CHAPTER 6
TREASURY AND AGENCY SECURITIES MARKETS
CHAPTER SUMMARY
The second largest sector of the bond market (after the mortgage market) is the market for U.S.
Treasury securities. The smallest sector is the U.S. government agency securities market. We
discuss these two sectors together in this chapter. As explained in Chapter 11, a majority of the
securities backed by a pool of mortgages are guaranteed by a federally sponsored agency of the
U.S. government. These securities are classified as part of the mortgage-backed securities market
rather than as U.S. government agency securities.
TREASURY SECURITIES
Two factors account for the prominent role of U.S. Treasury securities: volume (in terms of
dollars outstanding) and liquidity. The Department of the Treasury is the largest single issuer of
debt in the world. The large volume of total debt and the large size of any single issue have
contributed to making the Treasury market the most active and hence the most liquid market in
the world. The dealer spread between bid and ask price is considerably narrower than in other
sectors of the bond market.
Types of Treasury Securities
The Treasury issues marketable and nonmarketable securities. Our focus here is on marketable
securities. Marketable Treasury securities are categorized as fixed-principal securities or
inflation-indexed securities. Fixed-income principal securities include Treasury bills, Treasury
notes, and Treasury bonds.
Treasury bills are issued at a discount to par value, have no coupon rate, and mature at par
value. The current practice of the Treasury is to issue all securities with a maturity of one year or
less as discount securities. As discount securities, Treasury bills do not pay coupon interest.
Instead, Treasury bills are issued at a discount from their maturity value; the return to the
investor is the difference between the maturity value and the purchase price.
All securities with initial maturities of two years or more are issued as coupon securities. Coupon
securities are issued at approximately par and, in the case of fixed-principal securities, mature at
par value. Treasury coupon securities issued with original maturities of more than one year and
no more than 10 years are called Treasury notes. Treasury coupon securities with original
maturities greater than 10 years are called Treasury bonds. Callable bonds have not been issued
since 1984. On January 29, 1997, the U.S. Department of the Treasury issued for the first time
Treasury securities that adjust for inflation. These securities are popularly referred to as
Treasury inflation protection securities, or TIPS. The principal that the Treasury Department
will base both the dollar amount of the coupon payment and the maturity value on is adjusted
semiannually. This is called the inflation-adjusted principal.
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The Treasury Auction Process
The Public Debt Act of 1942 grants the Department of the Treasury considerable discretion in
deciding on the terms for a marketable security. An issue may be sold on an interest-bearing or
discount basis and may be sold on a competitive or other basis, at whatever prices the Secretary
of the Treasury may establish.
Treasury securities are sold in the primary market through sealed-bid auctions. Each auction is
announced several days in advance by means of a Treasury Department press release or press
conference. The announcement provides details of the offering, including the offering amount
and the term and type of security being offered, and describes some of the auction rules and
procedures. Treasury auctions are open to all entities.
The Treasury auctions securities on a regular cycle: Treasury bills with maturities of 4 weeks, 13
weeks (3 months), and 26 weeks (6 months). At irregular intervals the Treasury issues cash
management bills with maturities ranging from a few days to about six months. The Treasury
auctions 2-, 5-, and 10-year Treasury notes. The Treasury does not issue Treasury bonds on a
regular basis. The Treasury had issued 30-year Treasury bonds on a regular basis but suspended
doing so in October 2001.
The auction for Treasury securities is conducted on a competitive bid basis. A noncompetitive
bid is submitted by an entity that is willing to purchase the auctioned security at the yield that is
determined by the auction process.
When a noncompetitive bid is submitted, the bidder only specifies the quantity sought. The
quantity in a noncompetitive bid may not exceed $1 million for Treasury bills and $5 million for
Treasury coupon securities. A competitive bid specifies both the quantity sought and the yield at
which the bidder is willing to purchase the auctioned security.
The highest yield accepted by the Treasury is referred to as the stop-out yield (or high yield).
Bidders whose bid is higher than the stop-out yield are not distributed any of the new issue (i.e.,
they are unsuccessful bidders). Bidders whose bid was the stop-out yield (i.e., the highest yield
accepted by the Treasury) are awarded a proportionate amount for which they bid.
Within an hour of the auction deadline, the Treasury announces the auction results including the
quantity of noncompetitive tenders, the median-yield bid, and the ratio of the total amount bid
for by the public to the amount awarded to the public (called the bid-to-cover ratio). For notes
and bonds, the announcement includes the coupon rate of the new security.
Secondary Market
The secondary market for Treasury securities is an over-the-counter market where a group of
U.S. government securities dealers offer continuous bid and ask prices on outstanding
Treasuries. There is virtual 24-hour trading of Treasury securities. The three primary trading
locations are New York, London, and Tokyo. The normal settlement period for Treasury
securities is the business day after the transaction day (“next day” settlement).
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The most recently auctioned issue is referred to as the on-the-run issue or the current issue.
Securities that are replaced by the on-the-run issue are called off-the-run issues. At a given point
in time there may be more than one off-the-run issue with approximately the same remaining
maturity as the on-the-run issue. Treasury securities are traded prior to the time they are issued
by the Treasury. This component of the Treasury secondary market is called the when-issued
market, or wi market. When-issued trading for both bills and coupon securities extends from
the day the auction is announced until the issue day.
