What's the difference between dirty price and clean price, and why do bond markets quote the clean price but settle at the dirty price?
CFA Level I fixed income. I understand that dirty price = clean price + accrued interest, but I don't understand the economic rationale. If the dirty price is what you actually pay, why not just quote that? And how do you calculate accrued interest between coupon dates?
This is a great conceptual question that the CFA exam tests frequently. The clean/dirty price distinction exists for a very practical reason: to make bond prices comparable over time.
The Problem with Dirty Prices
Imagine a bond paying a 6% annual coupon semi-annually ($30 every 6 months). On the day after a coupon payment, the dirty price might be $1,000. One day before the next coupon, it would be roughly $1,030 (because $30 of accrued interest has built up). A chart of the dirty price would show a sawtooth pattern -- steadily rising between coupon dates, then dropping sharply on payment dates.
This sawtooth pattern makes it impossible to see whether the bond's value is actually changing due to interest rates, credit quality, or other fundamentals. The clean price strips out this predictable accrual pattern.
Accrued Interest Calculation
AI = (Coupon Payment) x (Days Since Last Coupon / Days in Coupon Period)
The day-count convention determines how you count 'days':
| Convention | Numerator | Denominator | Used For |
|---|---|---|---|
| 30/360 | Assume 30 days/month | 360 | US corporate, agency bonds |
| Actual/Actual | Actual calendar days | Actual days in period | US Treasuries |
| Actual/360 | Actual calendar days | 360 | Money market instruments |
Worked Example: Carrington Municipal Holdings 5% bond (fictional)
| Detail | Value |
|---|---|
| Par value | $1,000 |
| Coupon rate | 5% semi-annual |
| Semi-annual coupon | $25 |
| Last coupon date | January 15, 2026 |
| Settlement date | March 20, 2026 |
| Next coupon date | July 15, 2026 |
| Day count convention | 30/360 |
| Quoted (clean) price | 98.50 |
Days since last coupon (30/360): January has 15 remaining days (15 to 30) + February 30 days + March 20 days = 65 days
Days in period (30/360): 6 months x 30 = 180 days
Acrrued interest = $25 x (65/180) = $25 x 0.3611 = $9.03
Clean price = 98.50% x $1,000 = $985.00
Dirty (invoice) price = $985.00 + $9.03 = $994.03
Why Quote Clean but Settle Dirty?
Quoting clean lets traders and investors compare bonds on a level playing field. Two identical bonds with different coupon dates would have different dirty prices simply due to accrual timing. Clean pricing isolates the market's assessment of value. But when money changes hands, the buyer must compensate the seller for interest earned but not yet received -- hence settling at the dirty price.
Exam Tip: The CFA exam will give you dates and a day-count convention and ask you to compute the invoice price. Make sure you can handle both 30/360 and actual/actual calculations.
Practice bond pricing in our CFA Level I fixed income section.
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