure that seeks to make a discount instrument like a Treasury bill
or an agency discount note comparable to coupon Treasuries is the bond-
equivalent yield as discussed earlier in the chapter. This yield measure
makes the quoted yield on a bank discount basis more comparable to yields
on Treasury notes and bonds that use an Actual/Actual day count conven-
tion. The calculations depend on whether the short-term discount instru-
ment has 182 days or less to maturity or more than 182 days to maturity.

Discount Instruments with Less Than 182 Days to Maturity
To convert the yield on a bank discount to a bond-equivalent yield for a
bill with less than 182 days to maturity, we use the following formula:

T ( Yd )
Bond-equivalent yield = -----------------------------
360 “ t ( Y d )

where T is the actual number of days in the calendar year (i.e., 365 or
366). As an example, using a Treasury bill with 91 days to maturity
yielding 5.56% on a bank discount basis, the bond-equivalent yield is
calculated as follows:

365 ( 0.0556 )
Bond-equivalent yield = --------------------------------------------- = 0.0572 = 5.72%
-
360 “ 91 ( 0.0556 )

Note the formula for the bond-equivalent yield presented above assumes that
the current maturity of the discount instrument in question is 182 days or less.
18 THE GLOBAL MONEY MARKETS



Discount Instruments with More Than 182 Days to Maturity
When a discount instrument (e.g., a 52-week Fannie Mae Benchmark
bill) has a current maturity of more than 182 days, converting a yield on
a bank discount basis into a bond-equivalent yield is more involved.
Speci¬cally, the calculation must re¬‚ect the fact that a Benchmark bill is
a discount instrument while a coupon Treasury delivers coupon pay-
ments semiannually and the semiannual coupon payment can be rein-
vested. In order to make this adjustment, we assume that interest is paid
after six months at a rate equal to the discount instrument™s bond-equiv-
alent yield (BEY) and that this interest is reinvested at this rate.
To ¬nd a discount instrument™s bond-equivalent yield if its current
maturity is greater than 182 days, we solve for the BEY using the fol-
lowing formula:7

7
We can derive this using the following notation:
P = price of the discount instrument
BEY= bond-equivalent yield
t = number of days until the discount instrument™s maturity
then,
P[1 + (BEY/2)] = future value obtained by the investor if $P is invested for six
months at one-half the BEY
(BEY/365)[t ’ (365/2)][1 + (BEY/2)]P = the amount earned by the investor on a sim-
ple interest basis if the proceeds are reinvested at the BEY for the discount instru-
ment™s remaining days to maturity
Assuming a face value for the discount instrument of $100, then
P[1 + (BEY/2)]+ (BEY/365)[t ’ (365/2)][1 + (BEY/2)]P = 100
This expression can be written more compactly as
P[1 + (BEY/2)][(1+(BEY/2))(2T/365 ’ 1)] = 100
Expanding this expression, we obtain

(2t/365 ’ 1)BEY2 + (4t/365)BEY + 4(1 ’ 100/P) = 0
The expression above is a quadratic equation which is an equation which can be
written in the form:

ax2 + bx + c = 0
which can be solved as follows:
1„2
2
“ b ± ( b “ 4ac )
x = ------------------------------------------------
-
2a
19
Money Market Calculations



1„2
“2 — t
-------------- + 2 « --- “ « 2 — t “ 1 — « 1 “ 100
t2
- ----------- ---------
-
T T 
T P
BEY = ------------------------------------------------------------------------------------------------------------------
-
2—t
---------- “ 1
-
T

As an example, let™s use a Fannie Mae 52-week Benchmark bill that
yields 5.87% on a bank discount basis and suppose there are 350 days
remaining until maturity. The price of this bill would be 94.0647 (per
$100 of face value). Suppose further that the year in question such that
T = 366. Substituting this information in the expression above gives the
bond-equivalent yield for this 52-week bill:

1„2
“ 2 — 350
---------------------- + 2 « 350 “ « 2 — 350 “ 1 — « 1 “ -------------------- 
2 100
------------------- -
---------
-
 366  366 
366 94.2931
BEY = ----------------------------------------------------------------------------------------------------------------------------------------------------
-
2 — 350
------------------ “ 1
-
366
= 0.0624 = 6.24%



INTEREST AT MATURITY INSTRUMENTS
In contrast to discount instruments, some money market instruments
pay interest at maturity on a simple interest basis. Notable examples
include federal funds, repos, and certi¬cates of deposit. Interest accrues
for these instruments using an Actual/360 day count convention. We
de¬ne the following terms:

F = face value of the instrument
I = amount of interest paid at maturity
t = actual number of days until maturity
Y360 = yield on a simple interest basis assuming a 360 day year

The following formula is used to calculate the dollar interest on a certif-
icate of deposit:

I = F — Y360 — (t/360)

As an illustration, suppose a bank offers a rate of 4% on a 180-day
certi¬cate of deposit with a face value of $1 million. Suppose an inves-
tor buys this CD and holds it to maturity, how much interest is earned.
The interest at maturity is $20,000 and determined as follows:
20 THE GLOBAL MONEY MARKETS



I = $1,000,000 — 0.04 — (180/360) = $20,000

Converting a CD Yield into a Simple Yield on a 365-Day Basis
It is often helpful to convert a CD yield which pays simple interest on a
Actual/360 into a simple yield on an Actual/365 basis. The transforma-
tion is straightforward and is accomplished using the following formula:

Y365 = Y360 (365/360)

To illustrate, let™s return to the 180-day certi¬cate of deposit yield-
ing 4% on a simple interest basis. We pose the question of what is this
investor earning on a ACT/365 basis. The answer is 4.056% and is cal-
culated as follows:

Y365 = 0.04 (365/360) = 0.0456

Converting a Periodic Interest Rate into an
Effective Annual Yield
Suppose that $100 is invested for one year at an annual interest rate of
interest of 4%. At the end of the year, the interest received is $4. Sup-
pose, instead, that $100 is invested for one year at an annual rate, but
the interest is paid semiannually at 2% (one-half the annual interest
rate). The interest at the end of the year is found by ¬rst calculating the
future value of $100 one year hence:

$100(1.02)2 = $104.04

Interest is therefore $4.04 on a $100 investment. The interest rate or
yield on the $100 invested is 4.04%. The 4.04% is called the effective
annual yield.
Investors in certi¬cates of deposit will at once recognize the differ-
ence between the annual interest rate and effective annual yield. Typi-
cally, both of these interest rates are quoted for a certi¬cate of deposit,
the higher interest rate being the effective annual yield.
To obtain the effective annual yield corresponding to a given peri-
odic rate, the following formula is used:

Effective annual yield = (1 + Periodic interest rate)m ’ 1

where m is equal to the number of payments per year.
21
Money Market Calculations



To illustrate, suppose the periodic yield is 2% and the number of
payments per year is two. Therefore,

Effective annual yield = (1.02)2 ’ 1
= 0.0404 or 4.04%

We can also determine the periodic interest rate that will produce a
given effective annual yield. For example, suppose we need to know
what semiannual interest rate would produce an effective annual yield
of 5.25%. The following formula can be used:

Periodic interest rate = (1 + Effective annual yield)1/m ’ 1

Using this formula to determine the semiannual interest rate to pro-
duce an effective annual yield of 5.25%, we ¬nd

Periodic interest rate = (1.0525)1/2 ’ 1
= 0.0259 or 2.59%
3
CHAPTER

U.S. Treasury Bills



he U.S. Treasury is the largest single borrower in the world. As of Sep-
T tember 2001, its total marketable securities outstanding totaled
$3.339 trillion. Of this total, $734.86 billion represents Treasury bills.1
Treasury bills are short-term discount instruments with original maturi-
ties of less than one year. All Treasury securities are backed by the full
faith and credit of the U.S. government. This fact, combined with their
volume (in terms of dollars outstanding) and liquidity, afford Treasury
bills a central place in the money market. Indeed, interest rates on Trea-
sury bills serve as benchmark short-term rates throughout the U.S. econ-
omy as well as in international money markets.
This chapter provides an in-depth treatment of Treasury bills. We will
describe the types of Treasury bills, how they are auctioned, price and
yield calculations, and how the secondary market is organized. We will
also discuss the time series behavior of Treasury bill yields relative to
other key money market rates. Finally, we will discuss one time-tested
portfolio strategy using Treasury bills”riding the yield curve.