Government dealers trade with the investing public and with other dealer firms. When they trade
with each other, it is through intermediaries known as interdealer brokers. Dealers leave firm
bids and offers with interdealer brokers who display the highest bid and lowest offer in a
computer network tied to each trading desk and displayed on a monitor. Dealers use interdealer
brokers because of the speed and efficiency with which trades can be accomplished.
The convention for quoting bids and offers is different for Treasury bills and Treasury coupon
securities. Bids and offers on Treasury bills are quoted in a special way. Unlike bonds that pay
coupon interest, Treasury bill values are quoted on a bank discount basis, not on a price basis.
The quoted yield on a bank discount basis is not a meaningful measure of the return from
holding a Treasury bill. There are two reasons for this. 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 difficult to compare Treasury bill
yields with Treasury notes and bonds, which pay interest on a 365-day basis.
The measure that seeks to make the Treasury bill quote comparable to Treasury notes and bonds
is called the bond 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 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 Treasury bill rather than its face value.
Treasury coupon securities are quoted in a different manner than Treasury bills—on a price basis
in points where one point equals 1% of par. The points are split into units of 32nds, so that a
price of 96-14, for example, refers to a price of 96 and 14 32nds, or 96.4375 per 100 of par
value. The 32nds are themselves often split by the addition of a plus sign or a number. In
addition to price, the yield to maturity is typically reported alongside the price.
When an investor purchases a bond between coupon payments, if the issuer is not in default, the
investor must compensate the seller of the bond for the coupon interest earned from the time of
the last coupon payment to the settlement date of the bond. This amount is called accrued
interest. When calculating accrued interest, three pieces of information are needed: (i) the
number of days in the accrued interest period, (ii) the number of days in the coupon period, and
(iii) the dollar amount of the coupon payment. The number of days in the accrued interest period
represents the number of days over which the investor has earned interest.
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The calculation of the number of days in the accrued interest period and the number of days in
the coupon period begins with the determination of three key dates: the trade date, settlement
date, and date of previous coupon payment. The trade date is the date on which the transaction
is executed. The settlement date is the date a transaction is completed. For Treasury securities,
settlement is the next business day after the trade date. Interest accrues on a Treasury coupon
security from and including the date of the previous coupon payment up to but excluding the
settlement date.
The number of days in the accrued interest period and the number of days in the coupon period
may not be simply the actual number of calendar days between two dates. For Treasury coupon
securities, the day count convention used is to determine the actual number of days between two
dates. This is referred to as the actual/actual day count convention.
STRIPPED TREASURY SECURITIES
The Treasury does not issue zero-coupon notes or bonds. However, because of the demand for
zero-coupon instruments with no credit risk, the private sector has created such securities.
In August 1982, both Merrill Lynch and Salomon Brothers created synthetic zero-coupon
Treasury receipts. Merrill Lynch marketed its Treasury receipts as Treasury Income Growth
Receipts (TIGRs), and Salomon Brothers marketed its receipts as Certificates of Accrual on
Treasury Securities (CATS). The procedure was to purchase Treasury bonds and deposit them
in a bank custody account. The firms then issued receipts representing an ownership interest in
each coupon payment on the underlying Treasury bond in the account and a receipt for
ownership of the underlying Treasury bond’s maturity value. This process of separating each
coupon payment, as well as the principal (called the corpus), and selling securities against them
is referred to as coupon stripping.
Other investment banking firms followed suit by creating their own receipts. They all are
referred to as trademark zero-coupon Treasury securities because they are associated with
particular firms.
In February 1985, the Treasury announced its Separate Trading of Registered Interest and
Principal of Securities (STRIPS) program to facilitate the stripping of designated Treasury
securities. Today, all Treasury notes and bonds (fixed-principal and inflation indexed) are
eligible for stripping. The zero-coupon Treasury securities created under the STRIPS program
are direct obligations of the U.S. government. Moreover, the securities clear through the Federal
Reserve’s book-entry system. Creation of the STRIPS program ended the origination of
trademarks and generic receipts.
On dealer quote sheets and vendor screens STRIPS are identified by whether the cash flow is
created from the coupon (denoted ci), principal from a Treasury bond (denoted bp), or principal
from a Treasury note (denoted np). Strips created from the coupon are called coupon strips and
strips created from the principal are called principal strips. The reason why a distinction is
made between coupon strips and principal strips has to do with the tax treatment by non–U.S.
entities, as discussed in the next section.
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Tax Treatment
A disadvantage of a taxable entity investing in stripped Treasury securities is that accrued
interest is taxed each year even though interest is not paid. Thus these instruments are negative
cash flow instruments until the maturity date. They have negative cash flow because tax
payments on interest earned but not received in cash must be made.
Reconstituting a Bond
Reconstitution is the process of coupon stripping and reconstituting that will prevent the actual
spot rate curve observed on zero-coupon Treasuries from departing significantly from the
theoretical spot rate curve. As more stripping and reconstituting occurs, forces of demand and
supply will cause rates to return to their theoretical spot rate levels.
