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CFA Level I Exam · Fixed-Income Bond Valuation: Prices and Yields

Discount Margin and Money Market Yield Measures

Updated 7 October 2026 · Fact-checked

A floating-rate note pays an index rate plus a fixed quoted margin. Its price depends on the discount margin, the spread investors now require. Money market instruments are quoted as a discount rate or an add-on rate. To compare them, convert to an add-on rate, then to a bond equivalent yield on a 365-day year.

Understand Yield Measures for Floating-Rate Notes and Money Market

A floating-rate note (FRN) pays a coupon that resets to a reference rate plus a spread. The spread set at issue is the quoted margin (QM). It stays fixed for the life of the note. The reference rate changes at each reset, so the coupon follows market rates.

The discount margin (DM), also called the required margin, is the spread investors demand today over the same reference rate. It reflects the issuer's current credit risk and the note's liquidity. If DM = QM, the FRN prices at par on a reset date. If DM > QM, the price is below par. If DM < QM, the price is above par. Because the coupon resets, price moves are small unless the credit spread changes.

Money market instruments, such as T-bills, commercial paper and certificates of deposit, last one year or less. They are quoted in simple-interest terms, not as a compounded yield to maturity. Two quoting styles matter. A discount rate is quoted against the face value, and the investor pays face value minus the discount. An add-on rate is quoted against the amount invested, and interest is added to it at maturity.

The discount rate understates the true return because it divides the interest by the face value, which is larger than the amount invested. To compare instruments, convert the discount rate to an add-on rate. Then, if the add-on rate uses a 360-day year, multiply by 365/360 to get the bond equivalent yield. Bond equivalent yield is an add-on yield on a 365-day year. It is the basis for comparing money market instruments with bonds.

Key formulas to remember

Price from discount rate
PV = FV × (1 − (Days ÷ Year) × DR)
Year is usually 360 for the discount rate. The discount is FV × (Days ÷ Year) × DR.
Price from add-on rate
PV = FV ÷ (1 + (Days ÷ Year) × AOR)
The add-on rate is measured against the amount invested, not the face value.
Discount rate to add-on rate (360-day year)
AOR = (360 × DR) ÷ (360 − Days × DR)
The add-on rate is always higher than the discount rate for the same instrument.
Bond equivalent yield
BEY = AOR(360-day) × 365 ÷ 360
Equivalently, BEY = (FV ÷ PV − 1) × 365 ÷ Days for instruments of one year or less.
FRN price
PV = Σ(t=1 to N) [(Index + QM) ÷ m × FV] ÷ [1 + (Index + DM) ÷ m]^t + FV ÷ [1 + (Index + DM) ÷ m]^N
m is payments per year and N is the number of periods. The standard exam assumption is that the index stays at its current level.
Margin rule
DM = QM → price = par; DM > QM → price < par; DM < QM → price > par
This holds on a reset date, when the index in the coupon equals the index in the discount rate.

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

Decide first whether the question is about an FRN or a money market instrument. Then follow the matching steps.

  1. 1Identify the instrument and the quote type: discount rate, add-on rate, or FRN margin. Note the day-count basis, 360 or 365.
  2. 2For a money market question, find the price first. With a discount rate, use PV = FV × (1 − Days/360 × DR).
  3. 3Compute the holding period return: FV ÷ PV − 1. This is the interest earned over the days held.
  4. 4Annualize with simple interest. Multiply by 360 ÷ Days for an add-on rate on a 360-day year, or by 365 ÷ Days for the bond equivalent yield.
  5. 5For an FRN, set the periodic coupon as (Index + QM) ÷ m and the periodic discount rate as (Index + DM) ÷ m. Both use the same index.
  6. 6Count the periods N and use the time value of money keys: N, I/Y, PMT, FV, then CPT PV.
  7. 7Check the answer against the margin rule. A DM above QM must give a price below par.
  8. 8Read the options. They are listed smallest to largest, so confirm the direction before you pick.

Quickest way: Direction check, then compute only if needed

When to use it: Use this when the options are clearly separated. You have about 90 seconds per question.

  1. For an FRN, compare DM with QM. This often removes one or two of the three options, depending on how the options are set. For example, if one option is par and another is on the wrong side of par, two options go.
  2. For discount rate to add-on rate, remember the order: discount rate < add-on rate (360) < bond equivalent yield (365). Rule out any option below the discount rate.
  3. If more than one option remains, compute PV from the discount rate. Then find (FV ÷ PV − 1) × 365 ÷ Days.
  4. For the FRN price, use the calculator in one pass: N = periods, I/Y = (Index + DM) ÷ m in percent, PMT = (Index + QM) ÷ m, FV = 100, then CPT PV.

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

  • Treating the discount rate as the yield the investor earns

    Both are quoted as annual percentages, so they look comparable.

