Clean Price

Valuation always begins with the full price: the present value of every remaining coupon and the principal, discounted back to the settlement date at the bond's yield. That figure moves upward each day as the next coupon draws nearer, then drops when the coupon is paid. The clean price is what remains after subtracting accrued interest from that full price.

Accrued interest is the seller's share of the coupon currently being earned. In words, take the coupon amount for the period and multiply it by the fraction of the period that has elapsed: days from the last coupon date to settlement, divided by total days in the coupon period. The day-count convention determines how those days are counted, typically actual/actual for government bonds and 30/360 for most corporate and municipal issues. Clean price plus accrued interest returns the full price, and the full price is the cash amount that changes hands.

If markets quoted full prices, a screen would show a bond rising steadily for six months and then falling by the coupon amount overnight, even with yields perfectly unchanged. That pattern would make it impossible to compare two bonds at a glance, or to judge whether a price move reflected credit and rate news or merely the passage of time.

Quoting flat removes the mechanical component. A clean price of 98.40 today versus 98.30 yesterday signals a genuine yield change. It also lets a trader compare a bond that paid a coupon last week with one that pays next week on the same scale, and makes the pull to par visible: as maturity approaches, a premium or discount bond's clean price converges toward 100 in a smooth path rather than a jagged one. The convention is a display standard, not a valuation model.

US Treasury notes and bonds, gilts, bunds and the overwhelming majority of corporate bonds are quoted clean. Trade reporting systems such as TRACE publish clean prices, and index vendors construct bond index levels from clean prices plus a separately tracked accrued interest and income component. Bond fund factsheets follow the same split, which is why a fund's price return and income return are reported separately.

The trade confirmation is where the two pieces reunite: it shows the quoted price, the accrued interest calculated to settlement, and the invoice or settlement amount the buyer pays. Two exceptions matter. Defaulted and deeply distressed bonds trade flat, meaning no accrued interest is added because the coupon is not expected to be paid. And a handful of markets and instruments, including some money market and emerging market conventions, quote on a full-price basis.

Expect three linked tasks. First, price a bond between coupon dates: discount the remaining cash flows over a fractional first period to obtain the full price, then subtract accrued interest to report the quoted price. Second, reverse the process: given a quoted price and a settlement date, add accrued interest to recover the cash the buyer pays and the price used in any yield calculation. Third, apply the correct day count, since the same bond produces different accrued interest under actual/actual and 30/360.

The conceptual point that examiners test most often is directional: yield measures, including yield to maturity and money market yields, are derived from the full price, because that is the amount actually invested at settlement. Using the clean price as the investment outlay understates the cost and overstates the yield.