What Is the Dirty Price of a Bond? Explained

Bonds serve as fundamental investment tools, representing a loan made by an investor to a borrower, such as a corporation or government. These debt instruments offer fixed-income opportunities, providing bondholders with periodic interest payments over a specified term. While the concept of a bond might seem straightforward, understanding its true cost in the market involves more than just a single quoted price. The actual amount an investor pays for a bond can be more complex due to how interest accumulates.

Understanding Bond Pricing Basics

Bonds are issued with a “face value” or “par value,” which is the principal amount the issuer promises to repay bondholders at maturity. This par value is typically set at $1,000, though it can vary. Bonds also feature “coupon payments,” which are the periodic interest payments made to bondholders. The “coupon rate” is the annual interest rate the bond issuer pays on the bond’s face value, remaining fixed for the security’s life. For instance, a bond with a $1,000 par value and a 5% coupon rate would pay $50 in interest annually, often distributed in semi-annual payments.

Accrued Interest

Interest on a bond accumulates daily between its scheduled coupon payment dates. This accumulated interest is known as “accrued interest.” Even if a bond pays interest semi-annually, the interest is continuously earned by the bondholder each day the bond is held. When a bond is traded between these payment dates, the seller is entitled to the portion of the next coupon payment that has accumulated since the last payment date. This ensures the seller receives compensation for interest earned during their holding period, even though the full coupon payment goes to the new buyer.

Clean Price and Dirty Price

The bond market uses two primary price quotations: the clean price and the dirty price.

The “clean price,” also called the quoted price or flat price, represents the bond’s value without including any accrued interest. This price allows for easier comparison between different bonds.

Conversely, the “dirty price,” also known as the full price or invoice price, is the actual amount a buyer pays for a bond. This price includes both the clean price and any accrued interest since the last coupon payment.

The relationship between these two prices is straightforward: Dirty Price = Clean Price + Accrued Interest. The dirty price is the transactional price that accounts for the interest earned by the seller up to the settlement date.

Calculating the Dirty Price

Calculating the dirty price involves determining the accrued interest and adding it to the clean price. Accrued interest is typically calculated using a formula that considers the bond’s coupon payment, the number of days since the last coupon payment, and the total days in the current coupon period. A specific “day count convention” influences how these days are counted.

As an example, consider a bond with a $1,000 par value and a 4% annual coupon rate, paid semi-annually, meaning each semi-annual payment is $20 ($1,000 4% / 2). If the bond was last paid on January 1 and is being traded and settled on February 15, assuming a 30/360 day count convention, there are 45 accrued days (30 days in January + 15 days in February). The accrued interest would be calculated as ($20 coupon payment 45 days) / 180 days in a semi-annual period, which equals $5. If the clean price of this bond is $980, the dirty price the buyer pays would be $985 ($980 clean price + $5 accrued interest).