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And interest

What Is Accrued Interest?

Accrued interest is the interest that has accumulated on a bond or other debt securities since the last coupon payment up to the current date, but has not yet been paid. It represents the portion of the next interest payment that the seller of a security is entitled to receive when the security is sold between payment dates. As a concept within fixed income analysis, accrued interest is crucial for determining the true cost of a bond transaction in the secondary market.

History and Origin

The need for calculating accrued interest arose directly from the mechanics of interest-earning investments, particularly bonds, which make periodic interest payments. When a bond is bought or sold between these scheduled payment dates, the buyer would otherwise receive the full upcoming coupon payment, even though the seller held the bond for part of the period. To ensure fairness, a system was developed where the seller receives a pro-rata share of the interest earned during their holding period. This necessitated the creation and standardization of "day count conventions." These conventions are specific methodologies used to determine the exact number of days for which interest has accumulated, and how a year or month is defined for interest calculation purposes. Different day count conventions, such as Actual/Actual or 30/360, were developed to meet varying requirements for calculation ease and consistency across different financial instruments and jurisdictions, predating modern computing.

Key Takeaways

  • Accrued interest is the portion of the next coupon payment that has accumulated since the last payment date.
  • It is paid by the buyer to the seller in a bond transaction that occurs between coupon payment dates.
  • Accrued interest ensures that the seller receives their fair share of interest earned for the period they held the bond.
  • It is added to the clean price to arrive at the dirty price, which is the total amount paid by the buyer.
  • The calculation of accrued interest depends on the bond's coupon rate, the number of days since the last coupon payment, and the applicable day count convention.

Formula and Calculation

The formula for accrued interest typically depends on the specific day count convention used for the bond or financial instrument. A common way to express it is:

Accrued Interest=Face Value×Coupon Rate×Days Since Last CouponDays in Coupon Period\text{Accrued Interest} = \text{Face Value} \times \text{Coupon Rate} \times \frac{\text{Days Since Last Coupon}}{\text{Days in Coupon Period}}

Where:

  • Face Value (or par value) is the principal amount of the bond.
  • Coupon Rate is the annual interest rate paid by the bond.
  • Days Since Last Coupon refers to the number of days from the last coupon payment date up to, but not including, the settlement date of the trade.
  • Days in Coupon Period refers to the total number of days in the current coupon period.

For example, if a bond pays interest semi-annually with a 6% annual coupon and a face value of $1,000, and is traded 45 days into a 182-day coupon period:

Accrued Interest=$1,000×0.06×45182$14.84\text{Accrued Interest} = \$1,000 \times 0.06 \times \frac{45}{182} \approx \$14.84

This calculation demonstrates how a portion of the total semi-annual interest payment, based on the bond's characteristics and the time elapsed, is determined.

Interpreting Accrued Interest

Accrued interest ensures that the total payment for a bond reflects the precise amount of interest earned by the seller up to the point of sale. When a bond is quoted at a market price, this is usually the "clean price," which excludes accrued interest. The actual amount a buyer pays, known as the "dirty price" or "full price," includes both the clean price and the accrued interest. This distinction is vital because the clean price reflects the bond's fundamental value based on factors like prevailing interest rates and credit risk, while the dirty price represents the total cash exchanged at settlement. A clear understanding of accrued interest allows market participants to accurately compare bond valuations without the distortion caused by the time elapsed since the last coupon payment.

Hypothetical Example

Imagine an investor, Sarah, buys a corporate bond with a face value of $1,000, a 5% annual coupon rate paid semi-annually, on May 15th. The last coupon payment was on March 1st, and the next is due on September 1st.

  • Annual coupon payment = $1,000 * 0.05 = $50
  • Semi-annual coupon payment = $25
  • Days from last coupon (March 1st) to settlement date (May 15th) = 75 days (assuming Actual/Actual day count for simplicity)
  • Total days in the current coupon period (March 1st to September 1st) = 184 days

Using the accrued interest formula:
Accrued Interest = $1,000 * 0.05 * (75/184) = $20.38

If the bond's clean price is $980, Sarah will pay $980 (clean price) + $20.38 (accrued interest) = $1,000.38 (dirty price) to the seller. When the bond pays its full $25 coupon on September 1st, Sarah will receive the entire payment, effectively recouping the accrued interest she paid and receiving the interest earned during her holding period.