FEDERAL AGENCY SECURITIES
Federal agency securities can be classified by the type of issuer: those issued by federally related
institutions and those issued by government-sponsored enterprises.
Federally Related Institutions
Federally related institutions are arms of the federal government and generally do not issue
securities directly in the marketplace. With the exception of securities of the TVA and the
Private Export Funding Corporation, the securities are backed by the full faith and credit of the
United States government. However, TVA securities are rated AAA by Moody’s and Standard
and Poor’s. The rating is based on the TVA’s status as a wholly owned corporate agency of the
U.S. government and the view of the rating agencies of the TVA’s financial strengths.
Government-Sponsored Enterprises
Government-sponsored enterprises (GSEs) are privately owned, publicly chartered entities.
They were created by Congress to reduce the cost of capital for certain borrowing sectors of the
economy deemed to be important enough to warrant assistance.
Today there are six GSEs that currently issue debentures: Federal National Mortgage
Association, Federal Home Loan Mortgage Corporation, Federal Agricultural Mortgage
Corporation, Federal Farm Credit Bank System, Federal Home Loan Bank System, and Student
Loan Marketing Association.
The interest earned on obligations of the Federal Home Loan Bank System, the Federal Farm
Credit Bank System, and the Student Loan Marketing Association is exempt from state and local
income taxes.
The price quotation conventions for GSE securities will vary between types of debt. Short-term
GSE discount notes are quoted on a yield basis, the same as that for Treasury bills explained
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earlier in this chapter. The most liquid GSE issues are generally quoted on two primary bases: (i)
a price basis, like Treasury securities, where the bid and ask price quotations are expressed as a
percentage of par plus fractional 32nds of a point; (ii) a spread basis, as an indicated yield spread
in basis points, off a choice of proxy curves or issue.
Federal National Mortgage Association (Fannie Mae) is charged with the responsibility to
create a liquid secondary market for mortgages. In 2001, Fannie Mae began issuing subordinated
securities (Fannie Mae Subordinated Benchmark Notes).
Federal Home Loan Mortgage Corporation (Freddie Mac) provides support for conventional
mortgages. These mortgages are not guaranteed by the U.S. government. Freddie Mac issues
Reference Bills, discount notes, medium-term notes, Reference Notes, Reference Bonds,
Callable Reference Notes, Euro Reference Notes (debt denominated in euros), and global
bonds. In 2001, Freddie Mac also began issuing subordinated securities (called Freddie Mac
Subs). These securities have the same feature as the Fannie Mae Subordinated Benchmark
Notes.
The Federal Home Loan Bank System (FHL Banks) consists of the twelve district Federal
Home Loan Banks and their member banks. The major source of debt funding for the Federal
Home Loan Banks is the issuance of consolidated debt obligations, which are joint and several
obligations of the twelve Federal Home Loan Banks.
The Federal Agricultural Mortgage Corporation (Farmer Mae) provides a secondary market
for first mortgage agricultural real estate loans. Federal Farm Credit Bank System (FFCBS) is
to facilitate adequate, dependable credit and related services to the agricultural sector of the
economy. Student Loan Marketing Association (Sallie Mae) provides liquidity for private
lenders participating in the Federal Guaranteed Student Loan Program, the Health Education
Assistance Loan Program, and the PLUS loan program.
GSE Credit Risk
With the exception of the securities issued by the Farm Credit Financial Assistance Corporation,
GSE securities are not backed by the full faith and credit of the U.S. government, as is the case
with Treasury securities. Consequently, investors purchasing GSEs are exposed to credit risk.
The yield spread between these securities and Treasury securities of comparable maturity reflects
differences in perceived credit risk and liquidity. The spread attributable to credit risk reflects
any financial difficulty faced by the issuing GSEs and the likelihood that the federal government
will allow the GSE to default on its outstanding obligations.
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ANSWERS TO QUESTIONS FOR CHAPTER 6
(Questions are in bold print followed by answers.)
1. What are the differences among a Treasury bill, Treasury note, and Treasury bond?
Fixed-principal Treasury securities are fixed-income principal securities that include Treasury
bills, Treasury notes, and Treasury bonds. As discussed below the main differences involve
maturity and how earnings are received over time.
Treasury bills are issued at a discount to par value, have no coupon rate, and mature at par value.
The current practice of the Treasury is to issue all securities with a maturity of one year or less as
discount securities. As discount securities, Treasury bills do not pay coupon interest. Instead,
Treasury bills are issued at a discount from their maturity value; the dollar return to investors is
the difference between the maturity value and the purchase price.
All securities with initial maturities of two years or more are issued as coupon securities. Coupon
securities are issued at approximately par and, in the case of fixed-principal securities, mature at
par value. Treasury coupon securities issued with original maturities of more than one year and
no more than 10 years are called Treasury notes. Treasury coupon securities with original
maturities greater than 10 years are called Treasury bonds. (On quote sheets, an “n” is used to
denote a Treasury note. No notation typically follows an issue to identify it as a bond.) While a
few issues of the outstanding bonds are callable, the Treasury has not issued new callable
Treasury securities since 1984.
