 # Fixed Income Prac. Exam question

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.

I believe that Macaulay duration always increases with increasing maturity.

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

Do you have a numerical example you can provide?

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

Very interesting.

Thanks!