Approximating Floating-Rate Note PV01 with a Short Bond

Summary

The document explains a practical approximation for estimating the interest-rate PV01 of a floating-rate note. The approach represents the floater using a short bond that pays the already-fixed next coupon and principal at the next payment date, then compares its price with that of a hypothetical Treasury paying principal on that date. The short bond’s yield sensitivity is used as an estimate of the floater’s PV01.

The rationale is a decomposition: the floater can be viewed as the short bond plus a forward bond beginning at the next coupon date and continuing to the floater’s maturity. The forward bond is treated as having approximately zero DV01 because its floating coupon and discount rate move together. The note emphasizes that this is a rule of thumb, not an exact result. A spread over the floating reference rate can leave the floater with some residual rate sensitivity.

Key ideas

• A floater can be decomposed into a short bond through the next coupon date and a forward bond thereafter.
• The short bond pays the already-fixed coupon and principal at the next payment date.
• The forward bond is approximated as having zero DV01 when its coupon and discount rate move together.
• The short bond’s yield sensitivity can therefore approximate the floater’s PV01.
• A spread over the floating rate can create residual sensitivity, so the method is approximate.

Tags

# Interest rate PV01 for a floating rate bond


# Interest rate PV01 for a floating rate bond












I have seen this approach in my work and I would like to understand the theoretical justification behind this approach.

To calculate the interest rate PV01 of a floating rate note. A synthetic bond is created that pays the next coupon (which was fixed already during the previous coupon payment date) and the face value (say 100) at the next coupon payment date. The price of this bond is equated to the price of a hypothetical treasury bond that pays 100 at the next coupon payment date. The yield of this synthetic bond is calculated and the yield based sensitivity (pv01) is termed as the pv01 of the original floater.

I haven’t been able to understand how the two prices are equal. Can anybody help me out here?

## Answer by dm63 (score 2)

https://quant.stackexchange.com/a/39916

It's because the FRN is equal to a portfolio of (a) the shorter dated bond you described and (b) a forward bond, purchased on the next coupon payment date, featuring a floating rate coupon and a maturity date the same as the FRN. If the bond in (b) has zero dv01, the result follows. We argue that indeed it has zero dv01, because when interest rates move, both the return on the bond and the discount rate move identically. Like any rule of thumb, it's an approximation. If there is a spread on the FRN over the floating interest rate, this will create a small dv01.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.