2. The following questions are about Treasury Inflation Protected Securities (TIPS).
(a) What is meant by the “real rate”?
In terms of TIPS, the real rate is the coupon rate. This is discussed below.
On January 29, 1997, the U.S. Department of the Treasury issued for the first time Treasury
securities that adjust for inflation. These securities are popularly referred to as Treasury
inflation protection securities, or TIPS. The first issue was a 10-year note. Subsequently, the
Treasury issued a 5-year note in July 1997 and a 30-year bond in 1998.
TIPS work as follows. The coupon rate on an issue is set at a fixed rate. That rate is determined
via the auction process. The coupon rate is called the “real rate” since it is the rate that the
investor ultimately earns above the inflation rate. The inflation index that the government has
decided to use for the inflation adjustment is the nonseasonally adjusted U.S. City Average All
Items Consumer Price Index for All Urban Consumers (CPI-U)
(b) What is meant by the “inflation-adjusted principal”?
For TIPS, the inflation-adjusted principal is the principal that the Treasury Department will base
both the dollar amount of the coupon payment and the maturity value on. It is adjusted
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semiannually. Part of the adjustment for inflation comes in the coupon payment since it is based
on the inflation-adjusted principal. However, the U.S. government has decided to tax the
adjustment each year. This feature reduces the attractiveness of TIPS as investments in accounts
of tax-paying entities.
Because of the possibility of disinflation (i.e., price declines), the inflation-adjusted principal at
maturity may turn out to be less than the initial par value. However, the Treasury has structured
TIPS so that they are redeemed at the greater of the inflation adjusted principal and the initial par
value.
An inflation-adjusted principal must be calculated for a settlement date. The inflation-adjusted
principal is defined in terms of an index ratio, which is the ratio of the reference CPI for the
settlement date to the reference CPI for the issue date. The reference CPI is calculated with a
three-month lag. For example, the reference CPI for May 1 is the CPI-U reported in February.
The U.S. Department of the Treasury publishes and makes available on its Web site
(www.publicdebt.treas.gov) a daily index ratio for an issue.
(c) Suppose that the coupon rate for a TIPS is 3%. Suppose further that an investor
purchases $10,000 of par value (initial principal) of this issue today and that the
semiannual inflation rate is 1%.
Answer the following questions.
(1) What is the dollar coupon interest that will be paid in cash at the end of the first
six months?
In our example, the coupon rate for a TIPS is 3%, the annual inflation rate is 2%, and an
investor purchases today $10,000 par value (principal) of this issue. The semiannual
inflation rate is 1% (2% divided by 2). The inflation-adjusted principal at the end of the
first six-month period is found by multiplying the original par value by one plus the
semiannual inflation rate. In our example, the inflation adjusted principal at the end of the
first six-month period is (1.01)$10,000 = $10,100. It is this inflation adjusted principal that
is the basis for computing the coupon interest for the first six-month period. The coupon
payment is then 1.5% (one-half the real rate of 3%) multiplied by the inflation-adjusted
principal at the coupon payment date ($10,100). The coupon payment is therefore
0.015($10,100) = $151.50.
(2) What is the inflation-adjusted principal at the end of the year?
As seen in part (1) when computing the coupon payment, we find that the inflation
adjusted principal at the end of the first six-month period is (1.01)$10,000 = $10,100.
Given the semiannual inflation rate for the next six months we could compute the
inflation-adjusted principal at year’s end. Assuming the semiannual inflation rate remains
at 1%, then we would get: (1.01)$10,100 = $10,201. The coupon payment would be
0.015($10,201) = $153.015.
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(d) Suppose that an investor buys a five-year TIP and there is deflation for the entire
period. What is the principal that will be paid by the Department of the Treasury at the
maturity date?
With deflation, the inflation-adjusted principal would fall. However, the Treasury has structured
TIPS so that they are redeemed at the greater of the inflation adjusted principal and the initial par
value. Thus, the investor who buys a five-year TIP is promised the original principle amount at
the maturity date.
(e) What is the purpose of the daily index ratio?
The purpose of the daily index ratio is to help compute an inflation-adjusted principal for a
settlement date. An inflation-adjusted principal must be calculated for a settlement date. The
inflation-adjusted principal is defined in terms of an index ratio, which is the ratio of the
reference CPI for the settlement date to the reference CPI for the issue date. The reference CPI is
calculated with a three-month lag. For example, the reference CPI for May 1 is the CPI-U
reported in February. The U.S. Department of the Treasury publishes and makes available on its
Web site (www.publicdebt.treas.gov) a daily index ratio for an issue. Exhibit 6-1 in the text
provides an example.
(f) How is interest income on TIPS treated at the federal income tax level?
For TIPS, the coupon payment is based on the inflation-adjusted principal. The U.S. government
taxes the adjustment each year. This feature reduces the attractiveness of TIPS as investments in
accounts of tax-paying entities.
3. What is the when-issued market?
Treasury securities are traded prior to the time they are issued by the Treasury. This component
of the Treasury secondary market is called the when-issued market, or wi market. When-issued
trading for both bills and coupon securities extends from the day the auction is announced until
the issue day.
