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FINE 4120
Analysis of Fixed Income
Laura Herencia
Time value of money  a $ tomorrow is more valuable than a $ today.
Interest rate for compounding periods
10% 12
APR= 10% Compounding monthly  FV= 100*(1+
𝐴𝑃𝑅 m*n 
FV = PV * (1+
FV = PV*(1+r)N
m=compounding periods in a year
Definition and Basic Features
・ Definition
・ Issuer
・ Maturity
・ Par value
・ Coupon rate and frequency
A fixed income security is a debt instrument that allows issuers to borrow money from investors.
 Obligations of issuer to the investor
 The issuer returns interest & principal on a fixed schedule.
 No ownership
 Prior claim compared to stocks
Shareholders are the residual owners of the company; they are the last ones to get paid. Creditors are the first ones to
get paid.
The difference between the price and the amount of money they receive after is the interest. It’s the profit.
 U.S. government
 Government agencies and government-sponsored enterprise (GSE)
 Municipality
o State and local governments
 Corporations
o Financial issuer (e.g., banks and insurance companies)
o Non-financial issuer
Maturity Date
The maturity date refers to the date when the issuer must redeem the bond by paying the outstanding principal amount.
⎼ Time to maturity: the time remaining until the security’s maturity date.
FINE 4120
Analysis of Fixed Income
Par Value
The principal amount that the issuer agrees to repay the investor on the maturity date.
- Also known as: face value, face amount, or simply par.
- In practice, bond prices are quoted as a percentage of their par value.
Example: Consider a bond with a par value of $1,000. A quote of 95 means the bond price is
95% × $1,000 = $950
Corporate bonds, are quoted in increments of 1/8
93 – 3  (95 + 3/8) %
Government bonds are quoted in increments of 1/32
96 – 15  (96+15/32) %
A bond with the same maturity, the government bond will be more liquid.
Coupon rate and frequency
Coupon rate (on an annual basis): the interest rate that the issuer agrees to pay each year.
Frequency: coupon payments are made periodically
 annually, semi-annually, quarterly, etc.
What is the coupon payment of a bond with a coupon rate of 6% and a par value of $1,000?
If coupon payments are made annually:
6% × $1,000 = $60.
What are the coupon payments if they are made semiannually?
6% / 2 * $1000 = $15
What are the coupon payments if they are made quarterly?
6% / 4 * $1000 = $15
In this class, we assume semiannual coupon payment unless otherwise specified.
Example: 2 years, 5%, $1000 (piece of paper)
By time of issuer:
U.S. Treasury securities
Issued by the U.S. government
Example: T-bills, T-notes, T-bonds, TIPS, etc.
“Free of credit risk”
o backed by the U.S. government's full faith and credit
Highly liquid
o Easily to convert U.S. Treasury securities to cash in the secondary markets
o Over the counter & around the clock during the week.
o Daily trading volume reported by major dealers over $400 billion.
o Most liquid: on-the-run securities
Taxation: interest income is
o exempt from state and local income taxes
Laura Herencia
FINE 4120
Analysis of Fixed Income
but subject to federal income taxes.
Laura Herencia
Federal agency securities
Issued by
Federal agencies
 Federal Housing Administration (FHA)
 Small Business Administration (SBA)
 Government National Mortgage Association (GNMA)
or government-sponsored enterprise (GSE): private companies but serve a public purpose
 Federal National Mortgage Association (Fannie Mae)
 Federal Home Loan Mortgage (Freddie Mac)
 Federal Home Loan Bank
Low credit risk
 The interest from most, but not all, agency bonds is exempt from local and state taxes. Freddie Mac
and Fannie Mae agency bonds are fully taxable.
Municipal securities
Issued by state and local governments
Credit risk is low but varies across issues
o Interest income is exempt from U.S. federal income tax for most issues
o Commonly, a state exempts tax on bonds it has issued from the state income tax while taxing interest
on bonds sold by other states.
General obligation (GO) bonds: backed by full faith and credit of the issuing municipality.
o Example: The State of LA sold general obligation bonds in the amount of $310 million in Feb 2019
(rated Aa3 by Moody’s, AA- by S&P, and AA- by Fitch)
o Example: The City of New York issued $850 million in general obligation bonds in Oct 2019 (rated
Aa1 by Moody’s, AA by S&P and AA by Fitch)
Revenue bonds: backed by the cash flow generated from a particular project. For example, airport revenue
bonds, hospitality revenue bonds, etc.
