# Standard vs. Effective duration vs. key rate duration

Hello,

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

Thanks!

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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-....

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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?

Thanks,

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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%Simplify the complicated side; don't complify the simplicated side.

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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.

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Modified duration = Macaulay duration / (1 + YTM)

where YTM is the yield

for one coupon periodWhen 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.

Simplify the complicated side; don't complify the simplicated side.

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