4. Why do government dealers use government brokers?
When government dealers trade with each other, it is through intermediaries known as
interdealer brokers. They use interdealer brokers because of the speed and efficiency with which
trades can be accomplished. Also, interdealer brokers keep the names of the dealers involved in
trades confidential. The quotes provided on the government dealer screens represent prices in the
“inside” or “interdealer” market.
5. Suppose that the price of a Treasury bill with 90 days to maturity and a $1 million face
value is $980,000. What is the yield on a bank discount basis?
The convention for quoting bids and offers is different for Treasury bills and Treasury coupon
securities. Bids and offers on Treasury bills are quoted in a special way. Unlike bonds that pay
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coupon interest, 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:
Yd 
D  360 


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
and t = number of days remaining to maturity.
For our problem, a Treasury bill with 90 days to maturity, a face value of $1,000,000, and selling
for $980,000 would be selling with a dollar discount of D = F – P = $1,000,000 – $980,000 =
$20,000. Given D = $20,000, F = $1,000,000 and t = 90, the Treasury bill would be quoted at the
following yield:
Yd =
$20,000  360 

 = 0.02(4) = 0.0800 or 8.00%.
$1,000,000  90 
6. The bid and ask yields for a Treasury bill were quoted by a dealer as 5.91% and 5.89%,
respectively. Shouldn’t the bid yield be less than the ask yield, because the bid yield
indicates how much the dealer is willing to pay and the ask yield is what the dealer is
willing to sell the Treasury bill for?
The higher bid means a lower price. So the dealer is willing to pay less than would be paid for
the lower ask price. We illustrate this below.
Given the yield on a bank discount basis (Yd), the price of a Treasury bill is found by first solving
the formula for the dollar discount (D), as follows:
 t 
D = Yd(F) 
 . The price is then price = F – D.
 360 
For the 100-day Treasury bill with a face value (F) of $100,000, if the yield on a bank discount
basis (Yd) is quoted as 5.91%, D is equal to:
 t 
 100 
D = Yd(F) 
 = 0.0591($100,000) 
 = $1,641.67.
 360 
 360 
Therefore, price = $100,000 – $1,641.67 = $98,358.33.
For the 100-day Treasury bill with a face value (F) of $100,000, if the yield on a bank discount
basis (Yd) is quoted as 5.89%, D is equal to:
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 t 
 100 
D = Yd(F) 
 = 0.0589($100,000) 
 = $1,636.11.
 360 
 360 
Therefore, price is: P = F – D = $100,000 – $1,636.11 = $98,363.89.
Thus, the higher bid quote of 5.91% (compared to lower ask quote 5.89%) gives a lower selling
price of $98,358.33 (compared to $98,363.89). The 0.02% higher yield translates into a selling
price that is $5.56 lower.
In general, the quoted yield on a bank discount basis is not a meaningful measure of the 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
difficult 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 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.
7. Assuming a $100,000 par value, calculate the dollar price for the following Treasury
coupon securities given the quoted price.
(a) The quoted price for a $100,000 par value Treasury coupon security is 84-14. What is
the dollar price?
Treasury coupon securities are quoted in a different manner than Treasury bills—on a price basis
in points where one point equals 1% of par. (Notes and bonds are quoted in yield terms in whenissued trading because coupon rates for new notes and bonds are not set until after these
securities are auctioned.)
The points are split into units of 32nds, so that a price of 96-14, for example, refers to a price of
96 and 14 32nds, or 96.4375 per 100 of par value (96 + 14/32 = 96 + 0.4375 = 96.4375). The
32nds are themselves often split by the addition of a plus sign or a number. A plus sign indicates
that half a 32nd (or a 64th) is added to the price, and a number indicates how many eighths of
32nds (or 256ths) are added to the price. A price of 96–14+, therefore, refers to a price of 96 plus
14 32nds plus 1 64th, or 96.453125 (e.g., 96 + 14/32 + 1/64 = 96 + 0.4375 + 0.01563 =
96.453125), and a price of 96–142 refers to a price of 96 plus 14 32nds plus 2 256ths, or
96.4453125 (96 + 14/32 + 2/256 = 96 + 0.4375 + 0.0078125 = 96.4453125).
Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 84-14, the
dollar price is: 84 + 14/32 = 84 + 0.4375 = 84.4375 per 100 of par value. The dollar price is:
84.4375 ($100,000 / 100) = $84,437.50.
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(b) The quoted price for a $100,000 par value Treasury coupon security is 84-14+. What is
the dollar price?
Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 84-14+,
the dollar price is: 84 + 14/32 + 1/64 = 84 + 0.4375 + 0.015625 = 84.453125 per 100 of par
value. The dollar price is: 84.453125 ($100,000 / 100) = $84,453.13.
(c) The quoted price for a $100,000 par value Treasury coupon security is 103-284. What is
the dollar price?
Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 103-284
the dollar price is: 103 + 28/32 + 4/256 = 103 + 0.875 + 0.015625 = 103.89063 per 100 of par
value. The dollar price is: 103.89063 ($100,000 / 100) = $103,890.63.
(d) The quoted price for a $100,000 par value Treasury coupon security is 105-059. What is
the dollar price?
