Lesson 1 of 3 11–14% of the exam

By Daniil Tarakanov Updated Oct 21, 20262027 curriculum

Floating-rate notes: quoted margin and discount margin

Q: What is the discount margin on a floating-rate note?

The margin over the reference rate that investors require, set so the note would price at par on a reset date. It is also called the required margin and plays the role of a yield spread.

Q: Why do floating-rate notes trade near par?

Their coupons reset to current rates each period, so a change in interest rates is passed into the next payment. Only changes in credit, liquidity or tax status push the price away from par.

Q: What is the quoted margin?

The fixed spread over the reference rate written into the note's terms at issue. It is what the issuer actually pays, whatever investors later require.

Q: Why is the discount margin only an estimate?

The simplified model uses one reference rate for every period and a simple day count. Fuller models use projected rates in the cash flows and spot rates for discounting, so the margin depends on the model.

A floating-rate note (FRN) pays the market reference rate plus a fixed quoted margin, so rate changes barely move its price. Credit changes do: if investors now require a larger margin (the discount margin) than the quoted one, the note trades below par; if smaller, above par.

10 min cram, 40 min full read. Based on the 2027 CFA® Program Level I curriculum, Fixed Income, Learning Module 8. Also part of the 2026 curriculum, so it applies to the November 2026 exam too.

Tailor this to you: take the self-assessment

Before this: Yield and Yield Spread Measures for Fixed-Rate Bonds, Bond Valuation: Prices and Yields

On the exam

Calculate and interpret yield spread measures for floating-rate instruments

Calculate and interpret yield spread measures for floating-rate instruments. Expect to classify an FRN as premium, par or discount from its two margins, to price an FRN given a discount margin, and to solve for the discount margin given a price.

How deeply to learn each part

Know the idea: Understand it in general. It frames other topics, but you will not calculate with it.
Use it: Understand it well enough to solve a question with it. Recognize when it applies.
Memorize: Learn it by heart. The exam will not give it to you.

You know this one. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still do.

You tested strong here. The full lesson is folded away. The takeaways, formulas and checkpoint below are your quick refresher, and the checkpoint is a fair test of whether you still know it.

How does a floating-rate note pay?

A floating-rate note (FRN, or floater) replaces the fixed coupon with one that follows a short-term rate. Each period it pays a market reference rate (MRR), usually a short money market rate, plus a fixed spread called the quoted margin .

The rate is observed on a reset date at the start of the period and the interest is paid at the end. That timing is called paying in arrears . Day counts are usually actual/360 or actual/365.

What an FRN pays each period

FRN interest per periodset at the start of the period, paid at the end (in arrears)

Market reference rate Memorize a short money market rate, reset each period
Quoted margin Memorize fixed at issue; pays for the issuer's credit risk over the reference rate; can be negative for the strongest issuers

The quoted margin pays the investor for the issuer’s credit risk over the reference rate. The strongest issuers can even have a negative quoted margin.

FRN coupon per period Memorize

PMT = \frac{(MRR + QM) \times FV}{m}

Here $m$ is the number of payments a year. A quarterly note has $m = 4$ .

Why does an FRN trade near par?

Interest rate moves go straight into the next coupon, so at every reset the price returns toward par. Between resets the flat price drifts above or below par if rates have moved, and it is pulled to par as the next reset approaches. That is why an FRN has low interest rate risk.

How low depends on the reset period. The longer the gap between resets, the more the FRN behaves like a short fixed-rate bond and the more its price can move. A five-year FRN that resets quarterly has the rate risk of a three-month instrument, not a five-year one.

Credit is different. Changes in the issuer’s credit risk, and also in liquidity or tax status, change the spread investors want. The spread they want is the required margin , also called the discount margin (DM). The quoted margin is fixed at issue, so when the two drift apart the price leaves par.

On a reset date	Price	Why
Required margin = quoted margin	par	the coupon pays what the market wants
Required margin > quoted margin	discount	credit worsened; the coupon is “deficient”
Required margin < quoted margin	premium	credit improved; the coupon has an “excess”

FRN price on a reset date

Required margin against quoted marginthe market's margin against the one the note pays

Required margin above quoted margin Memorize credit worsened; priced at a discount (PV of the deficient margin)
Required margin equal to quoted margin Memorize priced at par
Required margin below quoted margin Memorize credit improved; priced at a premium (PV of the excess margin)

The size of the discount is the present value of the deficient margin, an annuity of $(DM - QM)$ per year for the remaining life. A premium is the present value of the excess margin. A fixed-rate bond works the same way with the coupon rate and the yield to maturity: the FRN applies that logic to the margin only.