Corporate securities
 Issued by corporations
o Financial companies: banks and insurance companies
o Non-financial companies: Ford, Google, etc.
 Example.
o Amazon raised $10 billion in the bond markets in June 2020, including $1 billion of debt yielding just
 Credit risk
o Varies across corporations and issues
Money market securities
• Maturity: overnight to one year
• Example
o T-bill
o Commercial paper: short-term unsecured promissory notes issued by companies
o The largest issuer: financial institutions
Typically less than three months
FINE 4120
Analysis of Fixed Income
Funding for working capital and seasonal demands for cash
In most cases, “rolling over the paper”.
Largest commercial paper market: the US commercial paper (USCP) market
Laura Herencia
Capital market securities
• Maturity: longer than one year.
• Example: T-notes, corporate bonds, etc.
Zero-coupon bonds
Do not pay coupon.
Issued at a discount to par and redeemed at par.
Example: T-bills
Coupon bonds
• Fixed-rate bonds
Coupon rate is fixed over the life of the security
• Floating-rate bonds
 Coupon rate is adjusted to market interest rates at a regular, short-term interval (e.g., quarterly).
Coupon rate = reference rate + spread
Example. FRNs (floating rate notes issued by the U.S. Treasury)
Reference rate
 Libor (London interbank offered rate)
o Rates at which a select set of banks believe they could borrow unsecured funds from other banks in
the London interbank money market.
 Discount rates on T-bills
 Usually set fixed at issuance and reflects the issuer’s creditworthiness.
 Expressed in basis points (bps): a basis point = 0.01%.
Assume that a floating-rate bond matures in December 2020. The bond makes semi-annual coupon payments. The
coupon rate is expressed as six-month Libor (known at the beginning of the coupon period) + 150 bps.
The coupon rate that will apply to the payment due in June 2020 will be 3.41% (= 1.91%+1.5%).
What is the coupon payment due in December 2020 per $1,000 face value?
FINE 4120
Analysis of Fixed Income
Laura Herencia
Primary and Secondary Markets
Primary markets
New issues of securities are sold to initial buyers.
Only time the issuer ever gets any money for the securities
Secondary bond markets
Existing securities are subsequently traded among investors.
Over the counter (OTC)markets
The primary dealers act as market makers.
o E.g., Goldman Sachs, Citigroup, etc.
o Buying and selling securities from customers for their own accounts at their quoted bid and ask prices.
Bond Issuance in Primary Markets
A bond issue can be sold via a
 public offering sold to any member of the public.
 private placement sold to a selected group of investors.
Public Offering
Underwritten offering (corporation bonds, munis)
 The underwriter (a single investment bank) or the syndicate (a group of investment banks) takes the
 buys the bond from the newly issued bonds for the issuer,
 and then resells them to investors or dealers who then sell them to investors.
Best effort offering (corporation bonds)
 An investment bank serves as a dealer,
 tries to sell the bond issue if it is able to for a commission fee.
Auctions (U.S. Treasury securities)
Private Placement
 Typical investors: institutional investors, such as insurance companies and pension funds.
 Investors can negotiate the term of the bonds.
Types of securities
 Treasury-bills(T-bills)
 Treasury-notes(T-notes)
 Treasury-bonds(T-bonds)
 Treasury inflation-protected securities (TIPS)
 Separate trading of registered interest and principal securities (STRIPS)
1. T-bills
No payment until maturity, sold at discount from par (face value).
 Example. A $100 bill may be auctioned for $98. You would pay $98 for the bill at purchase, and you would
get $100 when the bill matures. The difference of $2 is your interest.
FINE 4120
On maturity date: payment of face value.
Analysis of Fixed Income
Laura Herencia
Maturities (<=1 year):
 4, 8, 13, 26, and 52 weeks, offered on a regular schedule
 A few days (Cash management bills), offered from time to time
2. T-notes and bonds
Pay fixed coupon every six months until maturity.
On maturity date: payment of last coupon and face value.
 Notes (> 1 year but <= 10 years): 2, 3, 5, 7, and 10 years.
 Bonds (> 10 years): 30 years.
