Fixed Income Prac. Exam question

CFA Level I Fixed Income
#1

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.

#2

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.

#3

I believe that Macaulay duration always increases with increasing maturity.

#4

That’s not common but duration can decrease when the difference between the YTM and the coupon rate is large enough.

#5

Do you have a numerical example you can provide?

#6

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

#7

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

#8

Very interesting.

Thanks!