Which “duration” does it mean if it is not specifically mentioned ? Macaulay, Modified, or Effective ?
I believe that there is only one duration in the CFA curriculum - effective duration.
Yup: effective duration.
(I’d submit, however, that understanding Macaulay duration and modified duration is quite useful, and will improve your understanding of effective duration.)
Is Macaulay duration the one that takes the weighted average of the cash flows and then discounts them? That’s how I learned what duration was, and I think it’s easier to understand that way.
Close. It’s weighted average time-to-receipt-of-cash-flow, so the (PV of the) cash flows are the weights, multiplied by the time-to-receipt. I’m sure that’s what you were thinking.
It’s a great visualization, and it’s easy to see the effect of changing maturity and coupon, and somewhat easy to see the effect of changing YTM. A lot easier than for modified or effective duration.
I think that CFA Institute’s decision to drop Macaulay duration from the curriculum was . . . I’ll be charitable here . . . short-sighted. I was thinking of another adjective.
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Macaulay Duration and Modified Duration are stated in Reading 58 (Vol 5 of CFAI curriculum).
Yup: LOS 58.f; it says to distinguish and explain them.
When CFA Institute says “duration”, they mean “effective duration”.
I don’t know if CFA Institute says that Macaulay duration is a measure of interest rate sensitivity or not. It isn’t intended to be, and shouldn’t be used as such a measure. Modified duration is a measure of interest rate sensitivity . . . if the cash flows don’t change. Effective duration is a measure of interest rate sensitivity whether cash flows change or not.
By the way, all duration measures have time as their units: usually years. Unfortunately, CFA Institute has dropped the units, and writes things like, “the duration of this bond is 4.5.” What they mean is that it’s 4.5 years, whether they’re talking about Macaulay duration, modified duration, or effective duration.
Effective duration only…
For the Dec 2013 and Dec 2014 L1 materials, LOS 55B (Study Session 16) says “define, calculate, and interpret Macaulay, modified, and effective durations;”, so it’s still in there. Add I agree - understanding Macauley duration goes a long way towards understanding effective duration.
The way I’ve always taught durationis by first establishing that the FUTURE value N years hence changes by about (as an example) N% for every 1% change in the discount rate. Form there, they see that the the PV of mthe future cash flow behaves similarly. And from there, it’s a short hop to MAcauley Duration, and an even shorter hop from Macauley to effective duration.
Of course, Macauley always makes me think of Macallan’s, so I end up celebrating the topic later in the day appropriately (another reason why I’m glad Macauley is still in the curriculum - I’m teachin it shortly).
From the perspective of mathmatics, I my opinion :
1.Macaulay Duration has the unit of “year” and it is not a measure of I/R sensitivity.
- Modified Duration and Effective Duration shall have no unit, just as the elasticity of the demand in economics, and both of them are measues of I/R sensitivity.
The units on Macaulay duration are years, and Macaulay duration is not intended to measure interest rate sensitivity.
Modified duration and effective duration also have units of years – unlike elasticities in economics – and both are measures of interest rate sensitivity.
If you analyze the units in the formulae for modified duration or effective duration you get:
- P- has units of $ (or some currency)
- P+ has units of $
- P0 has units of $
- Δy has units of 1/year (when we talk about interest rates, the units are per year)
- The result is / ( × (1/year)) = years
S2000magician,
As you daid, P-,P+ and P0 all have the units of $.
Since (P- – P+) / (2×P0×Δy) = {[(P- – P+) / 2] / P0} / Δy , the numerator {[(P- – P+) / 2] / P0} has the unit of % and the denominator Δy has the unit of % too.
Therefore, from the perspective of mathmatics, the result shall not have an unit.
I am quite confused as it seems to me that the change in YTM shall be in unit of %.
If you pay $1,000 for a 10-year bond with a YTM of 5%, does it mean that over the 10 year period you’ll earn a total of $50 profit? Or (approximately) $50 per year?
The 5% means 5% per year.
(By the way, % isn’t a unit.)
Effective Duration (no units)
Effective duration has units of years, despite what CFA Institute and a large contingent of fixed income types claim.
As I wrote above, analyze the units in the formula, and remember that YTM has units of 1/years.
I agree by what you say… but what I mean by “No Units” is that we usually treat Effective duration as a sensitivity factor (Bond price change)… in that case … it shall not matter…
I agree that it’s used as a price sensitivity measure.
The reason that the units matter is that the yield that changes needn’t be given as an annual yield. (I cannot imagine why anyone would give something other than an annual yield in this situation; except, maybe, CFA Institute.) By understanding what the units are, you have a better understanding why it works as a price sensitivity measure.
It’s the mathematician in me.
It’s magician in you 
I agreed with you that Modified Duration and Effective Duration shall have the unit of years.
However, please refer to Page 579 of CFAI Curriculum Volume 5. It stated :
A mortgage-backed security that is an interest-only security, the duration is negative. What does a negative number, say, - 4 mean ? …
This is a very interesting issue to me !