An interesting property of Macaulay duration is revealed by letting *N*, the number of periods to maturity, get large and approach infinity. In equation 6.15, the general expression in equation 6.13 is simplified to apply to a coupon date (i.e., *t/T* = 0).

As *N* approaches infinity, the denominator in the second term gets larger faster than the numerator because *N* is an exponent in the former and a coefficient in the latter. That whole second term goes to zero and the Macaulay duration becomes just (1+*y*)/*y*. Such bonds, known as perpetuities, are rare but do exist. For instance, in the U.K. bonds ...

Start Free Trial

No credit card required