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Unformatted text preview: Chapter 11
Chapter
Bond Portfolios Bond Pricing Relationships
Bond Inverse relationship between price and yield Longterm bonds tend to be more price
Longterm
sensitive than shortterm bonds
sensitive As maturity increases, price sensitivity
As
increases at a decreasing rate
increases Price sensitivity is inversely related to
Price
coupon rate and YTM
coupon Change in Bond Price as a
Function of YTM
Function Duration
Duration Important considerations  Different effects of yield changes on the prices
and rates of return for different bonds
and
 Maturity: iinadequate measure of a bond’s
Maturity nadequate
economic lifetime
economic
 A measure is needed that accounts for both
size and timing of cash flows
size Duration
Duration Measure of a bond’s lifetime, stated in years,
Measure that accounts for the entire pattern (both size
and timing) of cash flows over the life of the
bond
bond The weighted average maturity of a bond’s
The weighted
cash flows
cash
» Weights determined by present value of cash flows
present Cash Flows of 8yr Bond with 9% annual
coupon and 10% YTM
coupon Calculating Duration
Calculating Duration depends on three factors
 Maturity of the bond
 Coupon payments
 Yield to maturity PV(CFt )
D=∑
×t
t =1Market Price
n Duration Relationships
Duration
Duration increases with time to maturity but at a
Duration
decreasing rate
decreasing
» For coupon paying bonds, duration is always
less than maturity
less
» For zero couponbonds, duration equals time
to maturity
to Yield to maturity is inversely related to duration
is Coupon is inversely related to duration
Coupon is Why is Duration Important?
Why Allows comparison of
Allows effective lives of bonds
effective
that differ in maturity, coupon
that differ Used in bond management strategies
Used
particularly immunization
immunization Measures bond price sensitivity to interest
Measures
rate movements
rate
» Directly measures interest rate risk
interest Estimating Price Changes
Using Duration
Using
Modified duration: Duration adjusted by the yield
Duration
to maturity
to
→ D* = D/(1+y)
D* D* can be used to calculate the bond’s
D*
percentage price change for a given change in
percentage
interest rates
interest
→ ChangeP/P = D* Changey
ChangeP/P Duration Conclusions
Duration Price change is proportional to duration, not to
Price
proportional
not
maturity
maturity
To obtain maximum price volatility, iinvestors
nvestors
To
maximum
should choose bonds with the longest duration
with
Duration is additive
Duration
Portfolio duration is a weighted average
Portfolio
weighted
Duration measures volatility
Duration
volatility Duration Example
Duration
Calculate the duration of a threeyear
bond that pays a semiannual coupon of
$30, has a $1,000 par value when the
YTM is 10%?
YTM ...
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This note was uploaded on 12/10/2011 for the course FIN 401 taught by Professor Staff during the Spring '08 term at Miami University.
 Spring '08
 STAFF

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