Accrued Interest: Clean vs Dirty Bond Prices

Key Takeaways

• Clean price (quoted) excludes accrued interest; dirty price (invoice) includes it, buyers pay the dirty price at settlement.
• Accrued interest runs to the settlement date, not the trade date; with T+1, this is usually one day after trade.
• US corporate bonds use the 30/360 day-count convention; US Treasuries use actual/actual.
• Zero-coupon bonds have imputed interest that accrues for tax purposes even though no cash is received until maturity.

What It Is

Bond coupons pay on a fixed schedule, usually every six months for US corporates and Treasuries. Between those dates the bond is still earning interest each day, even though nobody has received cash yet. That earned-but-unpaid amount is the accrued interest.

Accrued interest belongs to whoever owned the bond during the days it accrued. When a trade happens between coupon dates, the convention is that the buyer pays the seller for the accrued portion at settlement. On the next coupon date the buyer then collects the full coupon, which reimburses the accrued amount and adds the days since settlement.

The Intuition

If bonds traded without accrued interest, prices would jump up smoothly toward the next coupon and then fall off a cliff when the coupon paid. That sawtooth would make price comparisons across days confusing and would punish anyone who sold right before a coupon date.

Quoting the bond clean, meaning excluding accrued, and settling dirty, meaning including accrued, fixes the problem. The clean price is flat over time if nothing else changes, which is what traders want to see on a screen. The dirty price is what the cash actually changes hands for.

How It Works

Accrued interest is calculated from the last coupon payment date to the settlement date, not the trade date. The simple formula is:

accrued interest = face value * coupon rate * (days since last coupon / days in coupon period)

The day-count convention depends on the bond type. US corporate bonds use 30/360, treating every month as 30 days and every year as 360 days. US Treasuries use actual/actual, counting real calendar days. The day-count choice can change the accrued amount by a few cents per 1,000 dollars of face, which matters for institutional trades but rarely for retail.

The relationship between clean and dirty price is simple:

dirty price = clean price + accrued interest

The quoted clean price does not include accrued, so two bonds with different coupon dates can be compared fairly on a screen. The dirty price, also called the invoice price, is what the buyer actually pays at settlement.

Settlement dates matter because accrued runs to settlement, not to trade date. Since February 2023, US Treasuries have settled on T+1. On May 28, 2024, US equities and most corporate bonds also moved to T+1. Shorter settlement means slightly less accrued than under the old T+2 or T+3 conventions for any given trade.

Worked Example

An investor buys 10,000 dollars face of a corporate bond with a 6 percent annual coupon paying semi-annually. The last coupon paid 90 days ago. The quoted clean price is 98.

Using the 30/360 convention, the accrued interest is:

10,000 * 0.06 * (90 / 360) = 150 dollars

Clean price at 98 is 9,800 dollars. Dirty price, and the actual cash the buyer wires, is 9,800 + 150 = 9,950 dollars.

Ninety days later, the bond pays its semi-annual coupon of 300 dollars. The buyer receives the full coupon, which effectively reimburses the 150 dollars of accrued paid at purchase and leaves 150 dollars of net interest earned over the new holding period. On an economic basis, only the interest that accrued while the bond was actually owned belongs to the buyer.

Common Mistakes

1. Using the clean price to calculate cash needed. The clean price is for quoting, not for funding. The buyer must have the dirty price in cash on settlement day. This trips up newcomers who underestimate their required deposit.

2. Forgetting the day-count convention. 30/360 and actual/actual give different accrued amounts. Corporate bonds mostly use 30/360, Treasuries use actual/actual, and mixing them up produces small but real mispricings.

3. Measuring accrued to trade date. Accrued runs to settlement. With T+1, the difference is one day, so it is small but not zero. For a large block trade the discrepancy matters.

4. Double-counting on the next coupon. The full coupon goes to the registered holder on the coupon date, not pro-rated between buyer and seller. The accrued paid at purchase is what compensates the seller. Investors sometimes worry they will get shortchanged and do not realize the mechanics already balance out.

5. Ignoring accrued on zero-coupon bonds. Zeros do not pay coupons, but they do accrue interest for tax purposes in the United States as imputed interest. Investors can owe tax on accrued income they have not yet received in cash.

Frequently Asked Questions

Why do bonds quote a clean price if settlement happens at the dirty price? The clean price removes the sawtooth pattern that would result from accruing interest and then seeing it drop off on coupon payment days. Without this convention, a bond's price would increase predictably as the next coupon approaches and then fall sharply when paid, making daily price comparisons across different bonds on different coupon schedules difficult. The clean price provides a stable reference for market participants while the dirty price handles the actual cash transfer.

How much does the choice between 30/360 and actual/actual matter in practice? For most retail transactions, the difference is a few cents per thousand dollars of face value and is rarely material. For large institutional trades in the tens or hundreds of millions, the difference can be several thousand dollars. Sophisticated traders and systems must use the correct convention per bond type to avoid systematic small mispricings that accumulate across large portfolios.

What happens to accrued interest if a bond issuer defaults between coupon dates? In a default, interest payments stop accruing from the default date for practical purposes, though technically the obligation exists. Accrued but unpaid interest is typically included as part of the bankruptcy claim alongside outstanding principal. Recovery depends on the capital structure and the eventual settlement with creditors. The buyer who purchased the bond before the default is not specifically protected for the pre-purchase accrued they paid to the seller.

Does accrued interest affect yield calculations? Standard yield to maturity calculations are performed on the clean price. The accrued is added at the moment of purchase but does not change the bond's future cash flows, so it does not affect YTM directly. However, when comparing bonds at different stages of their coupon cycles, using dirty prices would distort the comparison, which is exactly why the market standardizes on clean prices for yield calculations.

Is accrued interest taxable income for investors? The accrued interest paid to a seller is generally taxable to the seller as ordinary income in the year received, not as capital gain. For the buyer, the accrued amount paid reduces the taxable portion of the first coupon received, since part of that coupon is technically a return of the accrued already paid. Tax treatment can be complex, particularly for bonds bought at a premium or discount, and investors should consult a tax professional for their specific situation.

Sources

1. SEC / Investor.gov. "New T+1 Settlement Cycle Investor Bulletin." https://www.investor.gov/introduction-investing/general-resources/news-alerts/alerts-bulletins/investor-bulletins/new-t1-settlement-cycle-what-investors-need-know-investor-bulletin
2. FINRA. "Understanding Settlement Cycles: What Does T+1 Mean for You?" https://www.finra.org/investors/insights/understanding-settlement-cycles
3. Corporate Finance Institute. "Dirty Price." https://corporatefinanceinstitute.com/resources/fixed-income/dirty-price/
4. BTRM Working Paper. "Bond Markets: Dirt In The Clean Price." https://btrm.org/wp-content/uploads/2024/03/BTRM_WP14_Bond-Markets-Clean-Price_KBoovendran.pdf

Disclaimer

This article is educational content only and is not financial advice. Nothing here is a recommendation to buy, sell, or hold any security. Consult a licensed advisor before making investment decisions.