Thus, assuming a $100,000 par value Treasury coupon security with a quoted price of 105-059
the dollar price is: 103 + 5/32 + 9/256 = 103 + 0.15625 + 0.0351562 = 103.19141 per 100 of par
value. The dollar price is: 103.19141($100,000 / 100) = $103,191.41.
8. Answer the following questions for a treasury auction.
(a) In a Treasury auction what is meant by a noncompetitive bidder?
A noncompetitive bidder is a bidder is who is willing to purchase the auctioned security at the
yield that is determined by the auction process. More details are supplied below.
The auction for Treasury securities is said to be conducted on a competitive bid basis. However,
there are actually two types of bids that may be submitted by a bidder: noncompetitive bid and
competitive bid. A noncompetitive bid is submitted by an entity that is willing to purchase the
auctioned security at the yield that is determined by the auction process.
When a noncompetitive bid is submitted, the bidder only specifies the quantity sought. The
quantity in a noncompetitive bid may not exceed $1 million for Treasury bills and $5 million for
Treasury coupon securities. A competitive bid specifies both the quantity sought and the yield at
which the bidder is willing to purchase the auctioned security.
(b) In a Treasury auction what is meant by the stop-out yield?
In a Treasury auction, the results are determined by first deducting the total noncompetitive
tenders and nonpublic purchases (such as purchases by the Federal Reserve) from the total
securities being auctioned. The remainder is the amount to be awarded to the competitive
bidders. The competitive bids are then arranged from the lowest yield bid to the highest yield bid
submitted. (This is equivalent to arranging the bids from the highest price to the lowest price that
bidders are willing to pay.) Starting from the lowest yield bid (or highest price bid), all
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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 referred to as the stop-out
yield (or high yield). Bidders whose bid is higher than the stop-out yield are not distributed any
of the new issue (i.e., they are unsuccessful bidders). Bidders whose bid was the stop-out yield
(i.e., the highest yield accepted by the Treasury) are awarded a proportionate amount for which
they bid. For example, suppose that $4 billion was tendered for at the stop-out yield but only $3
billion remains to be allocated after allocating to all bidders who bid lower than the stop-out
yield. Then each bidder who bid the stop-out yield will receive $3 billion / $4 billion = 0.75 =
75% of the amount for which they tendered. So, if an entity tendered for $5 million, then that
entity would be awarded only 0.75($5 million) = $3.75 million.
(c) In a Treasury auction what is meant by the bid-to-cover ratio?
The bid-to-cover ratio is the total amount bid for by the public to the amount awarded to the
public. More details are supplied below.
Within an hour following the 1:00 P.M. auction deadline, the Treasury announces the auction
results. Announced results include the stop-out yield, the associated price, and the proportion of
securities awarded to those investors who bid exactly the stop-out yield. Also announced is the
quantity of noncompetitive tenders, the median-yield bid, and the ratio of the total amount bid
for by the public to the amount awarded to the public (called the bid-to-cover ratio). For notes
and bonds, the announcement includes the coupon rate of the new security. The coupon rate is
set to be that rate (in increments of 1/8 of 1%) that produces the price closest to, but not above,
par when evaluated at the yield awarded to successful bidders.
9. In a Treasury auction, how is the price that a competitive bidder must pay determined in
a single-price auction format?
The competitive bidder pays the price associated with the stop-out yield. However, the price can
differ slightly from par to reflect adjustments to make the yield equal to the stop-yield. More
details are supplied below.
All bidders that bid less than the stop-yield are awarded the amount that they bid. The Treasury
will report what percentage someone will receive if their bid is equal to the stop-yield. For
example, the Treasury might report: “Tenders at the high yield were allotted 50%.” This means
that if an entity bid for $10 million at the stop-yield that entity was awarded $5 million.
Now that the winning bidders are determined along with their allotment, the price can be set
following the conventions of a single-price auction (because all U.S. Treasury auctions are
single-price auctions). In a single-price auction, all bidders are awarded securities at the highest
yield of accepted competitive tenders (i.e., the stop-out yield). This type of auction is called a
“Dutch auction.” Thus, all bidders (competitive and noncompetitive) are awarded securities at
the stop-yield
The Treasury does not actually offer securities with a coupon rate equal to the stop-yield because
it adjusts the coupon rate and the price so that the yield offered on the security is equal to the
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stop-out yield. This makes the yield a more common number (e.g., 3.025 becomes 3.000 and
price can differ slightly from par.
10. In a Treasury auction, how is the price that a noncompetitive bidder must pay
determined in a single-price auction format?
A noncompetitive bidder is a bidder is who is willing to purchase the auctioned security at the
yield that is determined by the auction process. This yield is the stop-yield. However, the price
can differ slightly from par to reflect adjustments to make the yield equal to the stop-yield. More
details are supplied below.
Once the winning bidders are determined along with their allotment, the price can be set
following the conventions of a single-price auction (because all U.S. Treasury auctions are
single-price auctions). In a single-price auction, all bidders are awarded securities at the highest
yield of accepted competitive tenders (i.e., the stop-out yield). This type of auction is called a
“Dutch auction.” Thus, all bidders (competitive and noncompetitive) are awarded securities at
the stop-yield.
