## What is Flat Bond?

Flat bond is a term given to the price of a bond when it does not include any accrued interest. Accrued interest is the portion of a bond's coupon payment that the holder earns in between scheduled coupon payments.

A flat bond's price is referred to as its clean price.

### Key Takeaways

- A flat bond is one that does not account for accrued interest owed to the bondholder.
- Flat bond prices are typically quoted in American markets, while the full price is more common in European markets.
- A bond can also be quoted as a flat bond if no interest is presently due, if it is in default, or if it settles on the same date as the interest payment date.

## Understanding Flat Bonds

Some bonds pay interest to bondholders periodically, known as its coupon payment. When prices of interest-bearing instruments are quoted, they are either quoted at a full price or flat price to reflect those interest payments. A bond that is quoted with a flat price is referred to as a flat bond. A flat price does not include any accrued interest. Since accrued interest on a bond does not change the yield-to-maturity (YTM), the flat bond price is typically quoted to avoid misleading investors on the daily increase in the full price as a result of interest accrued.

A full price, also known as a dirty price, includes the interest accrued owed to a bondholder since the last coupon payment, and is considered in the price of the bond. When an investor sells a bond sometime between the last coupon payment and the next coupon payment, they do so with interest accrued.

For example, if interest payments on a bond are scheduled for February 1 and August 1 every year until the bond matures, and the bondholder sells the bond on April 15, the bond will have accrued interest from February 1 to April 15. The seller gives up the interest from the time of the last coupon payment to the time until the bond is sold.

The price of a flat bond is calculated as:

Flat Price = Full(Dirty) Price – Accrued Interest

where:

Accrued Interest = Coupon Payment for the Period * (Time Held After the Last Coupon Payment / Coupon Period)

## When to Quote Flat Bonds

There are three typical reasons that a bond would trade flat, that is, not have any accrued interest attached to it:

- No interest is presently due on the bond according to the date of sale and terms of the bond's issue
- The bond is in default. Bonds that are in default are to be traded flat without calculation of accrued interest and with delivery of the coupons which have not been paid by the issuers.
- The bond settlement date is the same date as the interest is paid and, therefore, no additional interest has accrued beyond the amount already paid out

Note that the coupon period is the number of days between each coupon payment date. Corporate and municipal bond issuers assume a 30-day month and a 360-day calendar to calculate the accrued interest on a bond. However, the accrued interest on government bonds is usually determined on the basis of the actual calendar day from its date of issuance (called the actual/actual day count).

## Example: Flat Bond Calculation

Say the coupon rate on a $1,000 par value bond that pays interest semi-annually on February 1 and August 1 each year is 5%. The bondholder sells the bond on April 15 in the secondary market for a full price of $995.

The steps to calculate the flat bond price are as follows:

- Coupon payment per period = 5% ÷ 2 * $1,000 = $25
- Stated coupon period --- assume a 30-day month and a 360-day calendar. Using our example, the coupon payment per period is 6 months * 30 days = 180 days.
- Number of days the bond was held after the last coupon payment before selling = 2.5 months * 30 days = 75 days.
- Accrued Interest = $25 * (75 ÷180) = $10.42
- Price of Flat Bond = $995 - $10.42 = $984.58