Floating Rate Note

A floating rate note pays interest that resets periodically to a market benchmark — today typically an overnight-rate index like SOFR or €STR — plus a fixed margin. If rates rise, your next coupon rises with them; if rates fall, it falls.

That reset is the product's superpower: because coupons continually catch up with the market, the price barely moves when interest rates change. Rate risk, the thing that batters ordinary bonds, is largely engineered away.

What remains is credit risk: the issuer still has to pay. An FRN from a shaky borrower will fall in price when its spread widens, floating coupon or not. Investors buy FRNs to sit out rate turbulence while still earning issuer spread.

Coupon mechanics

• Formula: reference rate (e.g. compounded SOFR over the period) + quoted margin (fixed at issue, say +80bp).
• Reset frequency: usually quarterly; the coupon is known either at the period's start (legacy IBOR-style) or, for compounded overnight rates, only at its end.
• Floors: many FRNs floor the coupon (often at 0%) — a small embedded option that gains value when rates approach zero.

Why prices still move

Between resets, small rate sensitivity exists (duration ≈ time to next reset — weeks, not years). The real driver is the discount margin: the market's current required spread. Quoted margin 80bp but market now demands 120bp? The price drops below par so a buyer effectively earns the extra 40bp.

Who issues and who buys

Banks are the dominant issuers (matching their floating-rate assets); governments issue some (US Treasury FRNs). Buyers: money market funds, corporate treasuries and anyone bracing for hikes — FRN fund inflows are a classic rising-rate trade.

The par-at-reset theorem

A default-free floater paying exactly the discount rate resets to par at every coupon date: discounting rate-matched cash flows at that same rate telescopes to 100. Real FRNs deviate from par only through (a) the gap between quoted margin \(m\) and current required margin \(\bar{m}\), and (b) accrual within the period:

— the price is par plus the annuity value of the margin differential. Solving this for \(\bar{m}\) given price defines the discount margin, the FRN market's YTM-equivalent.

Risk decomposition

• Rate duration ≈ time to next reset (near zero) — but only for the index component.
• Spread duration ≈ that of a fixed bond of the same maturity: the margin differential annuity is a long-dated exposure. An FRN is short-duration in rates, long-duration in credit.

Post-IBOR conventions

Modern FRNs compound the overnight rate in arrears: coupon \(= \big[\prod_d (1 + r_d \tfrac{n_d}{360}) - 1\big]\tfrac{360}{N} + m\), with lookbacks/lockouts for payment operational lag. Valuation is straightforward on an OIS curve since projection and discounting use the same index — the basis complexity that plagued IBOR floaters largely dissolved.

Embedded floors

A floored FRN = plain FRN + strip of floorlets on the index; in low-rate regimes the floor can dominate returns and gives the "floater" genuine positive duration — priced with the cap/floor machinery (Bachelier quotes on the compounded index).

The formulas above are standard textbook formulations, simplified for teaching. They explain the mechanism — they are not a valuation tool, and they will not reproduce a dealer’s price.