Fixed Income Prac. Exam question

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madesofspades

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Holding other factors constant, increasing a bond’s maturity:
A. Will increase its macaulay duration
B. Will decrease its macaulay duration
C. May increase or decrease its Macaulay duration.
 
A longer maturity is supposed to increase duration.
But for some deep discount bonds, duration can decrease over some range of (long) maturities. So C must be correct.
 
That’s not common but duration can decrease when the difference between the YTM and the coupon rate is large enough.
 
fr_clem wrote:That’s not common but duration can decrease when the difference between the YTM and the coupon rate is large enough.
Click to expand...
Do you have a numerical example you can provide?
 
S2000magician wrote:
fr_clem wrote:That’s not common but duration can decrease when the difference between the YTM and the coupon rate is large enough.
Click to expand...
Do you have a numerical example you can provide?
Click to expand...
Yes sure - assume a bond with 2% coupon rate; current YTM = 12%.
Using excel, you should get the following (Macaulay) durations:
Maturity of 30 years > MacD = 12.02213
Maturity of 35 years > MacD = 11.39217
Maturity of 40 years > MacD = 10.80196
 
For a long maturity, duration converges to (1+YTM)/YTM. That’s why you can end up with a decreasing duration (when maturity is increasing) for some discount bonds.
The graph below may help understand
http://i.stack.imgur.com/O0WbO.png
Cheers
 
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