HI Girish,
This fascinated me, also, as I was preparing for Saturday's webinar b/c we reviewed an interest rate swap pricing problem (see #3 at
http://www.bionicturtle.com/forum/viewreply/6344/)
… and my sub-question included: what is the swap's duration.
Where I tried to be careful to say "in practice, we round down the duration of the FRN to zero" (i.e., the IRS = long a fixed plus short a FRM)
Starting with your final point: my preferred way of saying Macaulay duration, that I got from Sanjay Nawalkha @
http://www.fixedincomerisk.com/ is "w,eighted average maturity of bond, where weights are PV of cash flows." In which case, the FRN has Mac duration ~ time to next coupon because all of the subsequent cash flows have a weight of zero (as they do not contribute to price). So this is closely related to the idea that a FRN must price at par immediately upon coupon settlement. Some
further discussion on this phenomenon and a
very brief XLS "proof" here
So, FRN prices at par at the moment of settlement, such that FRN duration approximately (~=) time to next coupon. In the webinar, I said "round down to zero" b/c an FRM question (for example) would typically assume FRN duration = 0, but unless it is immediately before settlement that is strictly incorrect (although my example shows how minimal the error is).
So, I disagree, technically, with "the duration of the Floating Rate Note immediately after the rate adjust is zero" because at that point in time, the next coupon is essentially fixed as the rate has already been determined -- zero duration cannot be true as there is a bit of price risk until the next reset. (it is just a wrong as saying a six month zero fixed coupon bond has 0 duration). The Mac duration is nearer to 0.4xx years (< 0.5 years).
... but this is why I was worried about presenting it: in my example, the FRN duration is nearer to 0.5 but i "rounded down" to zero (and the impact on swap DV01 was only $2).
hope that helps, David
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