InteractiveFloating-rate note: quoted margin against discount margin

Try this 0 of 3

Set the discount margin equal to the quoted margin
With DM = QM, pick the rising MRR path and look between resets
Solve for the DM of a note priced above par

Market reference rate (MRR)3.6%

Quoted margin (in the coupon)85 bps

Discount margin (required)125 bps

Years to maturity3 years

Price on a reset date98.889

Coupon per period1.1125

Discount rate per period1.2125%

Discount: investors require 40 bps more than the quoted margin, so the price is 100 less the present value of that deficient margin.

MRR path:

Flat price per 100 (dots mark resets) with the MRR held at 3.6%.

Between resets the coupon is already fixed, so a moving MRR nudges the price only until the next reset. A gap between DM and QM shifts the whole line, and the shift shrinks as maturity nears.

Show working

Coupon per period = (MRR + QM) × 100 ÷ m = (3.6% + 0.85%) × 100 ÷ 4 = 1.1125; N = 3 × 4 = 12.

Discount rate per period = (MRR + DM) ÷ m = (3.6% + 1.25%) ÷ 4 = 1.2125%.

Price = Σ 1.1125 ÷ (1 + 0.012125)^t + 100 ÷ (1 + 0.012125)¹² = 98.889: a discount, because DM > QM.

Price the FRN on your calculator

2NDCLR TVMwith P/Y set to 1
12N1.2125I/Y1.1125PMT100FV
CPTPV−98.889, the price per 100

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · I/Y interest rate per year (per period when P/Y is 1) · PMT payment · FV future value · CPT compute · PV present value

fCLEAR FIN
12n1.2125i1.1125PMT100FV
PV−98.889, the price per 100

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Rates move the coupon; credit moves the price.

How do you price an FRN?

The simplified model treats the note on a reset date, with evenly spaced periods and the same MRR in every period. On a reset date there is no accrued interest, so the flat price and the full price are the same. Coupons use the quoted margin; discounting uses the discount margin.

Simplified FRN price on a reset date Use it

PV = \sum_{t=1}^{N} \frac{(MRR + QM)\,FV/m}{\left(1 + \frac{MRR + DM}{m}\right)^{t}} + \frac{FV}{\left(1 + \frac{MRR + DM}{m}\right)^{N}}

On the calculator this is an ordinary bond: PMT is the coupon per period, I/Y is $(MRR + DM) \div m$ in percent, N is the number of periods and the future value (FV) is 100.

Worked example Pricing a quarterly FRN

A 3-year FRN pays quarterly at MRR + 85 bps. MRR is 3.60% and investors require 125 bps. Price it on a reset date.

Coupon per period: $(3.60\% + 0.85\%) \times 100 \div 4 = 1.1125$ .
Discount rate per period: $(3.60\% + 1.25\%) \div 4 = 1.2125\%$ .
Periods: $N = 3 \times 4 = 12$ .
Price: PV = 98.89 per 100 of par.

It is a discount because the required margin (125 bps) is above the quoted margin (85 bps). The 40 bps shortfall is 10 bps a quarter for 12 quarters, discounted.

On your calculator

3.6+0.85=÷4= coupon, 1.1125
3.6+1.25=÷4= rate per period, 1.2125
2NDCLR TVM with P/Y set to 1
12N
1.2125I/Y
1.1125PMT
100FV
CPTPV −98.8895, so the price is 98.89

3.6ENTER0.85+4÷ coupon, 1.1125
3.6ENTER1.25+4÷ rate per period, 1.2125
fCLEAR FIN
12n
1.2125i
1.1125PMT
100FV
PV −98.8895, so the price is 98.89

ENTER enter (on the HP, puts the number on the stack) · f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Rearrange itFloating-rate note: solve for the price, discount margin or quoted margin

The question asks for

A floating-rate note with 12 periods left pays 4 times a year at MRR + 0.85%. MRR is 3.60% and the required margin is 1.25%. On a reset date its price per 100 is closest to:

Market reference rate, MRR (annual %)%Quoted margin, QM (annual %)%Discount margin, DM (annual %)%Payments a year, mPeriods to maturity, N

P V = t = 1 \sum N \frac{( M R R + QM ) F V / m}{( 1 + \frac{M R R + D M}{m} ) ^{t}} + \frac{F V}{( 1 + \frac{M R R + D M}{m} ) ^{N}}

coupon (3.60% + 0.85%) ÷ 4 = 1.1125; rate per period (3.60% + 1.25%) ÷ 4 = 1.2125%; price = 98.89

Price per 100 on a reset date98.89

On your calculator

2NDCLR TVMwith P/Y set to 1
12N
1.2125I/Y(MRR + DM) ÷ m, in percent
1.1125PMT(MRR + QM) ÷ m
100FV
CPTPV-98.89, shown negative

fCLEAR FIN
12n
1.2125i(MRR + DM) ÷ m, in percent
1.1125PMT(MRR + QM) ÷ m
100FV
PV-98.89, shown negative

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Exam tip Check the sign of the answer before you calculate: DM above QM must give a price below 100, and DM below QM a price above 100.

