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paid 0.045
0.045 n
(1+YTM)n  1 YTM2 0.045 + 11+YTM YTM
(1+YTM) 0.045
(1+YTM)n  1
YTM +1
+1 0.045
0.045 n
(1+0.04)n  1 0.042 0.045 + 11+0.04 0.04
(1+0.04) 0.045
(1+0.04)n  1
0.04 +1 0.045
0.045 20
(1+0.04)20  1 0.042 0.045 + 11+0.04 0.04
(1+0.04) 0.045
20
(1+0.04)20  1 0.04 +1
+1 =13.82 sixmonth periods
=13.82
= 6.91 years
6.91 Another Duration Example
Another
Find the duration of a 7% 15year bond
Find
sold to yield 9%. Assume interest is paid
annually.
annually. 0.07
0.07 15
(1+0.09)15  1 0.092 0.07 + 11+0.09 0.09
(1+0.09) 0.07
15
(1+0.09)15  1 0.09 +1
+1 = 9.24 years
9.24 Modified duration
calculated as Macaulay duration / (1 + YTM) Relationship between duration and bond
price changes:
approx. pct.
pct. point
change in
=  modified duration × change in YTM
bond price For this bond, if its yield to maturity
For
rises to 11 percent, its price will fall by
rises
fall
about
about
9.24/1.09 × 2, or 16.95 percent.
9.24/1.09 Convexity
The above formula suggests that the relationship between
bond price and yield to maturity is linear.
Actually, the relationship is convex to the origin.
This implies that regardless of which way interest rates move,
the percentage change in bond price is more favorable than
the above formula would suggest. YTM
7%
9%
11% Price*
Price*
Approx.
Actual
980.96
1000.00
838.79
838.79
69...
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This document was uploaded on 02/04/2014.
 Spring '14

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