Dirty Price
Candlefocus EditorDirty price, also known as the full or actual price, is the price of a bond that includes accrued interest from the last coupon payment up until the settlement date. Accrued interest is a bond’s contractual compensation for income not realized by the owner between coupon payment dates. A dirty price is the opposite of a clean price, which is the quoted price that excludes any accrued interest and often viewable on financial websites.
The typical process of a bond's life cycle involves the investment bank that handles the bond’s issuance providing a quote of the dirty price to the investor. The investor purchases a bond at the dirty price and settles the transaction. On the settlement date, the issuer of the bond pays a coupon payment to the investor and the investor pays the issuer the principal. After the principal is received, the investor is then paid the accrued interest.
Clean Price vs. Dirty Price
When an investor purchases a bond, they are usually quoted the clean price by their broker or investment platform as opposed to the dirty price. The clean price is the price excluding accrued interest, or the notional value, and is typically used for US-based bonds. In contrast, the dirty price is the closing quotation that includes any accrued interest, which is more commonly used for European-based bonds.
Calculating Accrued Interest
Accrued interest can be calculated using the following formula:
Accrued Interest = (notional value x coupon rate x number of days from last coupon payment to settlement date) divided by 365
For example, if the notional value of a bond is $5 million, with a coupon rate of 5.5%, and the settlement date is 5 days after the last coupon payment, the accrued interest would be calculated as:
Accrued Interest = (5m x 5.5% x 5) / 365 = $19,178
Conclusion
Dirty price is the price of a bond that includes accrued interest and often quoted at the time of purchase, while clean price excludes any accrued interest. A bond’s coupon payment and notional value are the two components of the dirty price calculation. If an investor purchases a bond at a given date, the issuer will pay the coupon payment on the settlement date and owe the investor the accrued interest as well. Calculations can soon be made using the notional value, coupon rate, and number of days from the last coupon payment to the settlement date.