Discount Margin for Floating Rate Notes

Yield to maturity works for a fixed-coupon bond because the coupon is known for the bond's entire life, so you can solve for one number that discounts every known cash flow back to today's price. A floating rate note (FRN) breaks that: its coupon resets periodically to track a reference rate like SOFR, so future coupons aren't known in advance. You can't quote a meaningful "yield to maturity" on an instrument whose future cash flows you can't pin down. What you can quote is the discount margin: the fixed spread, added to the reference rate at every reset, that makes the note's discounted cash flows equal its current market price.

Why you need a special measure

An FRN's coupon is typically quoted as "reference rate + quoted margin" (say, SOFR + 45bp), fixed at issuance. If the note trades at par, the discount margin equals the quoted margin — you're earning exactly the spread promised. But if the issuer's credit has deteriorated, or if similar notes now issue with wider spreads, the note will trade below par, and you're really earning more than 45bp once you account for buying at a discount. The discount margin captures that true, price-adjusted spread.

$$\text{Price} = \sum_{t=1}^{n} \frac{\text{Reference rate}_t + \text{Quoted margin}}{(1 + \text{Reference rate}_t + \text{Discount margin})^t} \times \text{Face}$$

In words: assuming the reference rate stays at today's forward-implied level for every future reset, find the constant extra spread (discount margin) that, when used to discount every coupon and the final principal payment, produces exactly the note's current market price.

Worked example

A 3-year FRN was issued at par with a coupon of SOFR + 40bp. Since issuance, the issuer's credit spreads have widened, comparable new issues now come at SOFR + 65bp, and the note now trades at 98.50 (a 1.50 point discount to par). Because the note pays only 40bp over SOFR but trades cheap, an investor buying at 98.50 today is effectively earning more than 40bp once the discount is amortized into the return. Solving the discount-margin equation with the note's remaining 3-year life and current price of 98.50 gives a discount margin of roughly 65bp — consistent with the note having repriced to match where new issuance is currently coming, entirely through a price change rather than a coupon change.

Worked example: comparing two FRNs

An investor is choosing between two FRNs from different issuers, both maturing in 2 years: Note A has a quoted margin of SOFR + 50bp and trades at par (discount margin = 50bp). Note B has a quoted margin of SOFR + 30bp but trades at 99.20 (discount margin works out to roughly 68bp given the discount and remaining life). Even though Note B's coupon looks less generous, its discount margin is higher, meaning at the current market price it actually compensates the investor more per unit of remaining credit and duration risk. Comparing quoted margins alone would have given the wrong answer.

What this means in practice

Discount margin is the number money-market and short-duration credit desks actually compare across FRNs, not quoted margin, precisely because quoted margin is frozen at issuance while the market's view of the issuer's credit risk isn't. It's also the number used to judge whether a floater is cheap or rich relative to where the issuer's fixed-rate debt or CDS is trading.