Could someone help me understand the difference between the three? I know that key rate duration is bond’s price sensitiivty to change in interest at one specific maturity.
However, I am not sure what the difference is between the standard duration (bond’s price change to parallel shift in yield curve) vs. what exactly is effective duration
There’s no such thing as “standard” duration.
Macaulay duration? Yes.
Modified duration? Yes.
Effective duration? Yes.
Key rate duration? Yes.
Spread duration? Yes.
Standard duration? No.
I wrote an article comparing Macaulay duration, modified duration, and effective duration here: http://www.financialexamhelp123.com/macaulay-duration-modified-duration-and-effective-duration/.
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I also wrote an article on key rate duration here: http://financialexamhelp123.com/key-rate-duration/. (It’s one of the free samples.)
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Maybe I am confused between what effective duration actually means.
From one source it means the price change in bonds with a parallel shift in the yield curve. However, I am confused on what it means when the effective duration on a zero would be the same as the maturity.
From what I read, it is due to the fact that the weighted average of the payments occur at maturity, but how does that have to do with the parallel shift in the yield curve?
Macaulay duration is the present-value-of-cash-flow-weighted time to receipt of cash flow.
Modified duration measures the sensitivity of a bond’s price to a change in its yield to maturity, assuming that the bond’s cash flows don’t change.
Effective duration measures the sensitivity of a bond’s price to a change in its yield to maturity, assuming that the bond’s cash flows could change.
The effective duration on a zero is not the time to maturity unless the YTM is 0%.
How would effective duration equate to TTM if the YTM is 0% on the bond? That is where I get confused on how that relationship works.
Modified duration = Macaulay duration / (1 + YTM)
where YTM is the yield for one coupon period
When the cash flows don’t change in response to a change in YTM (as is the case with fixed-rate bonds without embedded options), effective duration equals modified duration. And when YTM = 0%, modified duration equals Macaulay duration (from the formula above).
The Macaulay duration of a zero is its time to maturity (because 100% of the cash flow occurs at maturity), so when YTM = 0%, the effective duration of a zero is its time to maturity.