Suppose in May 2019 the U.S. Treasury issued a note with an annual coupon rate of 2% and a maturity date of May
15, 2024. The note pay coupon semiannually. What are the cash flow schedule and cash flows for $1,000,000 par
value of the note?
For $1 million face value, it pays a semi-annual coupon of:
$1,000,000 ∗
= $10,000 every six months.
Cash flow schedules and cash flows of the U.S 2s of May 15, 2024
・ Treasury inflation-protected securities, providing protection against inflation.
・ Semiannual interest payment are a fixed percentage of the inflation- adjusted principal at the time the interest
is paid.
o Adjusted principal increases with inflation and decreases with deflation, as measured by the
Consumer Price Index.
・ On maturity date, payment of the adjusted principal or original principal, whichever is greater.
o This provision protects you against deflation.
・ Maturities: 5, 10, and 30 years.
Assume in May 15, 2018, the Treasury issued a TIPS with an annual coupon rate of 2%. The TIPS pays coupon
semiannually. The first two coupon payments are determined as follows.
FINE 4120
Analysis of Fixed Income
Laura Herencia
・ Separate Trading of Registered Interest and Principal of Securities.
・ The Treasury introduced STRIPS program in 1985.
・ The program allows the individual components of eligible Treasury notes and bonds to be held separately in
the Federal Reserve’s system.
・ The Treasury does not issue STRIPS (STRIPS do not trade in the primary market).
・ An institution can request an eligible Treasury security to be stripped into separate components by sending
instructions to a Federal Reserve Bank (SRIPS trade in the secondary market).
A Treasury note with 10 years remaining to maturity consists of a single principal payment, due at maturity, and 20
interest payments, one every six months over a 10-year duration.
• When this note is converted to STRIPS form, each of the 20 interest payments and the principal payment becomes a
separate security.
Why zero coupons are attractive?
・ Sell at deep discounts.
・ Hedging: pension funds and insurance companies use them to match their liabilities.
・ Speculating: Prices of zero-coupon Treasury securities are more sensitive to changes in interest rates.
• U.S Treasury securities are issued through auctions (primary markets)
o Single-price or uniform-price auction.
o Non-competitive tenders: submit amount only.
o Competitive tenders: amount and yield.
Steps in the auction:
o Step 1. Subtract non-competitive tenders from total
o Step 2. Allocate remaining amount to competitive tenders, from the lowest yield (highest price) to the
highest yield (lowest price) until the offering amount is reached. The highest accepted yield is often
called stop-out yield.
o Step 3. All tenders receive the stop-out yield (the quantities awarded to the bidders at the stop-out
yield are allocated pro-rata).
, yield
and vice versa.
Suppose the Treasury auctions $10 billions of 90-day bills.  the total issuance amount is $10 billion.
• The competitive bids are:
o $8 billion at 1.670%
o $4 billion at 1.673%
o $2 billion at 1.675%
• Noncompetitive bids are $1 billion in total.
What would be the stop-out yield for the auction?
Total issuance – what each bidder will receives.  $10 billion - $1billion = $9 billion (available to distribute among
competitive bidders)
$9 billion (we have left) – $8billion (of the ones that require 1.670%) = $1 billion  still have $1 billion left
We are not able to satisfy the requirement of the $4 billion, but we can evenly distribute it: ¼ = 25%
Stop – out yield= 1.673% the highest at which the treasure securities can be assigned.
FINE 4120
Analysis of Fixed Income
Laura Herencia
Now Your Turn
Suppose the Treasury auctions $10 billions of 90-day bills.
The competitive bids are
o $2 billion at 1.570%
o $4 billion at 1.569%
o $3 billion at 1.568%
o $2 billion at 1.567%
Noncompetitive bids are $3 billion in total.
What would be the stop-out yield for the auction?
Total issuance – what each bidder will receives.  $10 billion - $3billion = $7 billion (available to distribute among
competitive bidders)
$7 billion (we have left) – $2billion (of the ones that require 1.567%) = $5 billion  still have $5 billion left
$5 billion (we have left) – $3 billion (of the ones that require 1.568%) = $2 billion  still have $2 billion left
We are not able to satisfy the requirement of the $4billion, but we can evenly distribute it: 2/4 = 50%
Stop – out yield= 1.569% the highest at which the treasure securities can be assigned. I can only receive 500 0f the
face value 1000.