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Lesson 1 of 5 · 12 min
Floating-rate notes: quoted margin vs required margin
A floater's coupon resets with the market reference rate, so its price moves away from par mainly when the margin investors require differs from the fixed margin the issuer promised.
In short
- A floating-rate note (FRN) pays a coupon of market reference rate (MRR) + quoted margin, reset on set dates. The rate is fixed at the start of each period and paid at the end (in arrears).
- The quoted margin (QM) is fixed in the contract. The required margin, also called the discount margin (DM), is the spread the market demands today.
- On a reset date: DM = QM → par; DM > QM → discount; DM < QM → premium.
- The discount (premium) equals the PV of the per-period shortfall (excess) of for the rest of the note's life.
- The required margin changes mainly with the issuer's credit risk, and also with liquidity or tax status. Macro, "top-down" factors work through the MRR instead.
- A floater's price risk from rate changes is small and depends on the time to the next reset: the longer the reset period, the more it behaves like a short fixed-rate bond.
How a floater's coupon works
A fixed-rate bond pays the same coupon whatever happens to interest rates. A floating-rate note (FRN, or floater) does not. Its coupon is tied to a short-term market reference rate (MRR), usually a money market rate, and is reset on predetermined dates, for example every quarter.
The coupon formula is MRR + quoted margin. The MRR is observed at the start of each period and the interest is paid at the end of that period. This is called paying in arrears. Accrued interest on floaters is usually counted on an actual/360 or actual/365 basis.
Because the cash flows follow market rates, the borrower's funding cost adjusts automatically and the lender bears far less price risk than with a fixed-rate bond. Most bank loans work the same way. Banks fund themselves largely with short-term deposits, so lending at floating rates keeps their assets and liabilities matched.
Think of a floater as a deposit that is repriced every few months. Whatever happened to rates, the next coupon will catch up, so there is little reason for the price to drift far from par.
Quoted margin and required (discount) margin
The quoted margin (QM) is the fixed spread over (or under) the MRR written into the bond's terms. It compensates investors for the issuer's credit risk compared with the risk built into the reference rate. A very strong issuer can even have a negative quoted margin.
The required margin is the spread over or under the MRR that would make the FRN price exactly at par on a reset date. The market sets it, and it changes over time. It is also called the discount margin (DM). It plays the same role for a floater that the yield spread plays for a fixed-rate bond.
At issue, a floater sold at par has DM = QM. Later, if the issuer is downgraded, investors want a bigger spread: DM rises above QM. The coupon still pays only the old QM, so each coupon is deficient. If the issuer's credit improves, DM falls below QM and each coupon contains excess interest.
What moves the required margin are "bottom-up" factors: the issuer's credit risk above all, plus liquidity and tax status. These are the same factors that move a fixed-rate bond's yield spread. Economy-wide forces such as inflation or a shift in the yield curve show up in the MRR, not in the margin.
| Relationship | Each coupon is… | Price vs par |
|---|---|---|
| DM = QM | exactly what investors require | At par |
| DM > QM | deficient by per period | Discount |
| DM < QM | in excess by per period | Premium |
Floaters and changes in benchmark rates
Where the two kinds of bonds differ sharply is a change in the benchmark rate. A fixed-rate bond's coupons are locked, so a rise in rates cuts its price for its whole remaining life. A floater's next coupon is reset to the new MRR, so its price is hit only until the next reset date.
Suppose the required margin stays equal to the quoted margin. Between reset dates, if the MRR rises, the floater's flat price dips below par because the coupon already fixed for the current period is now too low; if the MRR falls, the price rises above par. As the reset date approaches, the price is pulled back to par.
So a floater's interest rate sensitivity comes mainly from the time until its next reset. The longer the reset period, the more the floater behaves like a short-dated fixed-rate bond and the more its price can move.
Two separate questions: "Will the price move if rates move?" (only a little, until the next reset) and "Will the price move if the issuer's credit changes?" (yes, exactly like a fixed-rate bond).
Formulas
- Floater coupon for a period
MRR set at the start of the period, paid at the end (in arrears). m = coupon periods per year.
- Shortfall or excess per period
Positive → deficient coupon, price below par. Negative → excess coupon, price above par. The price gap from par is the PV of this amount over the remaining periods.
Worked examples
Example 1 Premium, par or discount?
Three quarterly floaters reference the same MRR and are on a reset date. Floater X: QM 90 bps, DM 75 bps. Floater Y: QM 110 bps, DM 110 bps. Floater Z: QM 80 bps, DM 120 bps. How is each priced, and what is the per-period gap per 100 of par?
Example 2 Valuing the deficient coupons
A 3-year quarterly floater pays MRR + 0.60%. The MRR is 3.00% and, after a downgrade, investors now require a discount margin of 0.90%. Using constant MRR, what is the price per 100 of par on a reset date?
On the exam
Expect a table of quoted and discount margins with the question "which floater trades at a discount/premium?", or a question on what drives the required margin (credit risk, not MRR moves) and on how the reset period affects price sensitivity.
- Reversing the rule: a higher required (discount) margin means a lower price, just as a higher YTM does for a fixed bond.
- Thinking a change in the MRR changes the required margin. MRR moves are top-down; the margin reflects issuer-specific risk.
- Believing a floater has zero price risk. Between resets the price moves with the MRR, and a credit change moves it like any bond.
- Assuming a longer reset period reduces price risk. It increases it: the coupon stays stale for longer.
Check yourself
Q1On a reset date, a floater has a quoted margin of 120 bps and a discount margin of 95 bps. It is most likely priced:
Q2A change in a floater's required margin most likely comes from:
Q3A quarterly-pay floater has a quoted margin of 70 bps and a discount margin of 100 bps. The deficient interest per period per 100 of par is closest to:
Q4Three otherwise identical floaters differ only in reset frequency. Which is most exposed to price changes when the MRR moves?
Q5Which statement about a floater's quoted margin is least accurate?
Q6A floater's required margin equals its quoted margin. Midway between reset dates the MRR rises sharply. The floater's flat price is most likely:
Answer the 6 questions: +10 XP for each one you get right first time.
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