How do you find the discount margin from a price?

Run the same bond calculation backwards. Find the coupon per period, enter the price, and solve for the rate per period. Then convert that rate back into an annual spread.

Discount margin from a price Use it

DM = m \times r - MRR

The easy mistake is stopping at $m \times r$ . That figure is the full discount rate (MRR plus the margin), so MRR has to come out.

Worked example Backing out the discount margin

A 2-year semiannual FRN pays MRR + 60 bps. MRR is 3.80% and the price is 98.60 on a reset date.

Coupon per period: $(3.80\% + 0.60\%) \times 100 \div 2 = 2.20$ .
Enter $N = 4$ , $PV = -98.60$ , $PMT = 2.20$ , $FV = 100$ and solve: $r = 2.5728\%$ per period.
Annualize and take out MRR: $DM = 2 \times 2.5728\% - 3.80\% = 1.3456\%$ .

The discount margin is 135 bps. Investors now want 75 bps more than the note pays.

On your calculator

3.8+0.6=÷2= coupon, 2.2
2NDCLR TVM with P/Y set to 1
4N
98.6+|-PV
2.2PMT
100FV
CPTI/Y 2.5728 per period
×2−3.8= 1.3456, so 135 bps

2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · +|- change sign · PV present value · PMT payment · FV future value · CPT compute · I/Y interest rate per year (per period when P/Y is 1)

3.8ENTER0.6+2÷ coupon, 2.2
fCLEAR FIN
4n
98.6CHSPV
2.2PMT
100FV
i 2.5728 per period
2×3.8− 1.3456, so 135 bps

ENTER enter (on the HP, puts the number on the stack) · f gold shift key · CLEAR FIN clear the financial registers · n number of periods · CHS change sign · PV present value · PMT payment · FV future value · i interest rate per period

Worked example A negative reference rate

A 2-year quarterly FRN pays MRR + 200 bps. MRR is −0.40% and the price is 99.00 on a reset date.

Coupon per period: $(-0.40\% + 2.00\%) \times 100 \div 4 = 0.40$ .
Enter $N = 8$ , $PV = -99$ , $PMT = 0.40$ , $FV = 100$ and solve: $r = 0.5280\%$ per period.
$DM = 4 \times 0.5280\% - (-0.40\%) = 2.512\%$ .

The discount margin is 251 bps, above the quoted 200 bps, so the note is at a discount. Subtracting a negative MRR adds 40 bps. The formula needs no change.

On your calculator

0.4+|-+2=÷4= coupon, 0.4
2NDCLR TVM with P/Y set to 1
8N
99+|-PV
0.4PMT
100FV
CPTI/Y 0.5280 per period
×4−0.4+|-= 2.5120, so 251 bps

+|- change sign · 2ND second function (the shifted label above a key) · CLR TVM clear the time value of money keys · N number of periods · PV present value · PMT payment · FV future value · CPT compute · I/Y interest rate per year (per period when P/Y is 1)

0.4CHSENTER2+4÷ coupon, 0.4
fCLEAR FIN
8n
99CHSPV
0.4PMT
100FV
i 0.5280 per period
4×0.4CHS− 2.5120, so 251 bps

CHS change sign · ENTER enter (on the HP, puts the number on the stack) · f gold shift key · CLEAR FIN clear the financial registers · n number of periods · PV present value · PMT payment · FV future value · i interest rate per period

Because the model is simplified, the discount margin it gives is an estimate. It depends on the assumptions behind the pricing equation.

Go deeper Why the simplified model uses one MRR for every period

A fuller FRN model projects a different forward rate for each future reset, puts those in the coupons, and discounts with spot rates from the term structure. The simplified model assumes today’s MRR applies to every period, which makes the cash flows an annuity and lets a bond calculator price the note. It also assumes a 30/360 day count so that $m$ is a whole number and the periods are evenly spaced.

Since the answer depends on those choices, the discount margin from one model is not directly comparable with one from another. Questions on this exam always tell you to use the simplified model.

Go deeper Floaters and bank balance sheets

The same pricing logic covers adjustable-rate loans. A large part of bank funding is short-term deposits and other floating-rate sources, so banks prefer to lend at floating rates. That keeps the interest they earn and the interest they pay moving together.

Memorize this

MemorizePremium, par or discount on a reset date

Required (discount) margin	Meaning	Price
> quoted margin	credit worsened	discount
= quoted margin	no change in credit	par
< quoted margin	credit improved	premium

Memory hook Same logic as coupon against YTM on a fixed-rate bond, applied to the margin. Pays less than the market wants: discount.

Know it cold The gap is an annuity: (DM − QM) ÷ m per period for the remaining life, valued at the discount rate.

MemorizeSimplified FRN model: which rate goes where

Memory hook QM sits in the coupon (the top), DM sits in the discount rate (the bottom). Both ride on MRR and both are divided by m.

Know it cold $PMT = (MRR + QM) \times FV/m$ and $r = (MRR + DM)/m$ . To back out DM: solve for $r$ , then $DM = m \times r - MRR$ .

MemorizeInterest rate risk versus credit risk

Memory hook Rates move the coupon. Credit moves the price.

Know it cold Price risk from rates is small and depends on the time to the next reset. A longer reset period makes the FRN behave more like a short fixed-rate bond.

What an FRN pays each period

FRN interest per periodset at the start of the period, paid at the end (in arrears)

Market reference rate Memorize a short money market rate, reset each period
Quoted margin Memorize fixed at issue; pays for the issuer's credit risk over the reference rate; can be negative for the strongest issuers

FRN price on a reset date

Required margin against quoted marginthe market's margin against the one the note pays

Required margin above quoted margin Memorize credit worsened; priced at a discount (PV of the deficient margin)
Required margin equal to quoted margin Memorize priced at par
Required margin below quoted margin Memorize credit improved; priced at a premium (PV of the excess margin)

FRN coupon per period

PMT = \dfrac{(MRR + QM) \times FV}{m}

Quick example

Semiannual FRN at MRR + 70 bps with MRR at 2.50%: (2.50% + 0.70%) × 100 ÷ 2 = 1.60 per 100 of par.

On your calculator

2.5+0.7=÷2= 1.6

2.5ENTER0.7+2÷ 1.6

ENTER enter (on the HP, puts the number on the stack)

Simplified FRN price on a reset date

PV = \sum_{t=1}^{N} \dfrac{(MRR + QM)\,FV/m}{\left(1 + \frac{MRR + DM}{m}\right)^{t}} + \dfrac{FV}{\left(1 + \frac{MRR + DM}{m}\right)^{N}}

Quick example

Two-year quarterly FRN, MRR 2.00%, QM 100 bps, DM 130 bps. PMT = 0.75; r = 0.825% per period; N = 8. Price = 99.42.

On your calculator

2NDCLR TVM with P/Y set to 1
8N
0.825I/Y
0.75PMT
100FV
CPTPV −99.4217

fCLEAR FIN
8n
0.825i
0.75PMT
100FV
PV −99.4217

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Discount margin from a price

DM = m \times r - MRR, \quad r \text{ solved from } PV, PMT, FV, N

Quick example

Three-year semiannual FRN, MRR 3.00%, QM 70 bps, price 99.00. PMT = 1.85; N = 6; r = 2.0287% per period. DM = 2 × 2.0287% − 3.00% = 1.057% (106 bps).

On your calculator

2NDCLR TVM with P/Y set to 1
6N
99+|-PV
1.85PMT
100FV
CPTI/Y 2.0287
×2−3= 1.057

fCLEAR FIN
6n
99CHSPV
1.85PMT
100FV
i 2.0287
2×3− 1.057

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · CHS change sign · PV present value · PMT payment · FV future value · i interest rate per period

How it is asked

Premium, par or discount from the margins

QM 140 bps, DM 128 bps on a reset date. Price?

DM < QM, so premium. Trap: reading the larger number as the discount.
Price from a required margin

3-year quarterly FRN, MRR 3.60%, QM 85 bps, DM 125 bps.

PMT 1.1125, r 1.2125%, N 12: 98.89. Trap: 100.00 (assumes par), 101.12 (QM and DM swapped).
Discount margin from a price (two steps)

2-year semiannual FRN, MRR 3.80%, QM 60 bps, price 98.60.

I/Y 2.5728, DM = 2 × 2.5728% − 3.80% = 135 bps. Trap: forgetting to subtract MRR (2.57%, or 5.15%).
Which change moves an FRN's price?

MRR rises 50 bps on a reset date, or the issuer is downgraded. Which hurts the price?

The downgrade. The MRR rise flows into the next coupon.

