Bond Market Overview and Bond Pricing
1. Overview of Bond Market
2. Basics of Bond Pricing
3. Complications
4. Pricing Floater and Inverse Floater
5. Pricing Quotes and Accrued Interest
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What is A Bond?
Bond: a debt instrument requiring the issuer (debtor)
to repay to lender/investor the amount borrowed plus
interest over a specified period of time
• Plain vanilla bonds
• Advanced debt contract – mortgage pass-through
securities
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Most Generic Classification
Government bonds – low/no risk, low yield, low
expected returns
-- return is high when yield goes down
Risky bonds – non-government bonds, including
corporate bonds, municipal bonds, mortgage
securities (subprime market securities)
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Sectors of US Bond Market
Treasury Sector
have you heard of saving bonds?
Agency Sector
Municipal Sector
Corporate Sector
Asset-Backed Security Sector
Mortgage Sector
See: www.investinginbonds.com
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More Info of Bonds
Federal Reserve Flow of Funds report:
http://www.federalreserve.gov/releases/z1/
TRACE:
http://www.finra.org/Industry/Compliance/Mark
etTransparency/TRACE/
Mergent FISD:
http://www.kellogg.northwestern.edu/rc/fisd.htm
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Stocks vs. Bonds
1. Different Characteristics
2. Different Markets
Stocks: traded on exchanges and OTC markets:
NYSE, AMEX, NASDAQ
Bonds: traded on OTC markets
3. Similarity: Buy stocks and bonds through online traders.
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Returns of Aggregate Stocks, Gov Bonds,
Corporate Bonds
0.4
0.3
Returns
0.2
0.1
0
1985
-0.1
1990
1995
2000
2005
-0.2
-0.3
ret_stock
Year
ret_gov
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ret_credit
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Overview of Bond Features
• Term to maturity
• Coupon rate
– Fixed rate bonds
– Floating rate bonds
—Reference rate + quoted margin
• Principal/Face Value
• Interest rate/yield to maturity
• Price
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Example of a fixed payment bond
10 years, face value $1000, coupon rate 8%, semi-annually
paid, interest rate 9%. What is the bond price?
There are many variations in bond designs:
(1) deferred-coupon
(2) amortizing securities: securities with a schedule of
periodical principle repayments.
(3) options could be embedded (page 6)
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FV versus PV
Future Value: Pn= P0(1+r)n
Present Value: P0= Pn/(1+r)n
Future value for a regular annuity
Present value for a regular annuity
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Examples
1. Cash flow (1): you receive $100 in year 1, $200 in year 2,
$300 in year 3. Interest rate is 9%. What is the value of
the cash flow?
2. Cash flow: you need to pay $100 in year 1, $200 in year 2,
and $300 in year 3. Interest rate is 9%. How much you
need invest today to pay for this loan?
3. Coupon Bond: 2 years, face value $1000, coupon rate $8,
semi-annually paid, interest rate 9%. What is the bond
price?
Using your financial calculator
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Zero-coupon bonds
Price of zero-coupon bond: P0= M/(1+r)n
Example
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Complications
• If the next payment is due in fewer than 6
months
• Cash flows may not be known
• What is the appropriate required yield and
whether one discount rate can be applied to
all cash flows
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Next Due Payment < 6 months
n
P
t 1

C
M

(1  r ) (1  r ) t 1 (1  r ) (1  r ) n1
days between settlement and next coupon
days in six - month period
In fact, this is a 3-step approach to calculate bond price.
(1) In the first step, we compute bond price if I buy the bond in the next payment date
(i.e., I won’t get any payment for it):
n 1
C
M
P

t
(1  r ) n1
t 1 (1  r )
(2) Add in the payment I receive in the next payment date, then
n 1
n
C
M
C
M
P C




t
(1  r ) n1 t 1 (1  r ) t 1 (1  r ) n1
t 1 (1  r )
(3) Discount the above price back to the date I purchase the bond.
The idea is to suppose I buy the bond right before the next payment day, thus I can have
the next payment, then discount the value back to time 0.
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Price Quoted and Accrued Interest
Price quoted: 100: meaning 100% of its par value/face value
Accrued interest: when an investor purchases a bond between
coupon payments, 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.
for a treasury bond, accrued interest is based on the actual
number of days the bond is held by the seller.
Full price/dirty price = price + accrued interest
Clean price
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Example
A bond face value $1000, YTM=5%, coupon
rate=6% semiannually paid, maturity=5 years. The
bond was issued on 7/1/2003, and bought on
11/1/2005. What is price of the bond.
v=?
n=?
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Procedures of computing price
Step 1
Step 2
Step 3
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Example (cont’d)
What is the accrued interest of the bond?
What is the dirty price of the bond?
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Floater and Inverse Floater
See Exhibit 2-4.
Inverse’s price = collateral’s price – floater’ price
Collateral is the fixed-rate security from which the
inverse floater is created
Floor: the minimum interest rate on the inverse floater
Cap: the maximum interest rate on the floater
The sum of interests paid on floater and inverse floater
must always equal interests on the collateral.
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Risk Associated with Bonds
1.
2.
3.
4.
5.
6.
7.
Interest-rate risk
Reinvestment risk
Call risk
Credit risk
Inflation risk
Exchange-rate risk
Liquidity risk – institutional investor must trade
frequently in some extent
8. Risk risk
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