The quoted margin is the spread only at par. The discount margin adds the pull to par, and it is the number to compare across floaters.
The discount margin is the spread over the reference rate that makes the present value of a floating-rate note's coupons and principal equal its price. On an illustrative four-year note paying SOFR plus 350 basis points, bought at 97.50 with SOFR assumed flat at 4.00 per cent, the discount margin is 424 basis points, 74 more than the quoted margin, for a yield of 8.24 per cent. It is the number to compare across floating-rate bonds and loans, because the quoted margin ignores the price.
Worked in full in The Credit Investor by Julian R. Sterling, with every figure reproduced in a free workbook.See the book on Amazon →
A fixed-rate bond has a yield to maturity. A floater's coupon resets, so its yield in money terms moves with the index; what does not move is the spread the investor earns over the index. The quoted margin is that spread only at par. Below par the investor also gains the pull to 100, and the discount margin folds that gain into one annual spread.
| Input | Value |
|---|---|
| Reference rate, assumed flat | 4.00% |
| Quoted margin | 3.50% (350 bp) |
| Coupon rate | 7.50% |
| Price per 100 | 97.50 |
| Years to maturity, quarterly coupons | 4, so 16 periods |
A flat index is the standard simplification for quoting a discount margin; a full model would use the forward curve for each coupon and its discount factor. Unless the curve is steep the two give nearly the same answer: the index sensitivity below shows how little the level of the index moves the result.
Price = Σ [(index + QM) ÷ 4 × 100] ÷ (1 + (index + DM) ÷ 4)k + 100 ÷ (1 + (index + DM) ÷ 4)n
Solve for DM. With a flat index the equation is an ordinary bond yield, so Excel's RATE does it in one cell, with the index in B2, the quoted margin in B3, the price in B4 and the years in B5: =RATE(B5*4,(B2+B3)/4*100,-B4,100)*4-B2.
Each quarter pays 1.875 per 100. The quarterly rate that discounts sixteen of those plus 100 at the end back to 97.50 is 2.0600 per cent. Annualised that is 8.24 per cent; take away the 4.00 per cent index and the discount margin is 4.2400 per cent, 424 basis points. Check: discounting at the quoted margin instead gives exactly 100.00, which is why a floater at par has a discount margin equal to its quoted margin.
Where the extra 74 basis points come from: the 2.50 points of discount, spread over an annuity factor of 13.5134 quarters at the discount rate, is 0.1850 a quarter, or 74 basis points a year on the face.
Simple margin = [QM + (100 − price) ÷ years] ÷ price × 100
= [3.50 + 2.50 ÷ 4] ÷ 97.50 × 100 = 4.2308%, or 423 bp.
Close enough for a screen. The version that forgets to divide by the price, 3.50 plus 2.50 over four years, gives 412 basis points and understates the spread, because the investor earns the margin on 97.50 of outlay, not 100.
| Price | Discount margin | Simple margin |
|---|---|---|
| 95.00 | 500 bp | 500 bp |
| 96.50 | 454 bp | 453 bp |
| 97.50 | 424 bp | 423 bp |
| 99.00 | 379 bp | 379 bp |
| 100.50 | 335 bp | 336 bp |
A point of price is worth roughly 30 basis points of margin on a four-year floater. The life matters as much as the price, because the same discount is earned over fewer or more years.
| Life assumed | Discount margin |
|---|---|
| 2 years | 488 bp |
| 3 years | 445 bp |
| 4 years (maturity) | 424 bp |
| 6 years | 403 bp |
Leveraged loans are usually repaid or refinanced well before maturity, which is why loan markets often quote the discount margin to an assumed three-year life rather than to the final date. On this loan that is 445 basis points against 424 to maturity. Two loans quoted on different life conventions are not comparable until both are put on the same one.
The index assumption matters far less: at a flat 3 per cent the discount margin is 423 basis points, at 5 per cent 425. That is the point of the measure: it isolates the credit spread from the rate.
In money, a 1,000,000 face holding costs 975,000, pays 75,000 a year at today's index, and pulls 25,000 to par over the life, 6,250 a year, before any credit loss.
Solve for the spread that prices the coupons and principal at the market price: 424 basis points for SOFR + 350 bp at 97.50 over four years. State the life you assumed, and compare floaters only on the same convention. The Credit Investor takes each line of a credit portfolio from the yield on the screen to the return earned after defaults, and the free workbooks for the book include the loan fund and every line's cash flows quarter by quarter.
The quoted margin is the fixed spread in the coupon. The discount margin is the spread the investor actually earns over the index at the price paid, including the pull to par. They are equal only at par; on an illustrative SOFR + 350 bp note at 97.50 the discount margin is 424 basis points.
With a flat index, use RATE on quarterly cash flows and subtract the index: =RATE(years*4,(index+margin)/4*100,-price,100)*4-index. For four years, a 4.00 per cent index, a 3.50 per cent margin and a price of 97.50, it returns 4.24 per cent, 424 basis points.
Because leveraged loans are usually repaid or refinanced before maturity, so spreading the discount over the full term understates what the investor earns if the loan is repaid early. On the illustrative loan at 97.50, the discount margin is 445 basis points to three years against 424 to the four-year maturity.
This article is one calculation from The Credit Investor. The book takes the same case from first principles to the decision, chapter by chapter, and every figure it prints is a live formula in the free companion workbooks.
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