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# Derivation of modified duration formula for par bond

#### Jose V

##### New Member
Subscriber
In which study guide or video can i find the derivation of the formula of modified duration of par bond?
I understand MD formula for par bond is: MD=[1-(1+y)˄-maturity] / y
But still searching for derivation..

#### Jose V

##### New Member
Subscriber
The MD formula for par bond is applied in the file R36.P2.T5_Jorion-mapping-backtest-v3.xlsx sheet: "VaR-Mapping-Jorion-Ch-11", cell D30. Just need to understand formula derivation and in which study guide is shown. Thanks.

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#### David Harper CFA FRM

##### David Harper CFA FRM (test)
Staff member
Hi @Jose V I'm not sure it's explicitly in a study note (we should add to the formula sheet revision, however ....). I think I derived it somewhere in the forum almost a decade ago (ha), but it's also based on Tuckman 4.45 (which in turn makes use of his own formula 4.37), please see (4.45) below where D(c = y) and notice his formula is for a semi-annual compound frequency; of course, (c=y) refers to a par bond. So in my XLS etc, I just used the annual compound frequency equivalent (Jorion assumes annual):

And recent note here: