Clean vs Dirty Bond Prices: Accrued Interest, Settlement and Real Returns

A bond is quoted at 98, yet buying 10,000 of face value costs 9,900 rather than 9,800. The extra amount is not necessarily a commission. A clean quote excludes accrued coupon interest; the settlement calculation normally adds it back.

The practical distinction matters most when calculating profit. Using the clean quote as the entire purchase cost, then treating the next full coupon as fresh income, counts part of the return twice. Start with cash paid, not the most prominent number on the trading screen.

From a quote of 98 to a cash payment of 9,900

Consider a hypothetical conventional fixed-rate bond: 100 face value, a 4% annual coupon, and two payments of 2 each year. To make the arithmetic transparent, stipulate 180 accrual units per coupon period and settlement 90 units after the last payment. All amounts use one currency. Ignore fees, tax, financing, default and special ex-coupon arrangements initially; this is not a quote for an actual security.

Accrued interest per 100 face value is 2 × 90 / 180 = 1. The clean price of 98 therefore becomes a dirty, or full, price of 99. For 10,000 face value, the bond consideration is 10,000 / 100 × 99 = 9,900: 9,800 for the clean value and 100 of accrued interest.

Full price = clean price + accrued interest. Multiply by face value divided by 100, then account separately for applicable charges. A quote of 98 ordinarily means 98% of par, not 98 currency units for every bond regardless of denomination. Coupon cash is calculated on face value, not on the 9,900 purchase outlay.

The accrued amount allocates part of the coming coupon to the seller, who owned the bond earlier in the period. It is neither an additional fee nor protected interest income. If the issuer fails to pay, the accrued amount already included in your purchase does not automatically come back.

A sale before the next coupon: separate price gain from accrual

Suppose you sell 45 accrual units later, before receiving any coupon, at a clean price of 99. The period is now 135 units old. Accrued interest is 2 × 135 / 180 = 1.5, making the full sale price 100.5.

The gain is 150: a 100 increase in clean value plus 50 of additional accrual. Holding-period return is 150 / 9,900, or about 1.5152%, not 150 / 9,800. This is neither an annualized return nor yield to maturity.

If total charges of 30 are deducted entirely at the sale, net profit becomes 120 and return about 1.2121%. Charges paid at purchase also increase the starting cash denominator; subtracting every cost from profit while leaving that denominator unchanged may not describe the actual investment.

Crossing a coupon date without counting the same interest twice

Now take an alternative path, not an additional trade: hold through the next coupon, receive 200, and sell 30 accrual units after that payment. The holding interval is 120 units from purchase. At a clean sale price of 99, new accrued interest is 2 × 30 / 180 = one-third per 100, giving sale proceeds of approximately 9,933.33. Keep the coupon as cash without reinvesting it.

Profit = 9,933.33 + 200 − 9,900 = approximately 233.33; return is about 2.3569%. The same result comes from 100 of clean-price gain, plus the 200 coupon, plus 33.33 of closing accrual, less the 100 of accrued interest purchased at entry. Omitting the last subtraction treats bought income as newly earned income.

The payment itself does not create wealth. Isolate the mechanics by holding the clean price at 99: immediately before payment, full value approaches 101; immediately afterwards it is 99 with 2 in cash. The combined value remains 101. Actual clean prices can move at the same time because yields, credit or liquidity change, so this is an accounting comparison, not a forecast.

Why two accrued-interest calculations can disagree

Check settlement first. The execution date is not necessarily the date used to exchange securities and cash or calculate interest. In this example, one extra accrual unit changes interest by 2 / 180 per 100 face value, or about 1.11 on a 10,000 position. A small date mismatch can explain a seemingly unexplained invoice difference.

Next, check the contractual day-count convention. Our 180, 90 and 135 are stipulated accrual units, not a claim that every half-year contains 180 calendar days. Actual-day conventions, different 30/360 methods, and short or long first coupon periods can produce different fractions. Month-end, leap-year and non-business-day treatment must follow the instrument's terms.

Coupon entitlement is a separate check. In an ex-coupon period, a buyer may not receive the approaching payment, and the adjustment can involve rebate interest rather than a normal positive accrual. Do not infer entitlement merely from the number of days left. Reconcile the prior coupon date, next coupon date, settlement, day count and entitlement before blaming the calculator.

Clean-price charts, full-price charts and total return

A clean-price series strips out the accrued coupon component and makes market repricing easier to inspect. It does not make prices stable. A full-price series includes current accrual and changes mechanically when the coupon is paid. Total return also accounts for cash actually received and what happens to it afterwards. Substituting one measure for another can turn a cash transfer into an apparent loss or an imaginary gain.

The same distinction underlies yield to maturity versus realized bond returns: identify the cash flows and investment horizon before selecting a percentage. Multiplying a short holding-period return by an annualization factor does not establish what can be earned repeatedly.

Rebuild the cash-flow model for defaulted bonds trading without a separate accrual, floating-rate or inflation-linked instruments, amortizing principal and unusual first coupons. A bond fund's unit value is not a single security's clean price awaiting the same adjustment. Tax and accounting classification can also differ from the economic profit measured here.

A five-part trade-confirmation check

1. Identify the security, face amount and currency. Determine whether the screen shows a clean price, full price or yield, and confirm the quotation unit.
2. Read the coupon, frequency, day-count basis and settlement date. Resolve ex-coupon or nonstandard-period terms before applying a routine formula.
3. Calculate accrual per 100, scale by face value, and reconcile clean consideration, interest, charges and the actual account debit.
4. Use an executable sale price and matching accrual, add coupons received, and subtract the complete initial outlay and other costs. Convert currencies separately where necessary.
5. Verify both cash and security delivery. Explain timing, rounding or entitlement differences instead of changing a yield assumption until the figures happen to match.

A move from 98 to 99 is only one line of the investment record. Separating price, accrued interest and cash—and then reconnecting them on the correct dates—reveals what was paid, what was recovered and what was genuinely earned.