Measuring Curve Risk in Floating-Rate Notes with Different Index and Discount Curves

Summary

The document examines a floating-rate note whose coupon resets every six months based on a five-year government yield, while its value is discounted using a curve that need not move in lockstep with the projection curve. It cautions that duration depends on how curve changes are defined. Under a parallel-shift assumption for both curves, the first-order duration is approximately zero, consistent with the usual intuition for a floating-rate note.

That single duration measure hides the note’s exposure to the shape of the curve. The answer interprets the position as a curve-steepening exposure: it benefits when projected five-year rates rise more than the six-month forward rates relevant to discounting. To describe that exposure more precisely, it recommends calculating partial durations by shocking separate curve segments. The response is brief and gives no valuation formula, calibrated example, or correlation model, so the near-zero result should be understood as conditional on the stated parallel-shift assumption rather than as a universal property of the instrument.

Key ideas

• An FRN’s duration depends on how projection and discount curves are shocked.
• A parallel move in both curves can imply approximately zero first-order duration.
• A coupon indexed to longer-term yields can leave exposure to curve steepening.
• Partial durations reveal sensitivities to distinct parts of the curve more clearly than one aggregate measure.

Tags

# FRN duration when discount curve and projection curve have non-perfect correlation


# FRN duration when discount curve and projection curve have non-perfect correlation












The textbook example assumes that discount curve and projection curve are the same (or have a perfect correlation). What happens with the FRN's duration when it is not the case?

For example, there are bonds with floating coupons every 6M, but the index for their coupon rate is linked to the 5Y point on the government bonds curve. Every 6M they pay the yield of 5Y government bond + spread.

How could we find the duration of such a bond (disregard the spread for clarity)?

## Answer by dm63 (score 2, accepted)

https://quant.stackexchange.com/a/78237

In that case the duration needs to be carefully defined and interpreted. To first order, the duration is approximately zero, because the simplest assumption is to move the projection curve (5yr Treasury forward rates) and discount curve in parallel. But this is obscuring key information : holding such a FRN amounts to having a curve steepening trade - you win if the 5yr projected rates go up more than the 6month forward rates. This can be more precisely measured by computing the partial durations by shocking different parts of the curve.

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.