Practical Applications

Accrued interest is fundamental in various aspects of financial markets, especially in bond trading and valuation.

  • Bond Pricing: In the bond market, prices are typically quoted as "clean prices" to isolate the bond's market value from the steadily accumulating interest. However, the actual transaction price, or "dirty price," always includes accrued interest. This ensures that the seller is compensated for the portion of the current coupon period they held the bond.4
  • Treasury Auctions: When new Treasury bonds are issued through auctions, the settlement date often falls a few days after the auction date. The concept of accrued interest is relevant in determining the precise payment amount from successful bidders, as interest might start accruing from the issue date rather than the auction date. The U.S. Department of the Treasury provides details on how auctions work and results are announced, which implicitly factor in such calculations for settlement.3
  • Portfolio Valuation: For investors holding fixed-income portfolios, accurately accounting for accrued interest is essential for precise portfolio valuation and performance tracking. It represents a receivable asset that contributes to the portfolio's total return.
  • Regulatory Reporting: Financial regulatory bodies, such as the Financial Industry Regulatory Authority (FINRA) in the U.S., require accurate reporting of bond transactions, which includes the proper accounting for accrued interest to ensure transparency and compliance.2

Limitations and Criticisms

While accrued interest is a necessary component of bond transactions, its calculation can introduce complexities due to the variety of day count conventions. Different conventions (e.g., Actual/Actual, 30/360, Actual/360) are used across various bond markets and types of financial instruments, which can lead to slightly different accrued interest amounts for the same period. For instance, U.S. Treasury bonds typically use the Actual/Actual convention, while many corporate bonds may use 30/360. This lack of a universal standard means that practitioners must be vigilant about which convention applies to a particular security, as misapplying a convention can result in small but material discrepancies in pricing and settlement amounts. The varying definitions of a "month" or "year" under these conventions can make cross-market comparisons or complex calculations challenging without precise knowledge of the underlying rules for each instrument.1

Accrued Interest vs. Clean Price

Accrued interest and clean price are two distinct but related components that together determine the total cost of a bond.

  • Accrued interest is the portion of the next coupon payment that has been earned by the seller from the last payment date up to the trade's settlement date. It compensates the seller for the time they held the bond and earned interest, even though the next full coupon has not yet been paid. It is a time-based calculation.
  • Clean price is the quoted market price of a bond that excludes any accrued interest. It reflects the bond's inherent value based on factors like prevailing interest rates, the issuer's creditworthiness, and the time to maturity. The clean price is the component that fluctuates due to changes in market demand and supply, and it is used to calculate the bond's yield to maturity.

The confusion often arises because most bond markets quote bonds using their clean price, but the actual cash exchanged at settlement is the "dirty price," which equals the clean price plus accrued interest. The clean price gives a clearer picture of the bond's value independent of when it is traded within a coupon period, while accrued interest adjusts the cash flow to account for the passage of time.

FAQs

How often does accrued interest change?

Accrued interest changes daily as each day passes, increasing the amount of interest earned since the last coupon payment. On the coupon payment date, it resets to zero, and a new period of accrual begins.

Who pays and who receives accrued interest?

When a bond is traded between coupon payment dates, the buyer pays the accrued interest to the seller. This ensures the seller is compensated for the interest earned during their holding period. The buyer then receives the full upcoming coupon payment on its scheduled date.

Is accrued interest included in the bond yield?

Accrued interest is not directly included in the calculation of a bond's yield to maturity (YTM), which is based on the clean price and the bond's future cash flows discounted at a consistent discount rate. However, it impacts the total cash paid by the investor and received by the seller.

Does accrued interest apply to all fixed income securities?

Accrued interest is primarily applicable to fixed-income securities that pay periodic interest, such as bonds and notes. It generally does not apply to zero-coupon bonds, as these securities do not make periodic interest payments but instead are bought at a discount and mature at par value.

Why do bond prices not simply include accrued interest in their quotes?

Bond prices are typically quoted as "clean prices" (excluding accrued interest) to provide a more stable and comparable valuation of the bond's underlying value. If accrued interest were included in quoted prices, the price would constantly increase until the coupon payment date, then drop sharply, obscuring actual market movements and making capital gains and losses harder to discern.