2.2.3.1.2. Accrued Interest and Total Invoice Price
The second step toward finding the price of the futures contract is to add accrued interest. Before launching into its application, perhaps a quick review of accrued interest is in order.
When an investor purchases a note or bond between coupon payments, the buyer must always compensate the seller for the coupon interest the seller has earned from the time of the last coupon payment up to but excluding the settlement date of the transaction. Interest earned but not yet received is called accrued interest. The reason the seller must be compensated is because the issuer will deliver the next coupon payment in its entirety to the new owner. Since the previous owner has earned the interest that has accrued while he owned the security, the buyer must pay him for that interest earned.
Accrued interest is calculated as follows:
The number of days in the accrued interest period is the number of days over which the previous owner has earned unpaid interest. The number of days in the coupon period will vary between 181 and 184 days, depending on which months are included in the six-month accrual period.
Remember that the buyer of a long-term Treasury futures contract does not earn interest, despite its designation as a 6% note or bond. However, the deliverable security does. Because the synthetic bond does not carry interest, the conversion factor cannot include accrued interest. Nor should it, since the conversion factor is a fixed number and accrued interest accumulates every day.
When a short seller delivers an underlying security to the buyer of a futures contract, however, she is going to want compensation for the interest she has earned. Accrued interest of the deliverable must be added to the adjusted futures price to arrive at the selling price of the futures contract.
Together, the adjusted futures price and accrued interest are called the total invoice price. The total invoice price is