Exam traps

Saying FRNs always trade at par. They trade at par on a reset date only if the required margin equals the quoted margin.
Mixing up the margins: the quoted margin is in the coupon, the discount margin is in the discount rate. Swapping them flips premium and discount.
Forgetting to divide the annual rates by m, or to subtract MRR after solving for the rate per period when backing out the discount margin.
Treating a change in the reference rate as a credit event. It changes the next coupon, not the margin.

Checkpoint

5 exam-style questions. About 90 seconds each.

1On a reset date, an FRN's issuer has been downgraded, so investors now require a margin above the note's quoted margin. The FRN most likely trades:
2A 3-year FRN pays quarterly at MRR + 150 bps. MRR is 2.80% and the FRN is priced at 101.00 on a reset date. Using the simplified model, the discount margin is closest to:
3A 3-year semiannual FRN pays MRR + 80 bps. MRR is 3.50% and the required margin is 110 bps. On a reset date its price per 100 is closest to:
4On a reset date, which event is most likely to move an FRN's price away from par?
5A 5-year semiannual FRN pays MRR + 140 bps. MRR is 2.60% and the FRN is priced at 102.50 on a reset date. Using the simplified model, the discount margin is closest to:

Key takeaways

FRN coupon = MRR + quoted margin, set at the start of the period and paid at the end.
Required margin above quoted margin: discount. Equal: par on a reset date. Below: premium.
Price with (MRR + QM) ÷ m coupons discounted at (MRR + DM) ÷ m per period.
To find DM, solve the rate per period on the calculator, multiply by m, then subtract MRR.
Rate moves flow into the coupon; credit and liquidity changes move the price.

FRN coupon per period

PMT = \dfrac{(MRR + QM) \times FV}{m}

Quick example

Semiannual FRN at MRR + 70 bps with MRR at 2.50%: (2.50% + 0.70%) × 100 ÷ 2 = 1.60 per 100 of par.

On your calculator

2.5+0.7=÷2= 1.6

2.5ENTER0.7+2÷ 1.6

ENTER enter (on the HP, puts the number on the stack)

Simplified FRN price on a reset date

PV = \sum_{t=1}^{N} \dfrac{(MRR + QM)\,FV/m}{\left(1 + \frac{MRR + DM}{m}\right)^{t}} + \dfrac{FV}{\left(1 + \frac{MRR + DM}{m}\right)^{N}}

Quick example

Two-year quarterly FRN, MRR 2.00%, QM 100 bps, DM 130 bps. PMT = 0.75; r = 0.825% per period; N = 8. Price = 99.42.

On your calculator

2NDCLR TVM with P/Y set to 1
8N
0.825I/Y
0.75PMT
100FV
CPTPV −99.4217

fCLEAR FIN
8n
0.825i
0.75PMT
100FV
PV −99.4217

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · i interest rate per period · PMT payment · FV future value · PV present value

Discount margin from a price

DM = m \times r - MRR, \quad r \text{ solved from } PV, PMT, FV, N

Quick example

Three-year semiannual FRN, MRR 3.00%, QM 70 bps, price 99.00. PMT = 1.85; N = 6; r = 2.0287% per period. DM = 2 × 2.0287% − 3.00% = 1.057% (106 bps).

On your calculator

2NDCLR TVM with P/Y set to 1
6N
99+|-PV
1.85PMT
100FV
CPTI/Y 2.0287
×2−3= 1.057

fCLEAR FIN
6n
99CHSPV
1.85PMT
100FV
i 2.0287
2×3− 1.057

f gold shift key · CLEAR FIN clear the financial registers · n number of periods · CHS change sign · PV present value · PMT payment · FV future value · i interest rate per period

All Fixed Income formulas, every lesson

Practice exam-style questions on Yield and Yield Spread Measures for Floating-Rate Instruments

Next lesson Money market rates: discount basis and add-on basis

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Where this comes back

Modified Duration, Money Duration and PVBP Fixed Income
Term Structure: Spot, Par and Forward Curves Fixed Income
Pricing and Valuing Interest Rate Swaps Derivatives

Questions candidates ask

What is the discount margin on a floating-rate note?

The margin over the reference rate that investors require, set so the note would price at par on a reset date. It is also called the required margin and plays the role of a yield spread.

Why do floating-rate notes trade near par?

Their coupons reset to current rates each period, so a change in interest rates is passed into the next payment. Only changes in credit, liquidity or tax status push the price away from par.

What is the quoted margin?

The fixed spread over the reference rate written into the note's terms at issue. It is what the issuer actually pays, whatever investors later require.

Why is the discount margin only an estimate?

The simplified model uses one reference rate for every period and a simple day count. Fuller models use projected rates in the cash flows and spot rates for discounting, so the margin depends on the model.

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