CFA Level I Exam · Yield and Yield Spread Measures for Floating-Rate Instruments

Discount Margin and Spread Measures for Floating-Rate Notes

Q: What is the difference between quoted margin and required margin?

The quoted margin is the fixed spread in the FRN's contract that sets its coupon. The required margin is the spread investors demand in the market now. The first does not change after issue; the second does.

Q: Is discount margin the same as required margin?

For the CFA Level I exam, yes. Both describe the spread over the reference rate used to discount the FRN's cash flows. Discount margin is the term used when you solve for it from a price.

Q: Why does an FRN trade at a discount?

It trades at a discount when the required margin is above the quoted margin. The coupon spread paid is lower than what the market wants, so investors pay less than par.

Q: How do I find the discount margin from a price?

Set up the FRN pricing formula with the known price and solve for the spread added to the reference rate. On the calculator, find the periodic rate from I/Y, multiply by m, and subtract the reference rate.

Updated 7 October 2026 · Fact-checked

A floating-rate note pays a reference rate plus a fixed quoted margin. The required margin, also called discount margin, is the spread investors demand today. Discount cash flows at the reference rate plus the required margin. If required margin equals quoted margin, the note prices at par; if higher, below par; if lower, above par.

Understand Spread Measures for Floating-Rate Notes

A floating-rate note (FRN) pays a coupon that resets with a reference rate, such as SOFR or Euribor. The coupon for each period is the reference rate plus a fixed spread. That fixed spread is the quoted margin (QM). It is set when the note is issued and written in the contract.

The required margin (RM) is different. It is the spread over the reference rate that investors demand today, given the issuer's credit risk, liquidity and market conditions. It changes as the market changes. The discount margin (DM) is the same idea seen from the pricing side: the spread added to the reference rate to discount the FRN's cash flows. On the exam, treat required margin and discount margin as the yield spread measure for FRNs.

Think of the QM as what the issuer promises and the RM as what the market wants. If they match, the note is worth par on a reset date. If the issuer's credit worsens, investors want more spread, so RM rises above QM and the price falls below par. If credit improves, RM falls below QM and the price rises above par.

The reference rate itself is not the source of price changes at a reset date, because the coupon resets with it. That is why FRNs have very low interest rate risk. Their price risk comes mainly from changes in the required margin, which is a credit and liquidity risk.

The standard pricing approach assumes the reference rate stays at its current level for all future periods. You then discount each coupon and the principal at (reference rate + DM), divided by the number of periods per year.

Key formulas to remember

FRN coupon per period: Coupon = (Reference rate + QM) ÷ m × Par; m is the number of payments per year. QM is fixed at issue.
FRN price: PV = Σ [(Index + QM) ÷ m] ÷ [1 + (Index + DM) ÷ m]^t + Par ÷ [1 + (Index + DM) ÷ m]^N; Assumes the index stays constant. Sum t from 1 to N, where N = years × m. Per 100 of par.
Shortcut price: Price ≈ 100 + [(QM − DM) ÷ m] × Annuity factor at (Index + DM) ÷ m for N periods; Valid on a reset date with the index held constant. Gives the same result as the full formula.
Pricing rule: DM = QM → par; DM > QM → discount; DM < QM → premium; Required margin above quoted margin means the price is below par.

How to solve Spread Measures for Floating-Rate Notes questions

Use this method for any question on quoted margin, required margin or FRN pricing.

1Identify the reference rate, the quoted margin, the required (discount) margin and the payment frequency m.
2Assume the reference rate stays constant at its current value unless told otherwise.
3Compute the periodic coupon: (reference rate + QM) ÷ m × par.
4Compute the periodic discount rate: (reference rate + DM) ÷ m.
5Set N = years × m, then solve for PV with N, I/Y, PMT and FV on your calculator.
6Check the direction: if DM is greater than QM the price must be below par; if less, above par.
7Answer the exact question: price, discount margin, or the direction of the price move.

Quickest way: Compare margins first, then size the gap

When to use it: Use it when options differ in direction or when a question asks only whether the FRN trades at a premium, par or discount.

Compare QM with RM. Equal means par. RM above QM means discount. RM below QM means premium.
Eliminate any option on the wrong side of 100.
If you need a number, use Price ≈ 100 + (QM − DM) ÷ m × annuity factor.
The annuity factor is about N for small rates, so a rough price is 100 + (QM − DM) ÷ m × N.
Pick the option nearest your estimate, then confirm with the calculator only if two options are close.

