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 $t$.


1 Answer 1


yes, definitely, see definition of Macaulay duration

  • $\begingroup$ 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
    Commented Mar 11, 2019 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
    Commented Mar 11, 2019 at 9:17
  • $\begingroup$ I see, thank you. $\endgroup$
    – sane
    Commented Mar 11, 2019 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
    Commented Mar 11, 2019 at 12:21
  • $\begingroup$ @Alex C: Interestingly, Wikipedia seems to suggest otherwise $\endgroup$
    – ZRH
    Commented Mar 11, 2019 at 20:09

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