TYPES OF TREASURY BILLS
Treasury bills are issued at a discount to par value, have no coupon rate,
and mature at par value. Currently, the Treasury issues four types of Trea-
sury bills that vary by their original maturity”28 day (1-month), 91 day
(3-month), 182 day (6-month), and cash management bills.2 As discussed
in the next section, 1-month, 3-month, and 6-month bills are offered for
sale each week.
1
Source: Treasury Bulletin.
2
The first six digits of the CUSIP for a Treasury bill are “912795.”
23
24 THE GLOBAL MONEY MARKETS



Cash management bills are offered from time to time with various
maturities. The time between the announcement of an issue, auction, and
issuance is usually a week or less. For example, on August 26, 1999, the
Treasury invited bids for approximately $33 billion of 15-day cash man-
agement bills. These bills were issued on August 31, 1999 at a bank dis-
count rate of 5.18% and matured on September 15, 1999. Cash
management bills are issued to bridge seasonal ¬‚uctuations in the Trea-
sury™s cash position. Owing to their variable issuance and maturity, cash
management bills can mature on any business day.
Since August 1998, all Treasury securities are sold and transferable in
increments of $1,000. Previously, Treasury bills were available in mini-
mum purchase amounts of $10,000. Treasury bills are issued in book-
entry form. This means that the investor receives only a receipt as evi-
dence of ownership instead of a paper certi¬cate. The primary advantage
of book entry is ease in transferring ownership of the security. Interest
income from Treasury securities is subject to federal income taxes but is
exempt from state and local income taxes.


THE TREASURY AUCTION PROCESS
The Public Debt Act of 1942 grants the U.S. Treasury considerable latitude
in deciding on the terms for a marketable security.3 An issue may be sold on
an interest-bearing or discount basis and may be sold on a competitive basis
or other basis, at whatever prices the Secretary of the Treasury may estab-
lish. However, Congress imposes a restriction on the total amount of bonds
outstanding. Although Congress has granted an exemption to this restric-
tion, there have been times when the Congress™ failure to extend the exemp-
tion has resulted in the delay or cancellation of a Treasury security offering.

Auction Schedule
As noted, the U.S. Treasury maintains a regular and predictable schedule
for their security offerings. Deviations from normal borrowing patterns are
announced ahead of time so that market participants can digest the news.
The Treasury believes its borrowing costs will be less if it provides buyers
of Treasury securities stable expectations regarding new issues of its debt.
The current auction cycles are as follows. There are weekly 4-week
(1-month), 3-month, and 6-month bill auctions. With the exception of
holidays and special circumstances, the 4-week bill offering is announced
on Mondays and is auctioned on Tuesdays. Correspondingly, 3-month
3
Nonmarketable Treasury securities are issued directly to U.S. Government accounts
and trust funds.
25
U.S. Treasury Bills



and 6-month bill offerings are announced on Thursdays and are auc-
tioned the following Monday. All bills are issued on Thursday. Because of
holidays, the maturities of each bill may be either longer or shorter by one
day. Prior to February 2001, 364-day (1-year) bills were issued on a regu-
lar cycle. However, due to large U.S. government budget surpluses in the
¬scal years 1998 and 1999, the 1-year bill was eliminated.
Exhibit 3.1 contains an announcement dated March 11, 2002, of an
offering of 4-week bills. The ¬rst 4-week bill issue was auctioned on
July 31, 2001.
EXHIBIT 3.1Treasury Auction of a 4-Week Bill
a. Announcement of a 4-Week Bill Auction




Source: U.S. Treasury
26 THE GLOBAL MONEY MARKETS



EXHIBIT 3.1 (Continued)
b. Highlights of Treasury Offering of 4-Week Bills to be Issued March 14, 2002




Source: U.S. Treasury

Determination of the Results of an Auction
Currently, Treasury bills (and indeed all marketable Treasury securities)
are sold in auctions and these auctions are conducted on the basis of
27
U.S. Treasury Bills



