Accrued interest
Bonds pay semi-annual interest to their bondholders. When an interest payment is due, the transfer agent makes a payment to whoever owns the issuer’s bonds on the interest payment date. They do not prorate their payments, which creates a problem.
Assume an interest payment is due on Friday, July 1st. If an investor purchases this bond on Monday, June 27th, they will receive interest for the past six months, even though they’ve only owned the bond for four days. Seems unfair, doesn’t it?
It would be unfair if it wasn’t worked out by the buyer and seller. When a bond trade occurs, the buyer pays the bond’s market price, plus accrued interest to the seller. To better understand this, let’s work through another example:
J&J 1 corporate bond trade occurs on Monday, April 10th
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J&J 1 = pays interest on January 1st and July 1st
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Trade will settle on Tuesday, April 11th (T+1)
The new owner (buyer) will receive interest for the previous six months on July 1st, even though they didn’t own the bond for the full six-month period. To resolve this issue, the buyer pays accrued interest to the seller. The accrued interest represents the time the seller held the bond during this interest payment period.
Specifically, the buyer owes the seller for the time they held the bond from the last interest payment date (January 1st), up to, but not including the settlement date of the trade (April 11th). They owe the seller interest for the months of January, February, and March. On the day the bond trade settles, the new owner starts accruing their own interest.
A testable point regarding accrued interest relates to how many days are counted while counting over months. Going back to our previous example, the bond trade settled on Tuesday, April 11th. Let’s focus on the two ways to count accrued interest:
30/360 method
- Used for corporate & municipal bonds
- Assumes 30 days in every month “counted over”
For example:
A J&J 1 corporate bond trade settles on Wednesday, April 12th. How many days of accrued interest does the buyer owe the seller?
Can you figure it out?
January: 30 days
February: 30 days
March: 30 days
April: 11 days
Overall accrued interest days: 101 days
With the 30/360 method, we always assume there are 30 days in the months we count over (even though there are not 30 days in January, February, or March). For the month the bond settles in, we count the specific days (up to, but not including the settlement date).
Actual/365 (a.k.a. actual/actual) method
- Used for US Government bonds
- Counts actual days in every month
For example:
A J&J 1 US Government bond trade settles on Wednesday, April 12th. How many days of accrued interest does the buyer owe the seller?
Can you figure it out?
January: 31 days
February: 28 days
March: 31 days
April: 11 days
Overall accrued interest days: 101 days
Although both methods produce the same amount of accrued interest days (101 days), this isn’t always the case. There can be some differences between two bonds settling on the same date with the same interest payment schedule, although the difference should be insignificant.
When July 1st comes around, the buyer will receive interest for the last six months. The difference between the interest received from the issuer and what they paid to the seller for accrued interest is the exact amount of interest they’re due.
With the actual/365 method, we always count the actual days in the months we count over. You’re probably wondering if you need to memorize the days in each month. Yes, you do. Most people utilize one of two ways to remember.
First, there’s the well-known verse:
Thirty days hath September,
April, June, and November,
All the rest have thirty-one.
February has twenty-eight,
but leap year coming one in four
February then has one day more.
Or, you can use something called the “knuckle method.” Here’s a link to a video describing this system.
The Series 7 could also take it a step further and ask how much accrued interest is owed. For example:
A $1,000 par, 5%, J&J 1 municipal bond trade occurs on Friday, September 15th. How much accrued interest does the buyer owe the seller?
Can you figure it out?
Answer: $10.69
The last interest payment date prior to September 15th was July 1st. We need to count from July 1st up to, but not including, the settlement of this trade. With a settlement timeframe of T+1, this trade will settle on Monday, September 18th. We must first calculate the number of days of accrued interest, knowing this is a 30/360 type of bond:
- July = 30 days
- August = 30 days
- September = 17 days
Total = 77 days
Next, we’ll calculate the amount of accrued interest due. This bond pays $50 a year in annual interest (5% of $1,000). The buyer must pay interest in the amount that equals 77 days of a 360-day year. Here’s the calculation:
Let’s try the same example, but with a US Government bond:
A $1,000 par, 5%, J&J 1 Treasury (US Government) bond trade occurs on Friday, September 15th. How much accrued interest does the buyer owe the seller?
How does it look different?
Answer: $10.82
The last interest payment date prior to September 15th was July 1st. We need to count from July 1st up to, but not including the settlement of this trade. With a settlement timeframe of T+1, this trade will settle on Monday, September 18th. We must first calculate the number of days of accrued interest, knowing this is an actual/365 type of bond:
- July = 31 days
- August = 31 days
- September = 17 days
Total = 79 days
Next, we’ll calculate the amount of accrued interest due. This bond pays $50 a year in annual interest (5% of $1,000). The buyer must pay interest in the amount that equals 79 days of a 365-day year. Here’s the calculation:
As you can see, both examples provided slightly different answers based on the different ways to approach the question. The key to getting the right answer is to remember settlement timeframes and how the bond accrues interest (30/360 or actual/365).
Most bonds trade with accrued interest, but not all of them. For example, if a bond settles on the interest payment date, no accrued interest is due. When a bond trade settles on the interest payment date, the seller will receive the interest for the past six months, and the buyer will begin to accrue interest for the next interest payment period.
Also, zero coupon bonds don’t pay semi-annual interest, so there is no accrued interest to be paid. These types of bonds trade flat, which means they trade without accrued interest.
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