What it means
Bonds pay interest in lumps, usually every six months, but the holder earns that interest every day. If prices were quoted with the accrued interest included, a bond's quoted price would climb steadily through the coupon period and then drop sharply on the payment date, purely because of the timing of a cash flow.
Stripping the accrued interest out produces the clean price, which moves only when the market's view of interest rates or credit risk changes. The distinction matters most when comparing bonds.
Two identical bonds sitting at different points in their coupon cycle would show different dirty prices even if the market valued them the same way, so traders, index providers and analysts all work in clean prices. Yield calculations are built on the clean price for exactly the same reason.
Buyers still have to settle the full amount. The purchaser pays the clean price plus accrued interest, and is then reimbursed by receiving the whole coupon on the next payment date, which effectively refunds the accrued portion.
In this sense accrued interest is not a cost, it is a reimbursement to the seller for the days of interest that seller earned but never collected. Conventions vary and are worth checking on any real trade.
Different markets count days differently, using actual over actual, thirty over three hundred and sixty, or actual over three hundred and sixty, and the choice changes the accrued figure slightly. Some instruments, notably deeply distressed bonds trading flat, are quoted without any accrued interest at all because the issuer has stopped paying coupons.
In practice
Real-world examples.
Example
A corporate treasurer buys $2,000,000 of five-year notes quoted at 101.25. The settlement figure includes four months of accrued interest, so the cash leaving the account is noticeably higher than 101.25% of face value, and the treasurer books the accrued portion separately.
Example
A fund manager compares two government bonds with identical maturities, one just after a coupon date and the other a week before the next. Working in clean prices shows the two are trading at essentially the same yield, a comparison the dirty prices would have obscured.
Example
An accountant reconciling a bond portfolio finds the custodian's valuation is higher than the front-office system's. The difference turns out to be accrued interest, which the custodian includes and the trading system does not, and the two are reconciled once both are expressed on a clean basis.
Formula
Calculation
The two formulas that matter are:
Accrued interest = face value x annual coupon rate x (days since last coupon / days in the coupon period)
Dirty price = clean price + accrued interest
Take a bond with a face value of $100,000 paying a 6% annual coupon in two equal instalments, so each coupon is $100,000 x 6% / 2 = $3,000 for a 180-day period.
The bond is bought 90 days after the last coupon payment, and it is quoted at a clean price of 98.50 per 100 of face value.
Clean price in dollars = 98.50% x $100,000 = $98,500
Accrued interest = $3,000 x (90 / 180) = $1,500
Dirty price paid at settlement = $98,500 + $1,500 = $100,000
So the screen shows 98.50 and the buyer wires $100,000. Ninety days later the buyer receives the full $3,000 coupon, of which $1,500 simply returns the accrued interest already paid to the seller.Case study
Seen in the real world.
Ridgeway Mutual is a fictional insurance company used here purely as an illustrative example. Its investment team bought $100,000 of a 6% corporate bond quoted at a clean price of 98.50, exactly 90 days into a 180-day coupon period.
The portfolio manager approved the trade at $98,500 and was surprised when the settlement instruction came through at $100,000. The extra $1,500 was accrued interest owed to the seller for the ninety days it had held the bond, and it was recorded as a receivable rather than as part of the cost of the investment.
Three months later the bond paid its $3,000 coupon. Ridgeway's income statement recognised $1,500 of that as interest earned during its own holding period, and the other $1,500 cleared the receivable. In this illustrative case nothing had gone wrong at all, but the confusion prompted the team to change its trade approval screen to display both clean and dirty prices side by side.
Watch out
Common mistakes.
- Budgeting cash for a bond purchase using the quoted price alone. The settlement amount is the dirty price, and on a high-coupon bond bought late in the period the difference can be meaningful.
- Treating accrued interest paid to the seller as a cost of the investment. It is a reimbursement that comes straight back in the next coupon, so it belongs in interest receivable rather than in the purchase price.
- Comparing bonds on dirty prices. Two bonds at different points in their coupon cycles will look mispriced against each other when the only real difference is how many days of interest have built up.
Questions
People also ask.
Why do markets quote clean prices at all?
Because the clean price moves only with interest rates and credit quality, so a chart of it shows genuine price movement rather than the mechanical sawtooth caused by accruing coupons.
Is the dirty price ever the quoted price?
Yes, a few markets and instrument types quote dirty prices by convention, so confirming the quoting basis before trading is standard practice.
Does accrued interest exist on a zero coupon bond?
No, because no coupon is ever paid, so the clean and dirty prices are the same and the return comes entirely from the discount to face value.
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