Clean Price Quotes Explained
Clean Price Quotes Explained
Bonds are quoted using clean prices, which strip out accrued interest. The clean price is what you see in the market; the dirty price (clean price plus accrued interest) is what you actually pay.
Key takeaways
- The clean price is the quoted price, excluding accrued interest between coupon dates.
- The dirty price is the clean price plus accrued interest, and it is the true economic price you pay when buying the bond.
- Accrued interest is the coupon earned since the last coupon payment date, prorated daily.
- Clean prices are used in public quotes and financial media to avoid confusion from varying coupon dates.
- Understanding the difference between clean and dirty prices is essential for understanding bond fund disclosures and trading economics.
Why separate clean and dirty prices?
Bonds pay coupons on specific dates (semi-annually for most US corporates and Treasuries, quarterly or monthly for some). If you buy a bond between coupon payment dates, you owe the seller the interest they have accrued since the last coupon date. This is fair: the seller held the bond and earned the interest, so they should receive it when they sell.
Without adjusting for accrued interest, the quoted price would jump on coupon payment dates. On the day after a $40 coupon is paid, the holder has earned no interest yet, so the bond price should theoretically include zero accrued. But one day before the next coupon payment (180 days later for semi-annual bonds), the holder has earned almost the full $40 in accrued interest, so the bond price should reflect that. If quoted prices included accrued interest, the price would jump or dip sharply on coupon payment dates, which is confusing and economically misleading.
To avoid this, the market quotes the clean price (also called the quoted price), which excludes accrued interest. This allows the quoted price to move smoothly based on market yields and creditworthiness, without jerky jumps from coupon payments.
Calculating accrued interest
Accrued interest is calculated as:
\text{Accrued Interest} = \text{Coupon Payment} \times \frac{\text{Days Since Last Coupon}}{\text{Days in Coupon Period}}
Example: A bond with a 4% annual coupon ($40 per year, paid semi-annually as $20 each period) is purchased 45 days into a 180-day coupon period.
Accrued interest = $20 × (45 / 180) = $5
The buyer owes the seller $5 in accrued interest, compensating them for the 45 days they held the bond and earned interest.
Clean price vs. dirty price example
Suppose the clean price of a bond is quoted as $1,020 (103% of par, or "103 points" in market parlance). The semi-annual coupon is $40. The bond is purchased 90 days into a 180-day coupon period.
Accrued interest = $40 × (90 / 180) = $20
Dirty price = Clean price + Accrued Interest = $1,020 + $20 = $1,040
The buyer receives the quote of $1,020 (clean price) but actually pays $1,040 (dirty price) at settlement. The extra $20 goes to the seller as compensation for accrued interest. At the next coupon payment (90 days later), the buyer receives the full $40 coupon, which offsets the $20 they paid upfront.
Real-world bond quotes
In financial media and bond fund prospectuses, you see clean prices. A quote like "US Treasury 4% due 2032 bid 102.5, asked 102.7" is the clean price. If you buy the bond, you pay the clean price plus accrued interest. If you sell, you receive the clean price plus accrued interest.
This convention is consistent across Treasuries, corporates, municipals, and international bonds. All are quoted as clean prices; all trades settle at dirty prices.
Accrued interest and bond fund pricing
For bond mutual funds and ETFs, the net asset value (NAV) reflects the dirty prices of the holdings. The fund's stated price (the price you see when you check a fund like BND, AGG, or TLT) is based on the sum of all holdings' dirty prices, divided by the number of shares outstanding.
In daily fund price quotes, accrued interest is typically "invisible" because the fund holds many bonds with different coupon dates. The overall accrued interest of the portfolio averages out and is included in the reported price. You do not separately negotiate accrued interest when buying or selling fund shares.
However, when you hold individual bonds, understanding accrued interest is important. If you buy a bond 10 days before a coupon payment, you are paying accrued interest upfront and will receive the full coupon 10 days later. You have not earned the full coupon; you have earned only the final 10 days' worth. The accrued-interest payment compensates the seller for the interest you will not actually receive.
The impact on yield calculations
Accrued interest affects the yield to maturity (YTM) calculation. The YTM is the internal rate of return on the dirty price (what you actually pay), not the clean price (what you see quoted). A bond quoted at a clean price of $1,020 has a different yield if you account for the $20 accrued interest—your actual cost is $1,040, which is lower than 102% of par.
Bond traders and financial calculators automatically account for this. When you see a bond quoted with a clean price and a YTM, the YTM is calculated using the dirty price, not the clean price. For practical purposes, the difference is small for most bonds, but it is mathematically precise.
Day-count conventions and accrued interest
The calculation of accrued interest depends on the day-count convention (Actual/Actual, 30/360, Actual/360, etc.). Different conventions define the number of days in a coupon period differently, which affects the accrued-interest fraction.
For US Treasuries (Actual/Actual convention), accrued interest is calculated using the actual number of days. For US corporates and most international bonds (30/360 convention), each month is assumed to have 30 days and each year 360 days, which is a simplification but widely used.
This is explained in detail in a later article, but the key point here is that accrued interest depends on the day-count convention, and the specific convention matters for precise pricing.
Visual comparison: clean vs. dirty price
Imagine a bond chart over a coupon period. The dirty price follows a smooth curve as time passes and yields change. The clean price is the same curve with a linear component removed: the accrued interest that accrues linearly from one coupon date to the next. The clean price is "flattened" at coupon payment dates, appearing to drop sharply, then rise as interest re-accrues. The dirty price has no such discontinuity.
For bond investors, the clean price is convenient for comparing bonds with different coupon dates. For those calculating returns and managing holdings, the dirty price is the economic reality. Most of the time, bond fund investors do not need to think about this distinction, but understanding it clarifies what happens between coupon payments.
Flowchart
Next
Clean prices make bonds with different coupon schedules easy to compare. But the clean price itself depends on the day-count convention used to calculate yields and accrued interest. Different conventions (30/360, Actual/Actual, Actual/360) yield slightly different results and are used in different markets. In the next article, we explore why the small print on day counting matters for pricing and returns.