CFA Level I Exam · Yield and Yield Spread Measures for Fixed-Rate Bonds

Yield Measures for Floating-Rate Notes and Money Market Instruments

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

Quoted margin is the fixed spread over the reference rate that the issuer promises in the contract. Discount margin is the spread the market currently requires to hold the FRN. When DM equals QM the FRN prices at par on a reset date with a flat projected index.

Q: How do you calculate the discount margin of a floating-rate note?

You find the DM that makes the present value of the projected cash flows equal to the observed price. Coupons use the index plus QM, and the discounting uses the index plus DM, with both divided by m. In practice, you solve it by trial or by the calculator's I/Y function.

Q: What is the difference between add-on rate and discount rate?

The discount rate is calculated on face value and gives the price as FV × (1 − Days ÷ Year × DR). The add-on rate is calculated on the price paid, so it is higher for the same instrument. Convert with AOR = (Year × DR) ÷ (Year − Days × DR).

Q: What is a bond equivalent yield in money market instruments?

It is the add-on yield expressed on a 365-day year so that it can be compared with bond yields. Compute it as (FV ÷ PV − 1) × 365 ÷ Days. For a 360-day add-on rate, multiply by 365 ÷ 360.

Updated 7 October 2026 · Fact-checked

For a floating-rate note, the quoted margin is the fixed spread over the reference rate set in the contract, and the discount margin is the spread the market requires today. Money market instruments use simple-interest yields: discount rate, add-on rate and bond equivalent yield. Convert to one basis to compare, then solve.

Understand Yield Measures for Floating-Rate Notes and Money Market Instruments

A floating-rate note (FRN) pays a coupon that resets to a reference rate plus a fixed spread. The fixed spread is the quoted margin (QM). Example: 6-month reference rate + 0.80%. The coupon moves with the reference rate, so the bond's price stays close to par.

The price is not exactly par because credit risk changes. The spread investors now demand is the required margin, also called the discount margin (DM). If DM equals QM, the FRN prices at par on a reset date with a flat projected index. If DM is higher than QM, the coupon is too low for the risk and the price is below par. If DM is lower than QM, the price is above par.

To price an FRN, project every coupon using today's reference rate and the quoted margin. Then discount the cash flows at the reference rate plus the discount margin. Both rates are annual, so divide by the number of payments per year (m) for each period.

Money market instruments are short-term debt such as T-bills, commercial paper and certificates of deposit. They are quoted with simple interest, not compound yields. Two quoting styles matter. A discount rate is quoted against the face value (the amount paid at maturity). An add-on rate is quoted against the price paid (the amount invested). Both use a year basis, usually 360 days for USD and EUR and 365 for GBP.

The discount rate understates the true return because it divides interest by face value, which is larger than the price. To compare instruments, convert to an add-on rate. The bond equivalent yield is the add-on rate restated on a 365-day year, so it can be compared with bond yields.

Key formulas to remember

FRN price (periodic): PV = Σ (t = 1 to N) {[(Index + QM) ÷ m × FV] ÷ (1 + (Index + DM) ÷ m)^t} + FV ÷ (1 + (Index + DM) ÷ m)^N; m = payments per year, N = number of periods, t = 1 to N. Use today's index for all projected coupons unless told otherwise.
QM versus DM and price: DM = QM → price = par; DM > QM → price < par; DM < QM → price > par; This holds on a reset date with a flat projected index, and lets you eliminate options without calculating.
Discount rate pricing: PV = FV × (1 − (Days ÷ Year) × DR); DR is quoted on face value. Year is 360 or 365 depending on the market.
Add-on rate pricing: FV = PV × (1 + (Days ÷ Year) × AOR); AOR is quoted on the price paid, so it is higher than the discount rate for the same instrument.
Discount rate to add-on rate: AOR = (Year × DR) ÷ (Year − Days × DR); Same as ((FV ÷ PV) − 1) × (Year ÷ Days).
Bond equivalent yield: BEY = ((FV ÷ PV) − 1) × (365 ÷ Days); For a 360-day add-on rate, BEY = AOR × 365 ÷ 360.

How to solve Yield Measures for Floating-Rate Notes and Money Market Instruments questions

Decide first whether the question is about an FRN or a money market instrument. Then follow a fixed sequence and watch the day-count basis.

1Identify the instrument: FRN (margins, reference rate) or money market (days, discount or add-on rate).
2For an FRN, write down the quoted margin, the discount margin, the reference rate and m (payments per year).
3Compare QM and DM first. This tells you whether the price should be above, at or below par, and it can eliminate options.
4For pricing, compute the periodic coupon as (Index + QM) ÷ m × 100 and the periodic discount rate as (Index + DM) ÷ m.
5Use the time value keys: N = periods, I/Y = periodic discount rate in %, PMT = coupon, FV = 100, then compute PV.
6For money market problems, note the quote type (discount or add-on) and the year basis (360 or 365).
7Find the price (PV) from the discount rate, or the maturity value (FV) from the add-on rate. Then convert to the requested yield using FV ÷ PV.
8Check the answer: add-on rate is above discount rate, and BEY on a 360 market is above the 360 add-on rate.