yield. For bills, the yields are on a bank discount basis. Noncompetitive
bids can be submitted from the public for up to $1 million face amount
of Treasury bills. These noncompetitive tenders, along with any non-
public purchases (e.g., purchases by the Federal Reserve) are subtracted
from the total securities being auctioned. The remainder is the amount
to be awarded to the competitive bidders.
The Treasury employs a single-price auction for all marketable secu-
rities it issues and has discontinued the use of multiple-price auctions. In
a multiple price auction, competitive bidders (e.g., primary dealers)
state the amount of the securities desired and the yields they are willing
to accept.4 The yields are then ranked from lowest to highest. This is
equivalent to arranging the bids from the highest price to the lowest
price. Starting from the lowest yield bid, all competitive bids are
accepted until the amount to be distributed to the competitive bidders is
completely allocated. The highest yield accepted by the Treasury is
called the “stop yield” and bidders at that yield are awarded a percent-
age of their total tender offer. The single-price auction proceeds in the
same fashion except that all accepted bids are ¬lled at the highest yield
of accepted competitive tenders (i.e., the stop yield).
The Treasury moved to single-price auctions for all Treasury securi-
ties in 1998 after conducting single-price auctions for monthly sales of
2- and 5-year notes since September 1992. Paul Malvey and Christine
Archibald conducted a study of the relative performance of the two auc-
tion mechanisms.5 Their empirical results suggest that single-price auc-
tions broaden participation and accordingly reduce concentration of
securities at issuance. Moreover, they also present somewhat weaker
evidence that the single-price auctions reduce the Treasury™s ¬nancing
costs by encouraging more aggressive bidding. In principle, single-price
auctions reduce ¬nancing costs by encouraging more aggressive bidding
relative to multiple-price auctions. Multiple-price auctions suffer from a
so-called “winner™s curse” problem because the winner of the auction
(i.e., whoever pays highest price/bids the lowest yield) pays a higher
price than the market consensus. Conversely, in a single-price auction,
all successful bidders pay the same price and have less incentive to bid
conservatively.
Exhibit 3.2 presents a Bloomberg screen that contains the results of
the 4-week Treasury bill auction on March 12, 2002. These bills were
issued on March 14, 2002. The screen provides the relevant data for the

4
Until the move to single-price auctions, Treasury bills had been sold using multiple-
price auctions since 1929.
5
Paul F. Malvey and Christine M. Archibald, “Uniform-Price Auctions: Update of
the Treasury Experience,” Washington, D.C., U.S. Treasury, October 1998.
28 THE GLOBAL MONEY MARKETS



current auction and the previous week™s auction. Two terms that appear
in this exhibit require some explanation. The bid-to-cover ratio is simply
the ratio of the total par amount of securities bid for by the public divided
by the total par amount of securities awarded to the public. The bid-to-
cover ratio excludes any bids or awards for accounts of foreign and inter-
national monetary authorities at Federal Reserve Banks and for the
account of the Federal Reserve Banks. The investment rate is simply the
bond-equivalent yield (discussed later) for the Treasury bill in question.
Between the auction™s announcement and the actual issuance of the
securities, trading of bills takes place in the when-issued or wi market.
Essentially, this when-issued market is nothing more than an active for-
ward market in the bills. Many dealers enter a Treasury bill auction
with large short positions and hope to cover these positions with bills
obtained at the auction. Dealers make commitments with their custom-
ers and other dealers to make/take delivery of bills for an agreed upon
price with settlement occurring after the bills are issued. In fact, all
deliveries on when-issued trades occur on the issue day of the security
traded. When-issued yields serve as important indicators for yields that
will prevail at the auction.

EXHIBIT 3.2 Bloomberg Screen for 4-Week Bill Auction Results




Source: Bloomberg Financial Markets
29
U.S. Treasury Bills



PRICE QUOTES FOR TREASURY BILLS
The convention for quoting bids and offers in the secondary market is
different for Treasury bills and Treasury coupon securities. Bids/offers
on bills are quoted in a special way. Unlike bonds that pay coupon inter-
est, Treasury bill values are quoted on a bank discount basis, not on a
price basis. The yield on a bank discount basis is computed as follows:

D 360
Y d = ---- — ---------
- -
F t

where:
Yd = annualized yield on a bank discount basis (expressed as a dec-
imal)
D = dollar discount, which is equal to the difference between the
face value and the price
F = face value
t = number of days remaining to maturity
For example, Exhibit 3.3 presents the PX1 Governments screen
from Bloomberg. Data for the most recently issued bills appear in the
upper left-hand corner. The ¬rst and second columns indicate the secu-
rity and its maturity date. In the third column, there is an arrow indicat-
ing an up or down tick for the last trade. The fourth column indicates
the current bid/ask rates. A bond-equivalent yield (discussed later) using
the ask yield/price is contained in column 5. The last column contains
the change in bank discount yields based on the previous day™s closing
rates as of the time posted. Exhibit 3.4 presents the same information
for all outstanding bills (page PX2). The current/when issued bills™
maturity dates are highlighted. Other important market indicators are
contained in the lower right-hand corner of the screen.
Given the yield on a bank discount basis, the price of a Treasury bill
is found by ¬rst solving the formula for Yd to obtain the dollar discount
(D), as follows:

D = Yd — F — (t/360)

The price is then

price = F ’ D
30 THE GLOBAL MONEY MARKETS



EXHIBIT 3.3 Bloomberg Current Governments Screen




Source: Bloomberg Financial Markets

EXHIBIT 3.4 Bloomberg Screen of All Outstanding Bills




Source: Bloomberg Financial Markets
31
U.S. Treasury Bills



Using the information in Exhibit 3.3, for the current 28-day bill with
a face value of $1,000, if the offer yield on a bank discount basis is
quoted as 1.76%, D is equal to

