Definition (plain)
– Discount margin (DM) is the annualized spread, expressed in percentage points, that a floating‑rate security is expected to earn above its reference index (the “reference rate”). It is the fixed spread which, when added to each projected reference-rate coupon and used to discount the bond’s future cash flows, makes the present value equal the bond’s current market price.
Why DM matters (brief)
– DM summarizes how much extra return the market is pricing into a variable‑rate bond beyond the benchmark rate. Traders and analysts use DM to compare floating‑rate instruments that reset at different times and to assess expected yield relative to other investments. DM is an estimate and depends on assumptions about future reference rates and the bond’s cash‑flow pattern.
Key terms
– Floating‑rate security (FRN): a bond whose coupon resets periodically based on a reference interest rate (e.g., LIBOR, SOFR, Treasury bill rate) plus a spread.
– Reference rate (I): the index rate used as the base (stated as an annual rate).
– Spread: the fixed extra yield over the reference rate (DM is one way to express this spread).
– Day‑count convention (d/360, ACT/365, etc.): the rule used to convert days to a fraction of a year for coupon calculation and discounting.
How DM works (conceptual)
– The FRN pays coupons that depend on the reference rate and the unknown DM. To find DM, you choose a spread such that the sum of all discounted expected cash flows equals the bond’s current market price. Because future coupons depend on DM itself (coupon = reference rate + DM), the calculation is implicit and usually requires numerical methods (iteration) or a spreadsheet solver.
What inputs you need
– Current market price (P)
– Par (face) value (usually 100)
– Reset schedule and number of remaining periods
– Known or assumed future reference rates for each period (I(1), I(2), …)
– Day counts for each period (d(1), d(2), …), and the day‑count convention used
– Any known coupons already paid or accrued interest
Step‑by‑step checklist for calculating DM
1. Gather bond facts: par, current clean price, next reset date and reset frequency, maturity date.
2. Decide on assumptions for future reference rates (flat vs. forward curve).
3. Compute expected coupon cash flows for each period as: coupon(i) = (I(i) + DM) * d(i) / 360 * par. (Adjust day‑count denominator if a different convention applies.)
4. Set up the present‑