Learning Module 8
Yield & Yield Spread Measures for Floating-Rate Instruments
Key Outcomes Summary & Practice Problems
What you must be able to do
Curriculum Year: 2026
Calculate and interpret yield spread measures for floating‑rate instruments — quoted margin, required margin (discount margin), and the relationship between them and FRN pricing.
Calculate and interpret yield measures for money market instruments — discount rates vs. add‑on rates, bond equivalent yield, and periodicity considerations.
1 · Yield and Yield Spread Measures for Floating‑Rate Notes
Quoted margin (QM): The spread over the MRR specified at issuance. Fixed for the life of the FRN (unless otherwise stated).
Required margin (discount margin, DM): The spread over the MRR that would price the FRN at par on a reset date. Reflects current credit risk, liquidity, and tax status.
Relationship:
QM > DM → FRN priced at a premium
QM = DM → FRN priced at par
QM < DM → FRN priced at a discount
Changes in the required margin usually come from changes in the issuer's credit risk.
FRNs have low interest rate risk because coupons reset periodically. Interest rate risk is limited to the time between reset dates.
PV = Σ [(MRR + QM) × FV / m] / (1 + (MRR + DM)/m)ⁿ + FV / (1 + (MRR + DM)/m)ᴺ
where m = periods per year, N = number of periods to maturity
The spread over MRR specified in the bond indenture. Fixed at issuance. Used in the coupon calculation: Coupon = MRR + QM
The spread required by investors to price the FRN at par. Changes with credit risk. Used in the discount rate: Discount rate = MRR + DM
2 · Yield Measures for Money Market Instruments
Money market instruments have original maturities ≤ 1 year.
Discount rate basis: Interest is included in the face value.
PV = FV × (1 − Days/Year × DR). Understates the rate of return because FV (not PV) is in the denominator. Used for T‑bills, commercial paper, bankers' acceptances.Add‑on rate basis: Interest is added to the principal.
PV = FV / (1 + Days/Year × AOR). Used for CDs, repos, MRR indexes.Bond equivalent yield (BEY): A money market rate stated on a 365‑day add‑on rate basis. Used to compare money market instruments.
Periodicity: Money market rates use simple interest (no compounding). The periodicity is Days/Year (e.g., a 90‑day rate has periodicity 365/90).
To convert money market rates to a semiannual bond basis, use the periodicity conversion formula.
Step 1: PV = FV × (1 − Days/360 × DR)
Step 2: BEY = (365/Days) × [(FV − PV)/PV]
BEY = (365/Days) × [(FV − PV)/PV]
(For add‑on rates, BEY ≈ AOR when Days = 365)
DR = (Year/Days) × (FV − PV)/FV
AOR = (Year/Days) × (FV − PV)/PV
Feature | Money Market | Bond Market |
|---|---|---|
Compounding | Simple interest (no compounding) | Compounded interest |
Periodicity | Varies by maturity (Days/Year) | Common periodicity (e.g., 2 for semiannual) |
Quoting conventions | Discount rate or add‑on rate | Yield‑to‑maturity |
Day‑count | 360 or 365 days | 30/360 or actual/actual |
3 · Quick Reference — Money Market Conversion
Instrument | Quote Basis | Year Convention | BEY Formula |
|---|---|---|---|
T‑bill | Discount Rate | 360 | BEY = (365/Days) × [(FV−PV)/PV] |
Commercial Paper | Discount Rate | 360 | BEY = (365/Days) × [(FV−PV)/PV] |
Bank CD | Add‑On Rate | 365 | BEY = AOR (if Days = 365) |
Repo | Add‑On Rate | 360 | BEY = (365/360) × AOR |