Dirty Price
The dirty price of a bond (also called the full price or invoice price) is the actual market price paid by the buyer in a bond transaction, equal to the quoted clean price plus any accrued interest that has accumulated since the last coupon payment date. The dirty price represents the true economic cost of purchasing a bond and is the amount that physically changes hands at settlement.
Key takeaways
- Dirty Price = Clean Price + Accrued Interest; accrued interest is calculated by multiplying the daily coupon rate by the number of days since the last coupon payment, using the applicable day count convention.
- Bond prices are conventionally quoted as clean prices (excluding accrued interest) in most markets, but settlement occurs at the dirty price—a distinction that can surprise inexperienced investors.
- Accrued interest resets to zero on each coupon payment date and builds up linearly between coupon dates, creating a sawtooth pattern in the dirty price even when the clean price remains constant.
- For U.S. Treasury bonds and corporate bonds, the Actual/Actual (ICMA) and 30/360 day count conventions, respectively, are standard for accrued interest calculation.
- When a bond is purchased between coupon dates, the buyer pays accrued interest to the seller as compensation for the portion of the next coupon earned during the seller's holding period.
Explanation
The dirty price convention reflects the practical reality of bond trading in secondary markets: buyers and sellers transact throughout the coupon period, and the party holding the bond at the next coupon payment date receives the full coupon—regardless of how long they have held the bond. To compensate the seller for the portion of the next coupon earned during their ownership, the buyer pays accrued interest as part of the settlement amount, producing a total payment equal to the dirty price.
The convention of quoting clean prices (excluding accrued interest) emerged from practical trading considerations. If bonds were quoted at dirty prices, the quoted price would rise continuously between coupon dates even if the underlying yield (and thus fair value) remained unchanged—simply because accrued interest builds day by day. This mechanical price appreciation would obscure genuine market movements in yield and value. By stripping out the accrued interest component, clean price quotes allow traders to focus on genuine changes in market value and compare bond prices across different stages of their coupon periods on a consistent basis.
The calculation of accrued interest requires two inputs: the coupon rate and the applicable day count convention. The day count convention specifies how to count the number of days elapsed since the last coupon and the total number of days in the coupon period—a seemingly simple question that has surprisingly complex answers across different markets and instrument types. U.S. Treasury bonds use an Actual/Actual (ICMA) convention, counting actual calendar days in both the numerator (days elapsed) and denominator (days in the coupon period). U.S. corporate bonds typically use a 30/360 convention that assumes every month has 30 days and every year has 360 days. Money market instruments use Actual/360, while sterling bonds historically used Actual/365. These conventions produce different accrued interest calculations for the same bond, requiring careful attention in cross-border transactions.
From a portfolio accounting perspective, the distinction between dirty and clean prices is crucial for performance measurement and risk management. A bond's dirty price will show apparent appreciation approaching a coupon date as accrued interest builds, followed by a sharp drop on the ex-coupon date when the coupon is paid and accrued interest resets to zero—even if yields are completely unchanged. Portfolio management systems must track both clean and dirty prices and properly attribute the coupon receipt versus the clean price change to avoid misstating income versus capital gains components of total return.
Formula
Dirty Price = Clean Price + Accrued Interest; Accrued Interest = (Coupon Rate × Face Value / Payment Frequency) × (Days Since Last Coupon / Days in Coupon Period)
Example
An investor purchases a corporate bond with a face value of $1,000,000, a 5.00% annual coupon (paid semi-annually, $25,000 per period), and a clean price of 98.50 (98.50% of face value = $985,000). Settlement occurs 75 days after the last coupon payment date. Using a 30/360 day count convention, accrued interest is: $25,000 × (75/180) = $10,416.67. The dirty price (invoice price) that the buyer must pay is: $985,000 + $10,416.67 = $995,416.67. On the next coupon date 105 days later, the investor receives the full $25,000 coupon payment. Of this, $10,416.67 represents the return of accrued interest paid at purchase, and $14,583.33 represents genuine interest income earned during the 105-day holding period. If the bond were held to maturity at par, the investor's yield would be calculated on the $985,000 clean price plus the $10,416.67 accrued interest paid—i.e., the dirty price is the true cost basis for yield calculations.
Related terms
Accrued Interest Asset Swap Spread Basis Bond Clean Price Corporate Bond Coupon Rate Day Count Convention Face Value Investment Grade Bond Negative Convexity Reverse Repo