1
Endof Chapter 9 Questions
1.
What are the two different general interpretations of the concept of
duration
, and
what is the technical definition of this term?
How does duration differ from
maturity?
Duration measures the average life of an asset or liability in economic terms.
As such,
duration has economic meaning as the interest sensitivity (or interest elasticity) of an
asset’s value to changes in the interest rate. Duration differs from maturity as a measure
of interest rate sensitivity because duration takes into account the time of arrival and the
rate of reinvestment of all cash flows during the assets life.
Technically, duration is the
weightedaverage time to maturity using the relative present values of the cash flows as
the weights.
2.
Two bonds are available for purchase in the financial markets.
The first bond is a
2year, $1,000 bond that pays an annual coupon of 10 percent.
The second bond is
a 2year, $1,000, zerocoupon bond.
a.
What is the duration of the coupon bond if the current yieldtomaturity (YTM)
is 8 percent? 10 percent?
12 percent?
(Hint: You may wish to create a
spreadsheet program to assist in the calculations.)
Coupon Bond
Par value =
$1,000
Coupon = 0.10
Annual payments
YTM =
0.08
Maturity = 2
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$100.00 0.92593
$92.59
$92.59
2
$1,100.00 0.85734
$943.07
$1,886.15
Price = $1,035.67
Numerator =
$1,978.74
Duration =
1.9106
= Numerator/Price
YTM =
0.10
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$100.00 0.90909
$90.91
$90.91
2
$1,100.00 0.82645
$909.09
$1,818.18
Price = $1,000.00
Numerator =
$1,909.09
Duration =
1.9091
= Numerator/Price
YTM =
0.12
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$100.00 0.89286
$89.29
$89.29
2
$1,100.00 0.79719
$876.91
$1,753.83
Price =
$966.20
Numerator =
$1,843.11
Duration =
1.9076
= Numerator/Price
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b.
How does the change in the current YTM affect the duration of this coupon
bond?
Increasing the yieldtomaturity decrease the duration of the bond.
c.
Calculate the duration of the zerocoupon bond with a YTM of 8 percent, 10
percent, and 12 percent.
Zero Coupon Bond
Par value =
$1,000
Coupon = 0.00
YTM =
0.08
Maturity = 2
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$0.00 0.92593
$0.00
$0.00
2
$1,000.00 0.85734
$857.34
$1,714.68
Price =
$857.34
Numerator =
$1,714.68
Duration =
2.0000
= Numerator/Price
YTM =
0.10
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$0.00 0.90909
$0.00
$0.00
2
$1,000.00 0.82645
$826.45
$1,652.89
Price =
$826.45
Numerator =
$1,652.89
Duration =
2.0000
= Numerator/Price
YTM =
0.12
Time
Cash Flow
PVIF
PV of CF
PV*CF*T
1
$0.00 0.89286
$0.00
$0.00
2
$1,000.00 0.79719
$797.19
$1,594.39
Price =
$797.19
Numerator =
$1,594.39
Duration =
2.0000
= Numerator/Price
d.
How does the change in the current YTM affect the duration of the zerocoupon
bond?
Changing the yieldtomaturity does not affect the duration of the zero coupon
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 Spring '09
 tsui
 Interest Rates, Bond duration, duration, Zerocoupon bond

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