DV01 Question from old Garp exam

[wrongsaidfred]

Hi David,

A question came up on an old FRM practice exam where it wanted us to list the DV01 of three bonds in order from greatest to least while "assuming other things constant".

Par bond, premium bond, zero coupon bond.

Since DV01 is Price * Dmod/10,000 I knew it was a tradeoff between the two and had no idea how to think about it. Their answer surprised me because it just talked about how DV01 is a multiple of dirty price and because a premium bond has a higher coupon it will probably have a higher dirty price.

Is it just me or is this a really bad answer for this question? I think I remember you saying that Dmod goes down with an increasing coupon but DV01 goes up so I guess the final answer is OK but does their explanation hold water? It just seems like there are lots of other things going on. Their "assuming other things constant" is pretty vague.

In another question, they also used called duration the PV01 of a bond, which is a little strange. I do not remember seeing PV01 in the readings anywhere.

Any explanation yuo could provide would be greatly appreciated.

Thanks,
Mike

 

[David Harper CFA FRM]

Hi Mike,

I have no idea why "dirty price" per se enters the answer, that sounds irrelevant. I totally agree, using DV01=price * D/10,000 leads to equivocal answer; e.g., as the coupon reduces (toward a zero coupon bond), duration (in the numerator) increases while price (also in the numerator) decreases. I think your instinct w.r.t. to the trade-off is spot-on.

Although the question may be weak, they likely mean to reflect Tuckman 6.1 where ceteris paribus refers to:

• hold constant: maturity (for example 10 years), yield (for example constant YTM = 6%), face value ($100)
• and vary the coupon, so would have a annual coupon @ 5% (price = $92.64), coupon at 6% (price = $100), coupon @ 7% (price = $107.36)

So, if we vary only the coupon, it is true (consistent with Tuckman Fig 6.1) that DV01 is ordered: discounted $92.64 the lowest and premium $107.36.

It is an esoteric feature of DVO1 that, with respect to the coupon, it acts the opposite of duration: ceteris paribus, higher coupon --> higher DV01
(because the price effect outweighs the duration effective in the numerator, for a given maturity; this is unlike changing maturity and is esoteric IMO)

FWIW, the old duration-type questions tend to be weak (as recently as 2006 or so, the exam would assume that coupon bonds have durations = 7, with no information). This is the one area where I think i've helped them make big strides, the new questions tend to be much more specific. This one feels old ...

PV01 = price value of a basis point and is a synonym (it means the same thing as) DVO1. I agree, i don't think it's ever been in an actual assignment, but practitioners may use it, so this is almost surely a case of a question originated from a practitioner. I hope that helps, David

 

[wrongsaidfred]

Thank you!

By the way, Tuckman chapter 6 was not assigned for this year. It sounds like it has a lot of good info, but if it is not assigned I wonder what kind of problems like this would still be given.

I obviously do not ask you to speculate on such a thing, just making an observation.

Thanks again.

Mike

 

[David Harper CFA FRM]

Hi Mike,

Oh right, I forget that Tuckman Chapter 6 is assigned in Level (Part) 2 ... I frankly don't see the logic of Tuckman 6 in L2, most of it is solid review of single factor sensitivity in Tuckman 5.
(come to think of it, i bet the idea is to keep some duration/convexity foundation in both levels ....)

your old exam may be prior to the L1/L2 split ... but i can tell you the exam likes to test duration/dv01 and, at least so far, it's not like the exam has distinguished explicitly or precisely between Tuckman 5 and 6

Thanks, David