## What is a Flat Bond

A flat bond is a debt instrument that is sold or traded without accrued interest. Accrued interest is the fraction of the bond's coupon payment that the holder earns between periods of bond payments.

## BREAKING DOWN Flat Bond

Some bonds pay interest to bondholders periodically. When the prices of interest-bearing instruments are quoted, they are either quoted at a full price or flat price. A full price is also referred to as a dirty price and means that the interest accrued since the last coupon payment is included in the price of the bond. When an investor sells a bond sometime between the last coupon payment and the next coupon payment, s/he does so with interest accrued. For example, if interest payments on a bond is 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.

## Price of a Flat Bond

Since accrued interest on a bond does not change the yield-to-maturity, the flat price is typically quoted to avoid misleading investors on the daily increase in the full price as a result of interest accrued. A bond that is quoted with a flat price is referred to as a flat bond. Also referred to as a clean price, a flat price does not include any accrued interest. The price of a flat bond is calculated as:

Flat Price = Full (or Dirty) Price – Accrued Interest

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

The coupon period is the number of days between each coupon payment dates. 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 date of issuance (called the actual/actual day count).

## How to Calculate the Flat Price

Let’s look at an example. 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.

Coupon payment per period = 5%/2 x $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 x 30 days = 180 days.

Number of days the bond was held after the last coupon payment before selling = 2.5 months x 30 days = 75 days.

Accrued Interest = $25 x (75/180) = $10.42

Price of Flat Bond = $995 - $10.42 = $984.58

## Reasons Why Bonds Trade Flat

There are three possible reasons that a bond would trade flat, that is, not have any accrued interest:

- 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 settles on the same date as the interest is paid and, therefore, no additional interest has accrued beyond the amount already paid out