# Discount Margin (DM)

### What is a discount margin (DM)

A discount margin (DM) is the expected average return earned in addition to the underlying index or the benchmark rate of the floating rate security. The size of the discount margin depends on the price of the floating rate security. As the yield on floating rate securities changes over time, the discount margin is therefore an estimate based on the expected structure of the security between issue and maturity.

### Understanding the margin of discount (DM)

There are three basic situations involving a discount margin:

1. If the price of the floating rate security, or the free float, is at par, the investor’s discount margin would be equal to the reset margin.
2. Due to the tendency of bond prices to converge at par as the bond matures, the investor may realize 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. If the floating rate bond were valued above par, the discount margin would be equal to the reference rate minus the reduced profit.

### DM calculation

Another way of looking at the discount margin is to consider it as the spread above the benchmark which equates the present value of all expected future cash flows to the current market price of the rate note variable in question. The discount margin formula is a complicated equation that takes into account the time value of money and usually requires a financial spreadsheet or calculator to calculate accurately. There are seven variables involved in the formula. They are:

1. P = the price of the variable rate ticket plus accrued interest
2. c (i) = the cash flow received at the end of period i (for the last period n, the principal amount must be included)
3. I (i) = the level of index assumed in period i
4. I (1) = the current index level
5. d (i) = number of actual days in period i, assuming the actual counting convention / 360 days
6. d (s) = number of days between the start of the period and the settlement date
7. DM = discount margin, the variable to solve for

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

The current price, P, is equal to the sum of the following fraction for all periods from start 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 xd (d) / 360)