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CFA® Level I · Fixed Income · free lesson
Yield and Yield Spread Measures for Floating-Rate Instruments
Floating-rate notes and money market instruments make up a large part of what banks, companies and funds hold, yet their yields are quoted very differently from those of fixed-rate bonds. This module explains how floating-rate notes are priced using the quoted margin and the discount margin, and how to calculate, convert and compare money market yields quoted on a discount or add-on basis and on 360- or 365-day years.
What you will learn
1. Describe how floating-rate note coupons are set and explain how the relationship between the quoted margin and the discount margin determines whether a floating-rate note trades at, above or below par.
- FRN coupon = market reference rate + quoted margin, reset each period; SOFR, SONIA and €STR have replaced LIBOR.
- Quoted margin: fixed at issuance. Discount (required) margin: what the market demands now.
- QM = DM: par at reset dates; QM < DM: discount; QM > DM: premium.
- FRN prices have little sensitivity to reference rate changes but are sensitive to changes in credit spreads.
- Caps limit the coupon from above, floors from below.
2. Calculate the price of a floating-rate note given its quoted margin and discount margin, and estimate the discount margin from its price.
- Assume the reference rate stays at today's level for all future periods.
- Coupon per period = (MRR + QM) x FV / m; discount rate per period = (MRR + DM) / m.
- QM = DM gives par; QM > DM gives a premium; QM < DM gives a discount.
- The discount margin is the FRN equivalent of a yield spread: solve for it from the price.
- Longer remaining life and a bigger QM-DM gap produce larger premiums or discounts.
3. Calculate and interpret money market yields quoted on a discount-rate basis and on an add-on-rate basis, and price money market instruments from each.
- Money market rates are simple (non-compounded) annual rates, often on a 360-day year.
- Discount rate: PV = FV x (1 - Days/Year x DR); interest is measured relative to face value.
- Add-on rate: FV = PV x (1 + Days/Year x AOR); interest is measured relative to the amount invested.
- For the same instrument the add-on rate exceeds the discount rate; the discount rate understates return.
- Convert through the price: price from DR, then AOR from that price.
4. Convert money market rates to a bond-equivalent yield and to a periodicity-adjusted basis in order to compare money market instruments with each other and with bonds.
- Bond-equivalent yield = 365-day add-on rate.
- From a discount rate: compute price first, then the 365-day add-on rate.
- From a 360-day add-on rate: multiply by 365/360.
- Periodicity of a money market rate = 365/Days; use it to compare with semiannual bond yields.
- For positive rates: discount rate < 360-day add-on rate < bond-equivalent yield.
Module at a glance
- FRN coupon = market reference rate + quoted margin; SOFR, SONIA and €STR have replaced LIBOR.
- QM vs DM: QM > DM premium, QM = DM par, QM < DM discount; FRN prices mainly track credit spreads.
- Price an FRN by assuming today's reference rate persists: coupons at MRR + QM, discounting at MRR + DM.
- Discount rate: interest relative to face value; add-on rate: interest relative to amount invested.
- Bond-equivalent yield = 365-day add-on rate; rank money market instruments only on this basis.
- Money market periodicity = 365/Days; compound to compare with bond yields.
This free module has 4 lessons, 13 practice questions with full explanations.