LECTURE 2 OUTLINE
OVERVIEW OF THE LECTURE
•
FIXED INCOME SECURITY (F.I.S.) PRICES AND YIELDS
The Standard Relationship between Bond Prices and Yields
Complexities in Fixed Income Security PriceYield Relationships (Different
Compounding Periods, ZeroCoupon Bonds, and Tbills)
•
MEASURING AND MANAGING INTEREST RATE RISK
The Problem of Interest Rate Risk
Duration and Convexity
FIXED INCOME SECURITY PRICES AND YIELDS
DEFINITION
F.I.S. are those securities where the issuer is to make payments to the investor at
specified future dates.
These payments are fixed in nominal terms at the time the securities are issued.
This is true of most bonds and mortgages.
Other F.I.S. stipulate future payments that are tied in some specified way to future
economic conditions, e.g. floating rate bonds.
THE STANDARD RELATIONSHIP BETWEEN BOND PRICES AND YIELDS
P=
C
y
F
y
t
t
n
n
(
)
(
)
1
1
1
+
+
+
=
∑
P = the current market price of the bond
n = the number of periods remaining until the bond matures
C = the bond’s promised/contractual coupon payment per period
F = the bond’s face value, or principal amount
y = the bond’s yield to maturity
Yield to Maturity:
The return the bond holder will earn on the bond if he/she buys it at its
current market price, receives all coupon and principal payments as promised, and holds
the bond until maturity.
Note:
When required market yields go up, bond prices go down.
1
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Question:
What is the current selling price of a Eurodollar bond with a $100 face value,
9.9178% yield to maturity, 10% coupon rate, and 10 years remaining to maturity?
(Coupon payments are made once a year)
Answer:
P=$ 100.507
Premium Bond:
A bond in which the PV of the bond is greater than its face value.
Discount Bond:
A bond in which the PV of the bond is less than its face value.
Par Bond:
A bond in which the PV of the bond is equal to its face value.
COMPLEXITIES IN FIXED INCOME SECURITY PRICEYIELD RELATIONSHIPS
Different Compounding Periods
When the coupon payments are made semiannually:
P=
C
y
F
y
t
t
n
n
/
(
/
)
(
/
)
2
1
2
1
2
1
+
+
+
=
∑
n = the number of semiannual periods remaining until the bond matures
Question:
Consider a domestic US bond with a 10% coupon rate and ten years remaining
to maturity, which sells for $102 (per $100 face value). What’s the yield to maturity
(annualized)?
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 Fall '08
 cobus
 Compounding, Bond duration

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