Common mistakes in Spread Measures for Floating-Rate Notes

Using the quoted margin as the discount margin when pricing.
Both are spreads over the reference rate and the names sound alike.
Fix: QM sets the coupon. RM or DM sets the discount rate. Always put each in its own place.
Forgetting to divide the annual rate by m.
Quotes are annual but cash flows are quarterly or semiannual.
Fix: Divide the coupon rate and discount rate by m, and set N = years × m.
Saying a higher reference rate lowers the FRN price at a reset date.
Students apply fixed-rate bond logic.
Fix: The coupon resets with the reference rate, so price stays near par if the margin is unchanged. Price moves with the required margin.
Getting the direction wrong: RM above QM gives a premium.
Mixing up yield and price.
Fix: A higher required spread is a higher yield, so the price is lower. RM above QM means a discount.
Treating the discount margin as a precise measure of credit risk alone.
It is often described as a credit spread.
Fix: It also reflects liquidity and other factors, and it relies on the assumption of a constant reference rate.

Worked examples

Example 1

A two-year FRN pays semiannual coupons of 6-month reference rate + 0.50%. The reference rate is 3.00% and is assumed constant. The required margin is 0.80%. Per 100 of par, the price is closest to: A) 99.43, B) 100.00, C) 100.57.

Show the solution

Coupon per period = (3.00% + 0.50%) ÷ 2 × 100 = 1.75.
Discount rate per period = (3.00% + 0.80%) ÷ 2 = 1.90%.
N = 2 × 2 = 4.
Calculator (BA II Plus): N = 4, I/Y = 1.9, PMT = 1.75, FV = 100, CPT PV = −99.43.
Check: RM 0.80% exceeds QM 0.50%, so the price must be below 100. This also removes B and C.

Answer: A) 99.43. The note trades at a discount because the required margin is above the quoted margin.

Example 2

A two-year FRN pays annual coupons of reference rate + 1.00%. The reference rate is 2.00% and assumed constant. The required margin is 0.60%. Per 100 of par, the price is closest to: A) 99.23, B) 100.40, C) 100.77.

Show the solution

Required margin 0.60% is below quoted margin 1.00%, so the price is above 100. This eliminates A.
Coupon = (2.00% + 1.00%) × 100 = 3.00.
Discount rate = 2.00% + 0.60% = 2.60%. N = 2.
Annuity factor = [1 − 1 ÷ 1.026²] ÷ 0.026 = 1.9246.
Price = 100 + (1.00% − 0.60%) × 100 × 1.9246 = 100 + 0.40 × 1.9246 = 100.77.
Check directly: 3.00 × 1.9246 + 100 ÷ 1.052676 = 5.774 + 94.996 = 100.77.

Answer: C) 100.77. The note trades at a premium because the required margin is below the quoted margin.

Exam tips

Most questions are three-option MCQs. Use the margin comparison to eliminate options on the wrong side of par before calculating.
Watch the wording: required margin and discount margin are used for the same measure. Quoted margin is the contractual one.
Check the payment frequency. Annual margins divided by the wrong m cause wrong answers that appear as options.
Remember the pricing assumption: the reference rate is held constant, and the price is par on a reset date when RM equals QM.
If a question says the issuer's credit quality deteriorated, think RM up, price down.

Practice questions from Yield and Yield Spread Measures for Floating-Rate Instruments

Spread Measures for Floating-Rate Notes: frequently asked questions

What is the difference between quoted margin and required margin?

The quoted margin is the fixed spread in the FRN's contract that sets its coupon. The required margin is the spread investors demand in the market now. The first does not change after issue; the second does.

Is discount margin the same as required margin?

For the CFA Level I exam, yes. Both describe the spread over the reference rate used to discount the FRN's cash flows. Discount margin is the term used when you solve for it from a price.

Why does an FRN trade at a discount?

It trades at a discount when the required margin is above the quoted margin. The coupon spread paid is lower than what the market wants, so investors pay less than par.

How do I find the discount margin from a price?

Set up the FRN pricing formula with the known price and solve for the spread added to the reference rate. On the calculator, find the periodic rate from I/Y, multiply by m, and subtract the reference rate.