1
$\begingroup$

As I know, Macaulay and modified durations are defined in terms of yield to maturity (YTM), in other words, in order to calculate durations we use yield to maturity as a discount factor. Suppose, that instead of YTM we want to calculate durations based on spot rates. Should I calculate Macaulay duration in the following way:$$MacD=\frac{\sum_{t=1}^{n}tCF_t/(1+s_t)^t}{\sum_{t=1}^{n}CF_t/(1+s_t)^t},$$ where $s_t$ is spot rate (zero-coupon rate) for period $t$.

$\endgroup$
0
$\begingroup$

yes, definitely, see definition of Macaulay duration

$\endgroup$
  • $\begingroup$ Thank you for your answer. I have considered the attached article about duration, but, unfortunately, I didn't find something about duration calculation based on spot rates. $\endgroup$ – sane Mar 11 at 9:14
  • $\begingroup$ The fact that the definition refers to the $PV_i$, i.e. the present values of each single cashflow, requires that you use spot rates. If you used yields, the $PV_i$ would not be correct $\endgroup$ – ZRH Mar 11 at 9:17
  • $\begingroup$ I see, thank you. $\endgroup$ – sane Mar 11 at 9:24
  • 1
    $\begingroup$ When you use the spot rates it is called the Fisher-Weil duration bondtutor.com/btchp6/topic6/topic6.htm Macaulay used ytm's in his work. $\endgroup$ – Alex C Mar 11 at 12:21
  • $\begingroup$ @Alex C: Interestingly, Wikipedia seems to suggest otherwise $\endgroup$ – ZRH Mar 11 at 20:09

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.