D = 0.0176 — $1,000 — 28/360 = $1.3689

Therefore,

price = $1,000 ’ $1.3689 = $998.6311

The quoted yield on a bank discount basis is not a meaningful measure
of the potential return from holding a Treasury bill, for two reasons. First,
the measure is based on a face-value investment rather than on the actual
dollar amount invested. Second, the yield is annualized according to a 360-
day rather than a 365-day year, making it dif¬cult to compare Treasury bill
yields with Treasury notes and bonds, which pay interest on a 365-day
basis. The use of 360 days for a year is a money market convention for some
money market instruments, however. Despite its shortcomings as a measure
of return, this is the method that dealers have adopted to quote Treasury
bills. Many dealer quote sheets and some other reporting services provide
two other yield measures that attempt to make the quoted yield comparable
to that for a coupon bond and other money market instruments.

CD Equivalent Yield
The CD equivalent yield (also called the money market equivalent yield)
makes the quoted yield on a Treasury bill more comparable to yield quo-
tations on other money market instruments that pay interest on a 360-day
basis. It does this by taking into consideration the price of the Treasury
bill (i.e., the amount invested) rather than its face value. The formula for
the CD equivalent yield is

360Y d
CD equivalent yield = -----------------------------
360 “ t ( Y d )

For example, using the data from Exhibit 3.3 for the 28-day bill that
matures on April 11, 2002, the ask rate on a bank discount basis is
1.76%. The CD equivalent yield is computed as follows:

360 ( 0.0176 ) -
CD equivalent yield = --------------------------------------------- = 0.0176 = 1.76%
360 “ 28 ( 0.0176 )

Because of the low rate, the CD equivalent yield is the same as the yield
on a bank discount basis.
32 THE GLOBAL MONEY MARKETS



Bond-Equivalent Yield
The measure that seeks to make the Treasury bill quote comparable to
coupon Treasuries is called the bond-equivalent yield. This yield measure
makes the quoted yield on a Treasury bill more comparable to yields on
Treasury notes and bonds that use an actual/actual day count conven-
tion.6 In order to convert the yield on a bank discount to a bond-equiva-
lent yield, the following formula is used:
T ( Yd )
Bond-equivalent yield = -----------------------------
360 “ t ( Y d )

where T is the actual number of days in the calendar year (i.e., 365 or 366).
As an example, using the same Treasury bill with 28 days to maturity
and a face value of $1,000 that would be quoted at 1.76% on a bank dis-
count basis, the bond-equivalent yield is calculated as follows:

365 ( 0.0176 ) -
Bond-equivalent yield = --------------------------------------------- = 0.0179 = 1.79%
360 “ 28 ( 0.0176 )

This number matches the bond-equivalent yield given by the Bloomberg
screen in Exhibit 3.3. There are a couple of points to note in this calculation.
First, we used 365 in the numerator because the year 2002 is a non-leap year.
Second, the formula for the bond-equivalent yield presented above assumes
that the current maturity of the Treasury bill in question is 182 days or less.



SECONDARY MARKET
The secondary market for Treasury securities is an over-the-counter mar-
ket in which a group of U.S. government securities dealers offer continu-
ous bid and ask prices on outstanding issues. There is virtual 24-hour
trading of Treasury securities. The three primary trading locations are
New York, London, and Tokyo. Trading begins at 8:30 a.m. Tokyo time
(7:30 p.m. New York time) and continues to about 4:00 p.m. Tokyo time
(3:00 a.m. New York time).7 Trading then moves to London where trad-

6
Day count conventions determine the number of days in a coupon period and the
number of days from the last coupon payment to the settlement date. For a coupon
Treasury, both are equal to the actual number of days. The day count convention is
referred to as “actual/actual.”
7
These trading hours apply when New York is on daylight savings time. The main
difference when New York is on standard time is that Tokyo starts an hour earlier
relative to New York (6:30 P.M. New York time.)
33
U.S. Treasury Bills



ing commences at 8:00 a.m. London time and then on to New York at
12:30 p.m. London time (7:30 a.m. New York time). In New York, trad-
ing starts at 7:30 a.m. and continues until 5:30 p.m.8
The most recently auctioned Treasury bill for a particular maturity is
referred to as the on-the-run issue. Issues auctioned prior to the on-the-

. 1
( 10)



>>