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Interactive visualization of bond pricing conventions. See how flat price evolves smoothly while full price follows a saw-tooth pattern. Explore accrued interest buildup, coupon payment drops, and settlement mechanics.
Key CFA Insight
Bonds are quoted using the flat price but traded at the full price. The accrued interest compensates the seller for the coupon earned but not yet received. At each coupon date, accrued interest resets to zero and the full price drops by the coupon amount ($50.00), creating the characteristic saw-tooth pattern.
Tasks:
• Move the settlement date and observe the linear growth of accrued interest
• Identify what happens to the full price on coupon dates (green dashed lines)
• Compare the smooth flat price with the saw-tooth full price
• Change the coupon rate and observe the size of the saw-tooth pattern
• Set YTM above the coupon rate to see a discount bond, and below for a premium bond
When a bond trades between coupon payment dates, two prices exist: the flat price (also known as clean price) and the full price (also known as dirty price). Understanding the difference is essential for bond trading and CFA exam preparation.
The flat price is the quoted price of a bond that does NOT include accrued interest. It changes smoothly over time, reflecting:
Pull-to-par: As the bond approaches maturity, the flat price converges toward face value regardless of whether it trades at a premium or discount.
Yield effect: If the yield to maturity equals the coupon rate, the flat price equals par. If YTM is below the coupon rate, the bond trades at a premium (above par). If YTM is above the coupon rate, the bond trades at a discount (below par).
The full price is what the buyer actually pays. It equals the flat price plus accrued interest:
The full price follows a saw-tooth pattern because accrued interest builds up linearly between coupon dates and then drops to zero when the coupon is paid.
Accrued interest compensates the seller for the portion of the coupon earned but not yet received:
Between coupon dates, AI increases linearly from 0 to the full coupon amount. On the coupon payment date, AI resets to zero.
The full price increases steadily between coupons (flat price change + AI buildup) and then drops sharply on the coupon date by exactly the coupon amount. This creates the characteristic saw-tooth pattern.
Flat prices are used for quotation because they reflect genuine changes in market conditions (yield changes, credit events) without the artificial jumps caused by accrued interest. Two traders can compare flat prices and immediately assess whether the bond has become cheaper or more expensive, regardless of where in the coupon cycle the comparison is made.
The sliders, formulas and analytics view need more room than a phone screen can give them. Open this chart on a desktop or larger tablet to use the full interactive experience.
Avoid these frequent errors
Confusing flat and full price: Students often forget which is quoted and which is paid. Remember: QUOTED = flat price (clean), PAID = full price (dirty)
Forgetting that accrued interest resets: On coupon dates, AI drops to zero. Some students add the coupon to the full price instead of recognizing the reset
Using wrong day count: The AI formula depends on the day count convention (Actual/Actual vs 30/360). CFA problems will specify which convention to use
Thinking flat price has jumps: The flat price is continuous and smooth. Only the full price has discontinuities at coupon dates
Ignoring the ordering: Between coupon dates, full price is always greater than or equal to flat price. They are equal only on coupon dates
Mixing up coupon frequency: A 6% annual coupon paid semi-annually means $30 per period, not $60. Always divide by the frequency
Forgetting pull-to-par: Both premium and discount bonds converge to par at maturity. Students sometimes think discount bonds stay below par
Strategic insights for success
Full price formula: P_full = P_flat + AI. This will be on the exam. Memorize it
AI formula: AI = C x (days since last coupon / days in period). Know both Actual/Actual and 30/360 conventions
Quick identification: YTM < coupon = premium. YTM > coupon = discount. YTM = coupon = par
Question type 1 - Calculate AI: Time 30 seconds. Identify coupon per period, days elapsed, days in period. Plug into formula
Question type 2 - Flat to full conversion: Time 15 seconds. Add AI to flat price. Subtract AI from full price
Question type 3 - Premium/discount identification: Time 15 seconds. Compare YTM to coupon rate
Question type 4 - Coupon date behavior: Time 30 seconds. Full price drops by coupon amount, flat price is continuous, AI resets to zero
Common trap: The exam may give you the full price and ask for the flat price. Always read carefully which price is given and which is requested