The Treasury does not actually offer securities with a coupon rate equal to the stop-yield because
it adjusts the coupon rate and the price so that the yield offered on the security is equal to the
stop-out yield. This makes the yield a more common number (e.g., 3.025 becomes 3.000 and
price can differ slightly from par.
11. Suppose that a Treasury coupon security is purchased on April 8 and that the last
coupon payment was on February 15. Assume that the year in which this security is
purchased is not a leap year.
Answer the following questions.
(a) How many days are in the accrued interest period?
The calculation of the number of days in the accrued interest period and the number of days in
the coupon period begins with the determination of three key dates: the trade date, settlement
date, and date of previous coupon payment. The trade date is the date on which the transaction is
executed. The settlement date is the date a transaction is completed. For Treasury securities,
settlement is the next business day after the trade date. Interest accrues on a Treasury coupon
security from and including the date of the previous coupon payment up to but excluding the
settlement date. In our problem, the settlement day of February 15th will be excluded when
determining the accrued interest period.
The number of days in the accrued interest period and the number of days in the coupon period
may not be simply the actual number of calendar days between two dates. The reason is that
there is a market convention for each type of security that specifies how to determine the number
of days between two dates. These conventions are called day count conventions. There are
different day count conventions for Treasury securities than for government agency securities,
municipal bonds, and corporate bonds.
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The day count convention used for Treasury coupon securities involves determining the actual
number of days between two dates. This is referred to as the actual/actual day count convention.
In our problem, we consider a Treasury coupon security whose previous coupon payment was
February 15. The next coupon payment would be on August 15. The Treasury security is
purchased with a settlement date of April 8.
In the figure below, we show the actual number of days between February 15 (the previous
coupon date) and April 8 (the settlement date):
February 15 to February 28 (count Feb. 15)
March (31 days in March)
April 1 to April 8 (don’t count April 8)
Actual number of days
14 days
31 days
7 days
52 days
The number of days in the accrued interest period represents the number of days over which the
investor has earned interest. For February we have 14 remaining days (e.g., the 13 days from
February 15 up to February 28 and the additional day of February 15th (since by convention we
count the day on which the last coupon was paid). We have 31 days for March. For April, we
have 7 days up to April 7 (by convention we do not count April 8th as a day since that is the
settlement day). Thus, the accrued interest period is 14 + 31 + 7 = 52 days.
[NOTE. The number of days in the coupon period is the actual number of days between February
15 and August 15, which is 182 days. The number of days between the settlement date (April 8)
and the next coupon date (August 15) is therefore 182 days – 52 days = 130 days. Notice that in
computing the number of days from February 15 to February 28, February 15 is counted in
determining the number of days in the accrued interest period; however, the settlement date
(April 8) is not included.]
(b) If the coupon rate for this Treasury security is 7% and the par value of the issue
purchased is $1 million, what is the accrued interest?
When an investor purchases a bond between coupon payments, if the issuer is not in default, the
investor must compensate the seller of the bond for the coupon interest earned from the time of
the last coupon payment to the settlement date of the bond. This amount is called accrued
interest.
When calculating accrued interest, three pieces of information are needed: (i) the number of days
in the accrued interest period, (ii) the number of days in the coupon period, and (iii) the dollar
amount of the coupon payment. The number of days in the accrued interest period represents the
number of days over which the investor has earned interest. Given these values, the accrued
interest (AI) assuming semiannual payment is calculated as follows:
AI =
annual dollar coupon
days in AI period
x
.
2
days in coupon period
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In our problem, we have 52 days in the accrued interest period, 182 days in a coupon period from
February 15 through August 15, and the annual dollar coupon per $100 of par value is $7. The
accrued interest is:
AI =
$7 52
annual dollar coupon
days in AI period
= x
= $1.00.
x
2
days in coupon period 2 182
12. Answer the following questions.
(a) What is meant by coupon stripping in the Treasury market?
Coupon stripping, in general, refers to detaching the coupons from a bond and trading the
principal repayment and the coupon amounts separately, thereby creating zero coupon bonds.
The Treasury does not issue zero-coupon notes or bonds. However, because of the demand for
zero-coupon instruments with no credit risk, the private sector has created such securities. The
profit potential for a government dealer who strips a Treasury security lies in arbitrage resulting
from the mispricing of the security. More details are given below.
To illustrate the process of coupon stripping, suppose that $500 million of a 10-year fixedprincipal Treasury note with a coupon rate of 5% is purchased by a dealer firm to create zerocoupon Treasury securities. The cash flow from this Treasury note is 20 semiannual payments of
$12.5 million each ($500 million times 0.05 divided by 2) and the repayment of principal (also
called the corpus) of $500 million 10 years from now. As there are 11 different payments to be
made by the Treasury, a security representing a single payment claim on each payment is issued,
which is effectively a zero-coupon Treasury security. The amount of the maturity value for a
security backed by a particular payment, whether coupon or corpus, depends on the amount of
the payment to be made by the Treasury on the underlying Treasury note. In our example, 20
zero-coupon Treasury securities each have a maturity value of $12.5 million, and one zerocoupon Treasury security, backed by the corpus, has a maturity value of $500 million. The
maturity dates for the zero-coupon Treasury securities coincide with the corresponding payment
dates by the Treasury.
