How a Floater’s Coupon Spread Relates to Its Z-Spread

Summary

This document clarifies the difference between a floating-rate bond’s contractual coupon spread and its z-spread. The coupon spread is generally specified when the bond is issued and determines the payment added to the reference rate. The z-spread, by contrast, is inferred from the bond’s observed price by adjusting the discount rates used to value its cash flows.

The answer says new issuance spreads are set at a level intended to attract investors at a price near par, with the issuer’s credit spread as a guide. Because the contractual spread usually remains fixed, changes in the bond’s price are reflected in its calculated z-spread and discount margin. Near par, the two measures may be close; pricing above or below par moves the calculated spread in the corresponding direction relative to the coupon spread. The explanation sets aside uncommon contracts with scheduled or rating-linked coupon changes and does not derive a precise formula for their relationship.

Key ideas

• The coupon spread on most floating-rate bonds is fixed at issuance.
• A z-spread is calculated from a bond’s price using its cash flows and a discount curve.
• Issuers set the coupon spread to help sell the bond near par, often with credit spreads as a reference.
• When the bond trades away from par, its calculated z-spread and discount margin diverge from the coupon spread.
• Scheduled or contract-triggered spread changes are exceptions to the usual fixed-spread structure.

Tags

# Do z-spreads and quoted margins move in sync?


# Do z-spreads and quoted margins move in sync?












Consider a floating bond with unit face value that pays $L_t + s$ at time $t$, where $L_t$ is some reference-rate at time $t$ and $s$ is a spread.

The $z$-spread is the value $z$ such that $P = \sum (L_t + s) (r_t + z)^{-t}$ where $P$ is the price of the bond and $r_t$ is the zero rate for time $t$.

My question is about $s$ and $z$.

Is there a meaningful relationship between these?

For example, it would seem intuitive to me that they exactly offset each other, i.e. if a bond has $z = 0, s = s$, then if it were to suddenly set $s = 0$, its $z$ would jump to $s$ (approximately). And vice-versa. And they would sort of "meet in the middle".

Is this true?

## Answer by Dimitri Vulis (score 3)

https://quant.stackexchange.com/a/81441

For almost all floaters, the spread $s$ is set at issuance and doesn't change.

(Actually, there are rare exceptions that we'll ignore - $s$ change triggered by the issuer's agency credit rating or ESG score changes, step-up floaters where $s$ changes according to a schedule set at issuance. In some markets they use gearing instead of spread.)

When a new bond is issued, the originator figures out the $s$, close to the issuer's CDS spread - the lowest $s$ that will entice enough investors to buy the desired amount of bond at price close to par. Once $s$ is set, it doesn't change.

In contrast, the Z-spread (and discount margin) are calculated from a given price. If you plug in price close to / above / below par, then you will get a Z-spread (and DM) close to / below / above $s$.

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.