What is a Discount Margin (DM)?
A Discount Margin (DM) represents the average expected return of a floating-rate security, typically a bond, in addition to the underlying index or reference rate of the security. The size of the DM hinges on the price of the floating- or variable-rate security. Because these securities’ returns fluctuate over time, the DM is an estimate based on the expected pattern between issue and maturity.
Think of the DM as the spread that, when added to the bond’s current reference rate, brings the bond’s cash flows in line with its current price.
Key Takeaways
- Discount margin is a yield-spread calculation estimating the average expected return of variable-rate securities like bonds.
- DM is the differential (a security’s yield relative to its benchmark) aligning the security’s projected cash flows with its current market price.
Understanding a Discount Margin (DM)
Bonds and other securities with variable interest rates typically trade close to their par value, adjusting their interest rate (coupon) to current market rates based on a reference rate. A security’s yield in relation to its benchmark’s yield is called a spread, involving different types of yield-spread calculations for various pricing benchmarks.
One of the most common calculations, the discount margin estimates the security’s spread above the reference index, aligning the present value of all expected future cash flows with the current market price of floating rate notes.
There are three basic scenarios involving a discount margin:
- At Par: If the floating rate security’s price equals par, the discount margin equals the reset margin.
- Priced at a Discount: As bonds typically converge to par as they approach maturity, an investor can achieve additional returns over the reset margin when floating rate bonds are bought at a discount. This additional return, combined with the reset margin, forms the discount margin.
- Above Par Pricing: When the floating rate bond is priced above par, the DM equals the reference rate minus the reduced earnings.
Calculating the Discount Margin (DM)
Calculating the discount margin involves a complex formula that accounts for the time value of money and typically requires a financial spreadsheet or calculator. The calculation considers seven critical variables:
- P = the floating rate note’s price plus any accrued interest
- c(i) = the cash flow received at the end of time period i (including the principal amount in the final period n)
- I(i) = the assumed index level at time period i
- I(1) = the current index level
- d(i) = actual days in period i, using the actual/360-day count convention
- d(s) = days from the start of the period until the settlement date
- DM = the discount margin, which needs to be calculated
All coupon payments, barring the first, are unknown and must be estimated to calculate the DM. The formula is solved iteratively to find the DM:
The current price P is the summation of the following fraction for all periods from the inception to maturity:
P = Σ [c(i) / ((1 + (I(1) + DM) / 100 * (d(i) - d(s)) / 360) * ∏ (i,j=2) (1 + (I(j) + DM) / 100 * d(j) / 360))]
Related Terms: Spread, Reset Margin, Variable Interest Rate.
