In plain language — The market price shown on screen is often not the cash amount that settles. Between coupon dates, the seller has earned part of the next coupon, and the buyer compensates that amount at settlement.
The clean price excludes interest accrued since the last coupon date. The dirty price, also called full price, includes it. Accrued interest is the fraction of the coupon earned during the current period under the bond's contractual conventions.
Dirty price = Clean price + Accrued interestThe identity is simple. The correct number still depends on the coupon calendar, day-count convention, settlement date and treatment of coupon events.
From the quote to settlement cash
Suppose a bond pays an annual coupon of 4 per 100 face value. If half the coupon period has elapsed under its convention, indicative accrued interest is 2. With a clean price of 98.50, the indicative dirty price is 100.50. This is not a universal settlement quote: holidays, settlement timing, ex-coupon periods, rounding and day count can change the actual amount.
Clean price makes price comparisons easier. Dirty price grows as the coupon accrues and normally drops by the corresponding amount when the coupon is detached, while cash is paid. Looking only at full price can make this transfer appear to be an economic loss even though price and cash must be read together.
An ordinary zero-coupon bond has no periodic coupon to accrue. Inflation-linked, floating-rate, defaulted or irregular securities require their own terms, especially for short or long coupon periods.
How to check the calculation
Start with the settlement date, not only the trade date. Retrieve the previous and next coupon dates, payment frequency, coupon rate, face value and day-count convention. A regular coupon accrual can be represented as:
Accrued interest = period coupon × accrued fraction of periodThe fraction is not always elapsed calendar days divided by all calendar days. Actual/Actual, 30/360 and Actual/360 define numerator and denominator differently. The bond documents and market convention govern the real calculation.
A professional reconciliation also checks quote units, quantity, face value, currency, rounding and sign. If the price is quoted per 100 face value, it must be converted to the position's cash value. Fees, taxes and foreign exchange are not part of the clean-dirty identity, although they can enter total settlement cash.
Why it matters for yield and risk
Yield and sensitivity calculations need a price consistent with cash flows. Yield to maturity is solved from full price and effective dates, even if an interface starts with a clean quote. Monetary DV01 and duration applied to a position require the same discipline around full value and units.
Accrued interest does not remove risk. Price, currency or counterparty conditions can change before settlement; the issuer retains credit risk; the bond may be illiquid. Interest that has accrued is not a guarantee that the future payment will occur.
Common error — Comparing a clean quote with the total debit and calling the difference a hidden fee. Reconcile accrued interest, face value and conventions first.
Questions this page answers
Is the displayed price clean or dirty? What accrual is included at settlement? Which date and day count were used? Was a coupon just paid and recorded as cash? These checks explain many apparent discrepancies; the final confirmation comes from the security documents and trade confirmation.
Sources
- Investor.gov — Bonds or Fixed Income Products
- TreasuryDirect — Glossary
- TreasuryDirect — When auctions happen