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# GARP.FRM.PQ.P1Doubts with DV01. (garp09)

#### Priyanka_Chandak23

##### New Member
Assuming other things constant, bonds of equal maturity will still have different DV01 per USD 100 face value. Their DV01 per USD 100 face value will be in the following sequence of highest value to lowest value:

a. Zero coupon bonds, par bonds, premium bonds
b. premium bonds, par bonds, zero coupon bonds
c. Premium bonds, zero coupon bonds, par bonds
d. Zero coupon bonds, premium bonds, par bonds

CORRECT: B

DV01 is certain multiple of Dirty Price (which includes Coupons) and not Clean Price. Thus, it is proportional to Base Price, which is Dirty Price. Ordinarily, Premium Bond will have the highest (dirty) price followed by Par Bond and with the least price of Zero Coupon Bond. Hence, DV01 of Premium Bond is the highest while that of Zero Coupon Bonds is the lowest.

INCORRECT: A – Premium Bond will have a higher Base Price and hence higher DV01 than that of

Zero Coupon Bond.

INCORRECT: C – Base Price of Par Bond is higher than that of Zero Coupon Bond and hence, its DV01

cannot be less than that of Zero Coupon Bond.
GARP 2010

If we take DV01 = Price * Modified Duration/10000 then the ZCB has the highest duration, i.e., the Macaulay’s duration is equal to its maturity. Then, why are we only considering the price effect in this question (I am a bit confused)!
Kindly, pinpoint where I am going wrong in my observation.
Thanks a lot.

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#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
HI @Priyanka_Chandak23 This question has been discussed before (eg, https://www.bionicturtle.com/forum/threads/dv01-question-from-old-garp-exam.4922/#post-13235). I think the answer's reliance on dirty (versus) clean price is misplaced. Of course you are correct to use DV01 = Price*Duration/10,000. In my opinion, the intuition here is challenging. Under annual coupon and yield assumptions, imagine a 10-year bond with a 6.0% (annual) yield and escalating coupons rates (from zero coupon to premium):
• zero coupon: price = $558.39, mod duration = 9.43, such that DV01 =$0.53
• 3% coupon: price = $779.20, mod duration = 8.10, such that DV01 =$0.63
• 6% coupon: price = $1,000.00, mod duration = 7.36, such that DV01 =$0.74
• 9% coupon: price = $1,220.80, mod duration = 6.89 such that DV01 =$0.84
Note that for a given maturity (10 years) and yield (6%), as the coupon rate increases, the duration is decreasing and the price is increasing, but DV01 is increasing because the price effect overwhelms the duration effect. So the DV01 is tracking with price, is the easiest way to remember this. I hope this is helpful!

#### Priyanka_Chandak23

##### New Member
I am sorry, I couldnot track it earlier. Thanks a lot, David.
Makes it clear now.