    Fix: The discount rate is measured against face value. Convert it to an add-on rate before comparing it with anything else.

  • Using 365 days when the question says a 360-day year, or the reverse

    Candidates apply one day-count habit to every quote.

    Fix: Read the basis in the stem. Discount rates and add-on rates in these questions are normally 360-day. The bond equivalent yield uses 365.

  • Mixing up quoted margin and discount margin

    Both are spreads over the index and the names are similar.

    Fix: QM sets the coupon and is fixed at issue. DM is the discount rate spread and changes with credit risk. Price depends on DM relative to QM.

  • Using the annual rate in the FRN price formula without dividing by m

    The index and margins are quoted as annual rates.

    Fix: Divide (Index + QM) and (Index + DM) by the number of payments per year. Use the number of periods for N.

  • Using different index levels for the coupon and the discount rate

    Candidates assume the coupon rate resets to a different level.

    Fix: In the standard exam setup, the index is the same in both. Only the margins differ, so the price gap comes entirely from DM − QM.

  • Forgetting to compound the wrong way when annualizing money market yields

    Candidates reflexively raise (1 + r) to a power.

    Fix: Money market yields are simple-interest. Multiply the periodic return by 360 ÷ Days or 365 ÷ Days. Do not compound.

Worked examples

Example 1

A 180-day T-bill is quoted at a discount rate of 4.00% on a 360-day year. Face value is 100. What is the bond equivalent yield? A) 4.08% B) 4.14% C) 4.21%

Show the solution
  1. Price = 100 × (1 − 180/360 × 0.04) = 100 × (1 − 0.02) = 98.00.
  2. Holding period return = 100 ÷ 98 − 1 = 0.020408, or 2.0408%.
  3. Add-on rate (360-day) = 0.020408 × 360 ÷ 180 = 4.0816%.
  4. Bond equivalent yield = 0.020408 × 365 ÷ 180 = 4.138%, which rounds to 4.14%.
  5. Check the order: 4.00% < 4.08% < 4.14%. Option A is the 360-day add-on rate, a trap. Option C is too high.

Answer: B) 4.14%

Example 2

A two-year FRN pays semiannual coupons of the 6-month reference rate plus a quoted margin of 0.50%. Face value is 100. The reference rate is 3.00% and stays there. The required discount margin is 0.80%. What is the price? A) 99.43 B) 100.00 C) 100.57

Show the solution
  1. Periodic coupon = (3.00% + 0.50%) ÷ 2 = 1.75 per 100.
  2. Periodic discount rate = (3.00% + 0.80%) ÷ 2 = 1.90%. N = 2 × 2 = 4.
  3. Direction check: DM (0.80%) > QM (0.50%), so the price is below par. This eliminates B and C.
  4. Calculate to confirm. The factor 1.019^4 = 1.078194, so the principal PV = 100 ÷ 1.078194 = 92.748.
  5. Coupon PV = 1.75 × (1 − 0.927477) ÷ 0.019 = 1.75 × 3.8170 = 6.680.
  6. Price = 92.748 + 6.680 = 99.43. On the TI BA II Plus: N = 4, I/Y = 1.90, PMT = 1.75, FV = 100, CPT PV = −99.43.

Answer: A) 99.43

Exam tips

  • Many FRN questions can be narrowed or answered with the margin rule. It often removes one or two options, depending on how the options are set. Check DM versus QM before you calculate.
  • Write the day-count basis next to each rate. Most errors in money market questions come from 360 versus 365.
  • Remember the ordering: discount rate < add-on rate on 360 < bond equivalent yield. Use it to eliminate options quickly.
  • Keep calculator keystrokes ready for the FRN price. Divide the annual rates by m before entering I/Y and PMT.
  • With three options and no penalty for wrong answers, always choose one. Eliminating one wrong option gives you a one-in-two guess.

Practice questions from Fixed-Income Bond Valuation: Prices and Yields

Yield Measures for Floating-Rate Notes and Money Market: frequently asked questions

What is the difference between quoted margin and discount margin?

Quoted margin is the fixed spread over the reference rate that sets the FRN coupon. Discount margin is the spread investors currently require, and it is used to discount the cash flows. If the two are equal, the FRN prices at par on a reset date.

How do I convert a discount rate to a bond equivalent yield?

Find the price: PV = FV × (1 − Days/360 × DR). Then compute (FV ÷ PV − 1) × 365 ÷ Days. This gives the add-on yield on a 365-day year.

Why is the add-on rate higher than the discount rate?

The discount rate divides the interest by the face value, which is larger than the price paid. The add-on rate divides the same interest by the smaller amount actually invested. The same dollar of interest therefore gives a higher percentage.

Does the index rate matter in FRN pricing questions?

Exam questions normally assume the index stays at its current level. It then appears in both the coupon and the discount rate and cancels out of the price gap. Only the margins determine whether the price is above or below par.