(b) What is created as a result of coupon stripping in the Treasury market?
As discussed in part (a), a zero-coupon Treasury security results from the coupon stripping in the
Treasury market.
13. Why is a stripped Treasury security identified by whether it is created from the coupon
or the principal?
On dealer quote sheets and vendor screens STRIPS are identified by whether the cash flow is
created from the coupon (denoted ci), principal from a Treasury bond (denoted bp), or principal
from a Treasury note (denoted np). Strips created from the coupon are called coupon strips and
strips created from the principal are called principal strips. The reason why a distinction is made
between coupon strips and principal strips has to do with the tax treatment by non–U.S. entities
where some foreign buyers have a preference for principal strips. This preference is due to the
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tax treatment of the interest in their home country. The tax laws of some countries treat the
interest as a capital gain, which receives a preferential tax treatment (i.e., lower tax rate)
compared with ordinary interest income if the stripped security was created from the principal.
14. What is the federal income tax treatment of accrued interest income on stripped
Treasury securities?
Interest income from Treasury securities is subject to federal income taxes but is exempt from
state and local income taxes. A disadvantage of a taxable entity investing in stripped Treasury
securities is that accrued interest is taxed each year even though interest is not paid. Thus these
instruments are negative cash flow instruments until the maturity date. They have negative cash
flow because tax payments on interest earned but not received in cash must be made.
15. What is the difference between a government-sponsored enterprise and a federally
related institution?
Government-sponsored enterprises (GSEs) securities and federally related institution securities
constitute the federal agency securities market. GSEs are privately owned, publicly chartered
entities created to reduce the cost of borrowing for certain sectors of the economy. The two
major GSEs that have issued debentures are Fannie Mae and Freddie Mac. Federally related
institutions are arms of the federal government whose debt is generally guaranteed by the U.S.
government. The only issuer of federally related institution securities is the Tennessee Valley
Authority. The securities of this federal agency are not guaranteed by the U.S. government.
16. Explain whether you agree or disagree with the following statement: “The securities
issued by all federally related institutions are guaranteed by the full faith and credit of the
U.S. government.”
Federally related institutions are arms of the federal government and generally do not issue
securities directly in the marketplace. Federally related institutions include the Export-Import
Bank of the United States, Tennessee Valley Authority (TVA), Commodity Credit Corporation,
Farmers Housing Administration, General Services Administration, Government National
Mortgage Association, Maritime Administration, Private Export Funding Corporation, Rural
Electrification Administration, Rural Telephone Bank, Small Business Administration, and
Washington Metropolitan Area Transit Authority. Most federally related institutions do not issue
securities. With the exception of securities of the TVA and the Private Export Funding
Corporation, the securities are backed by the full faith and credit of the United States
government. In recent years, the major issuer of federally related institutions has been the TVA.
Thus, for the most part, the securities being issued involve institutions whose securities are not
guaranteed by the full faith and credit of the U.S. government.
While TVA debt obligations are not guaranteed by the U.S. government, they are rated AAA by
Moody’s and Standard and Poor’s. The rating is based on the TVA’s status as a wholly owned
corporate agency of the U.S. government and the view of the rating agencies of the TVA’s
financial strengths. These strengths include (i) the requirements that bondholders of power bonds
are given a first pledge of payment from net power proceeds, and (ii) electricity rates charged by
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the TVA are sufficient to ensure both the full payment of annual debt service and operating and
capital costs.
17. What are the major securities issued by Fannie Mae and Freddie Mac?
In the 1930s, Congress created a federally related institution, the Federal National Mortgage
Association, popularly known as “Fannie Mae,” which was charged with the responsibility to
create a liquid secondary market for mortgages. Fannie Mae was to accomplish this objective by
buying and selling mortgages.
Fannie Mae issues Benchmark Bills, Benchmark Notes, Benchmark Bonds, Callable Benchmark
Notes, Subordinated Benchmark Notes, Investment Notes, callable securities, and structured
notes. Benchmark Notes and Benchmark Bonds are noncallable instruments. In 2001, Fannie
Mae began issuing subordinated securities (Fannie Mae Subordinated Benchmark Notes). These
are unsecured subordinated obligations of Fannie Mae that rank junior in right of payment to all
of Fannie Mae’s existing and future obligations.
In 1970, Congress created the Federal Home Loan Mortgage Corporation (Freddie Mac).The
reason for the creation of Freddie Mac was to provide support for conventional mortgages. These
mortgages are not guaranteed by the U.S. government. Freddie Mac issues Reference Bills,
discount notes, medium-term notes, Reference Notes, Reference Bonds, Callable Reference
Notes, Euro Reference Notes (debt denominated in euros), and global bonds. In 2001, Freddie
Mac also began issuing subordinated securities (called Freddie Mac Subs). These securities
have the same feature as the Fannie Mae Subordinated Benchmark Notes.
Both Freddie Mac and Fannie Mae issue bullet and callable medium-term notes (MTNs) and
structured notes, instruments. There are securities denominated in U.S. dollars as well as issues
denominated in a wide range of foreign currencies.
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