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# DV01 vs duration

#### ravishankar80

##### New Member
I have a couple of question in the early bird episode number 7 .

1. I did not understand the difference between DV01 and duration -- both seem to indicate the change in price of a bond to to change in yield .
2. Also in the calculation of duration , when I change the yield how do I calculate the change in price . In the example given price is $851.23 @ 6% yield . The price is$864.86 at 5.8% yield so how is this calculated ?

Regards
Ravishankar

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Ravishankar,

1. Great question. I linked here to the (EditGrid) spreadsheet in case you would like to examine this. This is the XLS the underlies the EB episode to which you refer. I just added the four purple rows at top to show: the difference is merely units. There are many durations, but (aside from the Macaulay) we care about:

Modified duration (D) = 7.93
(D)(Price)/10,000 = DV01 (aka, PV01) = (7.93)(851.23)/10,000 = $0.68 Dollar duration = (D)(Price) = (7.93)(851.23) =$6,751

So, the (modified) duration is the *approximate* (read:linear) % change in price given a 1% change in yield. The DV01 is the *approximate* DOLLAR change given a 1 basis point change. So, the DV01 = (D)(Price)/10,000. The difference is merely units!

In words, dollar duration is duration times price, and DV01 is dollar duration re-scaled (/10000)

The dollar duration is the slope of the linear approximation (the line tangent to the P/Y) curve, contrary to popular belief that duration is the slope.

2. It's a "repricing" of the bond. You can see in the spreadsheet, I just treat it like a new bond with a new yield at 5.8%. So, it is:

N = 20 (10*2)
I/Y = 5.8/2
PMT = 20 (4% * 1000 / 2)
FV = 1000

CPT PV = \$864.86

Please note a tip about the TI BAII+ plus: once you price the initial bond, you don't need to re-enter any of the inputs that don't change, here you only need to re-enter the new I/Y

Thanks, David

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