Clean Price

The clean price is the price of a bond that leaves out the interest accrued since the most recent coupon date. It is the figure shown on trading screens and in price lists in most bond markets. The amount a buyer actually pays is higher: it equals the clean price plus the accrued interest and is called the dirty price, full price or invoice price.

The distinction exists because most bonds pay interest at fixed intervals, commonly every six or twelve months, while trades can settle on any day. A seller who has held a bond for part of a coupon period has earned part of the next coupon payment but will not receive it, since the whole coupon goes to whoever holds the bond on the payment date. The buyer compensates the seller for that portion at settlement.

The relationship is:

and accrued interest for a bond with regular coupons is:

• $C$ is the coupon paid for one coupon period.
• $d$ is the number of days from the last coupon date to the settlement date.
• $D$ is the number of days in the coupon period.

Both day counts follow the bond's day count convention. Take a bond with a face value of $1,000 and a 6 percent annual coupon rate, paid twice a year, so each coupon is $30. A trade settles 60 days after the last coupon date, in a period counted as 180 days. Accrued interest is 30 × 60 ÷ 180 = $10. If the bond is quoted at a clean price of 98.50, meaning 98.50 percent of face value, the clean amount is $985. The buyer pays the dirty price of 985 + 10 = $995.

When the next coupon is paid, the buyer receives the full $30. Of this, $10 repays the accrued interest handed to the seller and $20 is the interest earned over the 120 days the buyer held the bond.

If interest rates and credit quality did not change at all, the dirty price of a bond would still move every day. It would climb steadily as interest built up and then drop by the amount of the coupon on the payment date, tracing a sawtooth pattern. That movement says nothing about the market's view of the bond.

Removing accrued interest gives a figure that changes only when something of substance changes: the general level of interest rates, the issuer's credit standing, or the remaining time to maturity. A clean price can be compared directly from one day to the next and from one bond to another. A clean price above 100 means the bond trades at a premium to its par value, and one below 100 means it trades at a discount.

The clean price is a quoting convention, not the economic price. The fair value of a bond is the present value of its remaining cash flows, and that calculation yields the dirty price. A bond's yield to maturity is likewise the discount rate that makes the present value of the cash flows equal to the dirty price. In practice a trader converts the quoted clean price to a dirty price, solves for the yield, and reverses the steps to go from a yield to a quote. Standard bond pricing functions in spreadsheets and trading systems do this automatically.

Accounting and risk systems also work from the dirty price, since it is the amount for which a position could be sold. Portfolio valuations therefore show accrued interest as a separate line or include it in market value.

Quoting clean is the norm for government bonds and corporate bonds in the United States, the United Kingdom, the euro area and most other markets. The accrued interest calculation differs between them. US Treasury notes and bonds count actual days in both the numerator and the denominator, while US corporate and municipal bonds assume months of 30 days and a year of 360.

There are exceptions. A zero-coupon bond pays no coupons, so it has no accrued interest and its clean and dirty prices are the same. Bonds that are in default usually trade flat, meaning without accrued interest, because the next coupon is not expected to be paid. Some markets and some instruments, including certain convertible and index-linked bonds, are quoted on a dirty basis. In markets with an ex-dividend period, a bond bought shortly before a coupon date does not carry the right to that coupon, and accrued interest for those days is negative.

Investors comparing a quoted price with the cash needed to settle should expect the difference, which is largest just before a coupon date. Trade confirmations show the clean price, the accrued interest and the total consideration separately. For tax purposes many jurisdictions treat accrued interest paid or received as income and not as part of the purchase price, so it does not enter the calculation of a capital gain in the same way as the clean price.