Bond basics
Clean and dirty prices
Accrued interest, the clean price the market quotes and the dirty price the buyer actually pays.
Learning objectives
- Calculate accrued interest with a stated day-count convention
- Move between clean and dirty (full) prices and calculate the cash a buyer pays
- Price a bond between coupon dates from its yield
- Explain why markets quote clean prices
Bonds trade on any day, but coupons are paid only on coupon dates — and the whole coupon goes to whoever holds the bond on that date. If you sell halfway through a coupon period, you have earned half a coupon that the buyer will collect. So the buyer pays you that accrued interest on top of the price.
That gives two prices. The clean price is the quoted price, without accrued interest. The dirty price (also called the full or invoice price) is what actually changes hands: clean price + accrued interest.
Accrued interest = (C ÷ f) × days since last coupon ÷ days in the coupon period Dirty price = clean price + accrued interest Cash paid = dirty price ÷ 100 × face value
- C ÷ f
- the coupon per period (per 100), e.g. 2.5 for a 5% semi-annual bond
- Days
- actual calendar days, from the last coupon date up to the settlement date
- Settlement date
- the date cash and bonds change hands (usually a day or two after the trade)
Included with a Formula Quest membership
The rest of this lesson is for members. Members get the full lesson, including its 4 graded exercises, and every other Finance Quest lesson.