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FINA 221 Practice Problems
Fall 2010
Managing FixedIncome Portfolios (Suggested Solution)
1. True or False
(a) Holding other factors constant, the Macaulay’s Duration of a bond is always increasing
with the bond’s maturity.
Solution:
False.
For deep discount bonds, the Macaulay’s Duration of a bond can be decreasing
with the bond’s maturity.
(b) Using Duration and Convexity to approximate bond price sensitivity to interest rate is
more accurate than using Duration alone.
Solution:
True.
The actual bond price sensitivity to interest rate is a not a linear relationship.
Using Duration alone would give a straightline approximation, while using both
Duration and Convexity would give an approximation that is closer to the actual
sensitivity.
(c) The Macaulay’s Duration of a bond cannot be longer than the bond’s maturity.
Solution:
True.
For zerocoupon bonds the Macaulay’s Duration equals the maturity.
For
coupon bonds the Macaulay’s Duration is shorter than the maturity.
(d) If the Macaulay’s Duration is matched to the holding period, then reinvestment risk and
price risk would still offset each other under any yield curve changes.
Solution:
False.
When matching the Macaulay’s Duration to the holding period, reinvestment
risk and price risk would offset each other only under small parallel changes in the yield
curve.
(Note: Please remember this fact, even though we have not analyzed nonparallel
changes in the yield curve in our course.)
2. Managing Interest Rate Risk
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Suppose you purchase a fiveyear, 15% coupon bond (paid annually) with a yieldtomaturity
of 9% per year. The face value of the bond is $1000.
(a) Show that the duration of this bond is approximately equal to four years.
Solution:
First we calculate the bond price:
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ൌ
$
. ૢ
ሺ. ૢሻ
$
ሺ. ૢሻ
= $1233.379
Then we calculate the duration:
۲ܝܚ܉ܜܑܗܖ ൌ ܜ ൈ
ୀ
۱۴
ܜ
/ሺ ܡሻ
ܜ
۾ܚܑ܋܍
ൌൈ
/ሺ. ૢሻ
. ૠૢ
ൈ
/ሺ. ૢሻ
. ૠૢ
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 Spring '11
 Darwin
 duration, Zerocoupon bond

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