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# Discount Margin (DM): Definition, When It Applies, and Calculation

## What Is a Discount Margin—DM?

A discount margin (DM) is the average expected return of a floating-rate security (typically a bond) that's earned in addition to the index underlying, or reference rate of, the security. The size of the discount margin depends on the price of the floating- or variable-rate security. The return of floating-rate securities changes over time, so the discount margin is an estimate based on the security's expected pattern between issue and maturity.

Another way to view the discount margin is to think of it as the spread that, when added to the bond's current reference rate, will equate the bond's cash flows to its current price.

### key takeaways

• Discount margin is a type of yield-spread calculation designed to estimate the average expected return of a variable-rate security, usually a bond.
• A discount margin is the spread (a security's yield relative to the yield of its benchmark) that equates the security's future cash flow to its current market price.

## Understanding a Discount Margin—DM

Bonds and other securities with variable interest rates are usually priced close to their par value. This is because the interest rate (coupon) on a variable rate bond adjusts to current interest rates based on changes in the bond's reference rate. A security's yield relative to the yield of its benchmark is called a spread, and different types of yield-spread calculations exist for the different pricing benchmarks.

The discount margin is one of the most common calculations: It estimates the security's spread above the reference index that equates the present value of all expected future cash flows to the current market price of the floating rate note.

There are three basic situations involving a discount margin:

1. If the price of floating rate security, or floater, is equal to par, the investor's discount margin would be equal to the reset margin.
2. Due to the tendency for bond prices to converge to par as the bond reaches maturity, the investor can make an additional return over the reset margin if the floating rate bond was priced at a discount. The additional return plus the reset margin equals the discount margin.
3. Should the floating rate bond be priced above par, the discount margin would equal the reference rate less the reduced earnings.

## Calculating the Discount Margin—DM

The discount margin formula is a complicated equation that takes into account the time value of money and typically needs a financial spreadsheet or calculator to calculate accurately. There are seven variables involved in the formula. They are:

1. P = the floating rate note's price plus any accrued interest
2. c(i) = the cash flow received at the end of time period i (for final period n, the principal amount must be included)
3. I(i) = the assumed index level at time period i
4. I(1) = the current index level
5. d(i) = number of actual days in period i, assuming the actual/360-day count convention
6. d(s) = number of days from the start of the time period until settlement date
7. DM = the discount margin, the variable to solve for

All coupon payments are unknown, with the exception of the first, and must be estimated in order to calculate the discount margin. The formula, which must be solved by iteration to find DM, is as follows:

The current price, P, equals the summation of the following fraction for all time periods from the beginning time period to maturity:

numerator = c(i)

denominator = (1 + (I(1) + DM) / 100 x (d(1) - d(s)) / 360) x Product (i, j=2)( 1 + (I(j) + DM) / 100 x d(j) / 360)

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