Hi Sudeep,
You raise a valid point that is found by a careful reading of Tuckman. Strickly speaking, the DV01 is generic: the (absolute) dollar value change given a one basis point change in the “interest rate” where “interest rate” can refer to various metrics. For example, if we think about pricing a bond against an upward sloping term structure (where each bond cash flow is discounted at the appropriate zero spot rate), the we can refer (generically) to the dollar value in change of bond price if we shift the entire term structure down by 1 bps (so that each cash flow is discounted by: previous zero rate - 1 bps). But this is not how we use in the FRM; for practical (exam) purposes, this is a distraction…
What’s important is that DV01 and duration are crude “single factor models.” Notice above that we shift the entire structure by 1 bps; with a single factor metric we are “stuck” with a parallel shift. To be more realistic would require additional factors.
As Tuckman says, he means yield-based DV01 and, in the FRM for practical purposes, we are always referring to (really) a yield-based DV01. By yield, I mean, yield-to-maturity. And yield-to-maturity, by definition, implies a flat yield curve. (i.e., yield/YTM is flat yield curve that is implied by the bond’s price which, in turn, is informed by a non-flat term structure).
(as a detour, this point is very important.
Please see 4.c.3 YTM learning XLS http://www.bionicturtle.com/premium/spreadsheet/4.c.3_yield_to_maturity/.
it is important to see that yield (YTM) is single-factor flat term structure that equates to the more realistic spot and forward curves.
It takes a bit of study to see this, that the YTM is a single-factor equivalent to a multi-factor term structure. If we shift or shock the multi-factor term structure under a duration/DV01, it must mean that all rates shift the same: a parallel shift)
Okay, so now we have established:
* the zero term structure can be any shape; e.g., upward sloping
* The yield (YTM) is the “unrealistic” flat term structure that is associated (i.e., gives the same bond price)
* The DV01 can refer to any 1 basis point shift in “interest rate”
* But we (FRM) refer to the yield-based DV01: the change in price given a 1 bps change in the “yield” (YTM)
And, in this regard, the difference between DV01 and modified duration is *merely* units. The most important formula, for our purposes, is:
DV01 = Price * Duration / 10,000, or more exactly:
(yield-based) DV01 = Price * (Modified) Duration / 10,000
both give the (linear, approximate) estimate of bond price change for a shift in yield, DVO1 (in $, for 1 bsp), modified duration (in % terms, for 1 unit change). You can see your “confusion” IMO is more related to astute observation, but it’s easier to stick with the flat YTM for our purposes.
David
