The Dirty Price of a bond refers to the total price that a buyer pays to purchase the bond, which includes both the bond’s clean price and any accrued interest since the last coupon payment. The dirty price is often called the full price or invoice price because it represents the actual amount the buyer must pay.
Key Components:
- Clean Price:
- The clean price is the price of the bond without including any accrued interest. It is the quoted price of the bond in the market.
- Accrued Interest:
- Bonds typically pay interest periodically, such as semi-annually or annually. Accrued interest is the interest that has accumulated on the bond since the last coupon payment date up to the date of the transaction. The buyer of the bond must compensate the seller for this accrued interest because the seller will not be receiving the full coupon payment.
Formula:
$$ \text{Dirty Price} = \text{Clean Price} + \text{Accrued Interest} $$
Example:
If a bond has a clean price of \$1,000 and \$30 of accrued interest since the last coupon payment, the dirty price would be:
$$ \text{Dirty Price} = \$1,000 + \$30 = \$1,030 $$
Importance:
- Real Transaction Cost: The dirty price represents the true cost to the buyer, reflecting the bond’s current value plus any interest that has accrued.
- Bond Trading: Investors need to understand the difference between the clean and dirty prices, especially in markets where the clean price is typically quoted, but the dirty price is what they actually pay.
