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Homework 9
1.
Using a two year semiannual 8% coupon bond, 1000 par, with a 5% YTM. For
this question find all answers to at least the 6
th
decimal place.
A. Calculate the price of this bond
P
0
=(40/.025)(11/(1+.025)^4)+1000/(1+.025)^4=
1056.429613
B. Calculate duration and modified duration
D= (.5)*(40/(1+.025))/P
0
+ (1)*(40/(1+.025)^2)/P
0
+ (1.5)*(40/(1+.025)^3)/P
0
+
(2)*(1040/(1+.025)^4)/P
0
Slove for D using P
0
from above: D= 1.890971298 years
or 2(1.8684004)=3.781942596 periods
3.781942596 /(1+.025)= D*(modified duration)
D*= 3.689700094 periods
C. Using modified duration calculate Change in p over p for a change in y of 1%
and 5%.
3.689700094 (.01/2)= .0184485005
3.645659317 (.05/2)=
.0922425024
D.
Price the same bond with a YTM of 6% and 10% as you did in part A.
P
0
=(40/.03)(11/(1+.03)^4)+1000/(1+.03)^4=
1037.170984
P
0
=(40/.05)(11/(1+.05)^4)+1000/(1+.05)^4= 964.540495
E. Use the answer from part D to calculate the actual change in p over p,
compare this answer for 1% and 5%, with the answers to part C.
For 1% change
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This note was uploaded on 10/15/2011 for the course ECON 171 taught by Professor Hull during the Spring '09 term at Brandeis.
 Spring '09
 Hull

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