Quickest way: Shortcut: price gap equals PV of the margin difference

When to use it: Use for FRN questions on a reset date when QM and DM differ by a small spread. It is faster than discounting the full coupon stream.

Find the difference per period, (QM − DM) ÷ m, applied to 100. For example, QM 0.80%, DM 1.00% and m = 2 give (0.80% − 1.00%) ÷ 2 × 100 = −0.10.
Discount this per-period difference at the periodic discount rate for each period, and add up the present values.
Price = 100 + that sum. If QM < DM the sum is negative, so the price is below par.
On the BA II Plus, enter N, I/Y = periodic discount rate in %, PMT = (QM − DM) ÷ m × 100 = −0.10 (a negative number when QM < DM), FV = 0, then CPT PV. Because of the calculator's sign convention, a negative PMT gives a positive PV. Read that figure as the size of the discount and subtract it from 100. If you prefer to keep signs, treat the true present value as negative and add it to 100. Both routes give the same price.
For money market yields, compute the price first (PV = FV × (1 − Days ÷ Year × DR)). Every other yield follows from FV ÷ PV.

Common mistakes in Yield Measures for Floating-Rate Notes and Money Market Instruments

Treating the quoted margin as the required return on an FRN
Both are spreads over the reference rate, so they look like the same thing.
Fix: QM is a contract term and never changes. DM is the market's required spread and changes with credit risk. The coupon uses QM, and the discounting uses DM.
Forgetting to divide the annual rates by m
The index, margins and DM are all quoted as annual rates, and the cash flows are periodic.
Fix: Divide (Index + QM) and (Index + DM) by m before using them as the coupon rate and discount rate per period.
Treating the discount rate as a yield on the amount invested
It is called a rate, and it is quoted for the instrument.
Fix: The discount rate is based on face value. Convert it to price first, then compute the add-on rate or BEY using the price as the base.
Mixing 360 and 365 day years
Money market quotes use 360 for USD and EUR, but the BEY uses 365.
Fix: Use the year basis given in the question for the discount and add-on rate. Use 365 only for the BEY.
Getting the sign of the price effect backwards when DM and QM differ
Students think a higher spread means a higher price.
Fix: A higher DM raises the discount rate and lowers the price. DM above QM means the price is below par.
Compounding money market yields
Bond problems use compound yields, so the habit carries over.
Fix: Money market yields in this topic are simple interest: interest = principal × rate × Days ÷ Year.

Worked examples

Example 1

A 90-day T-bill has a face value of 100 and is quoted at a discount rate of 4.00% on a 360-day year. What is its bond equivalent yield (365-day year)? A) 4.00% B) 4.04% C) 4.10%

Show the solution

Price = 100 × (1 − 0.04 × 90 ÷ 360) = 100 × (1 − 0.01) = 99.00.
Holding period return = 100 ÷ 99.00 − 1 = 0.010101.
Add-on rate (360) = 0.010101 × 360 ÷ 90 = 4.04%. This is option B, the trap.
BEY = 0.010101 × 365 ÷ 90 = 0.010101 × 4.05556 = 4.10%.
Cross-check: 4.04% × 365 ÷ 360 = 4.10%.

Answer: C) 4.10%. The discount rate is the lowest figure, the 360-day add-on rate is next, and the 365-day BEY is the highest.

Example 2

A 1-year FRN pays semiannual coupons at the 6-month reference rate + 0.80%. The reference rate is currently 3.00% annualized, and the quoted margin is 0.80%. The market requires a discount margin of 1.00%. The reference rate is assumed constant. What is the price per 100 of par on a reset date? A) 98.04 B) 99.81 C) 100.00

Show the solution

m = 2, so coupon = (3.00% + 0.80%) ÷ 2 × 100 = 1.90 per period.
Periodic discount rate = (3.00% + 1.00%) ÷ 2 = 2.00%.
DM (1.00%) is above QM (0.80%), so the price must be below par. This eliminates C.
PV = 1.90 ÷ 1.02 + 101.90 ÷ 1.02² = 1.8627 + 97.9431 = 99.8058.
Calculator (BA II Plus): N = 2, I/Y = 2, PMT = 1.90, FV = 100, CPT PV = −99.81.
Check by the shortcut: the per-period difference is (0.80% − 1.00%) ÷ 2 × 100 = −0.10, so price = 100 − (0.10 ÷ 1.02 + 0.10 ÷ 1.0404) = 100 − (0.0980 + 0.0961) = 100 − 0.1942 = 99.81.

Answer: B) 99.81. The FRN trades slightly below par because the required spread is higher than the quoted spread.

Exam tips

Check QM versus DM before calculating. Many FRN questions can be answered by direction alone, and the options are in ascending order.
Write down the year basis (360 or 365) and the quote type (discount or add-on) before any calculation.
Compare the ordering of the answers: discount rate < add-on rate < BEY for the same T-bill on a 360 market. Use this to eliminate options.
Wrong answers are often the 360-day add-on rate or the discount rate itself, so finish the conversion.
At about 90 seconds per question, use the shortcut or the TVM keys, and do not discount cash flows one by one.

Practice questions from Yield and Yield Spread Measures for Fixed-Rate Bonds