4.2.5 Accrued Interest and Settlement
In the world of bonds and fixedincome securities, understanding the concepts of accrued interest and settlement is crucial for both investors and financial professionals. This section delves into these concepts, explaining how they affect bond transactions and the importance of accurate calculations to ensure fair dealings in the market.
Understanding Accrued Interest
Accrued interest is the interest that has accumulated on a bond since the last coupon payment but has not yet been paid to the bondholder. When a bond is sold between coupon payment dates, the buyer compensates the seller for the interest earned up to the sale date. This ensures that the seller receives a fair return for the period they held the bond.
Calculation of Accrued Interest
Accrued interest is calculated using the following formula:
$$ \text{Accrued Interest} = \frac{\text{Coupon Payment} \times \text{Number of Days Accrued}}{\text{Number of Days in Coupon Period}} $$
The number of days accrued is the number of days from the last coupon payment date to the settlement date of the bond transaction.
Example Calculation
Consider a bond with a semiannual coupon payment of $50, a last coupon payment date on January 1, and a settlement date on March 1. Assuming a 30/360 daycount convention, the accrued interest would be calculated as follows:
$$ \text{Accrued Interest} = \frac{50 \times 60}{180} = \frac{3000}{180} = 16.67 $$
Thus, the buyer would pay the seller an additional $16.67 as accrued interest.
Clean Price vs. Dirty Price
When discussing bond prices, it’s essential to differentiate between the clean price and the dirty price.

Clean Price: This is the price of the bond excluding any accrued interest. It represents the bond’s value based solely on its coupon payments and principal repayment.

Dirty Price (Full Price): This is the clean price plus the accrued interest. It reflects the total amount the buyer pays to the seller, including compensation for the interest accrued since the last coupon payment.
Importance of Price Distinction
Understanding the distinction between clean and dirty prices is vital for investors to accurately assess the cost of purchasing a bond and the return on investment. The dirty price is typically used in bond transactions to ensure that sellers are compensated for the interest earned during their holding period.
Settlement Conventions
Settlement refers to the process of transferring ownership of the bond from the seller to the buyer. Standard settlement conventions ensure that transactions are completed efficiently and accurately.
Standard Settlement Periods
In most bond markets, the standard settlement period is T+2, meaning the transaction is settled two business days after the trade date. This period allows for the necessary administrative processes to be completed, ensuring a smooth transfer of ownership.
DayCount Conventions
Daycount conventions are used to calculate the number of days accrued for interest calculations. Common conventions include:
 Actual/Actual: Counts the actual number of days in the interest period and the actual number of days in the year.
 30/360: Assumes each month has 30 days and a year has 360 days, simplifying calculations.
The choice of daycount convention can affect the accrued interest calculation and, consequently, the dirty price of the bond.
Example of Settlement and Accrued Interest Calculation
Let’s illustrate the process with a comprehensive example:

Bond Details:
 Face Value: $1,000
 Annual Coupon Rate: 5%
 Coupon Payment Frequency: Semiannual
 Last Coupon Payment Date: April 1
 Settlement Date: June 15
 DayCount Convention: 30/360

Calculate Accrued Interest:
 Coupon Payment = $1,000 × 5% / 2 = $25
 Days Accrued = 75 (April 1 to June 15 using 30/360)
 Accrued Interest = $25 × 75 / 180 = $10.42

Determine Prices:
 Assume Clean Price = $980
 Dirty Price = Clean Price + Accrued Interest = $980 + $10.42 = $990.42
In this example, the buyer would pay $990.42 to the seller, which includes the clean price of the bond and the accrued interest.
Importance of Understanding Settlement Procedures
Accurate calculation of accrued interest and understanding settlement conventions are essential for ensuring fair transactions in the bond market. Misunderstandings or errors in these calculations can lead to disputes or financial losses for either party involved in the transaction.
By mastering these concepts, investors and financial professionals can make informed decisions, optimize their investment strategies, and contribute to the efficient functioning of the bond market.
Quiz Time!
📚✨ Quiz Time! ✨📚
### What is accrued interest?
 [x] Interest earned since the last coupon payment but not yet received
 [ ] The interest paid on the settlement date
 [ ] The difference between the clean price and the dirty price
 [ ] The total interest paid over the life of the bond
> **Explanation:** Accrued interest is the interest that has accumulated since the last coupon payment but has not yet been paid to the bondholder.
### How is the clean price of a bond defined?
 [x] The price of the bond excluding accrued interest
 [ ] The price of the bond including accrued interest
 [ ] The price of the bond at maturity
 [ ] The price of the bond after taxes
> **Explanation:** The clean price is the price of the bond excluding any accrued interest, reflecting its value based on coupon payments and principal repayment.
### What is the standard settlement period for most bond markets?
 [x] T+2
 [ ] T+1
 [ ] T+3
 [ ] T+5
> **Explanation:** The standard settlement period for most bond markets is T+2, meaning the transaction is settled two business days after the trade date.
### Which daycount convention assumes each month has 30 days?
 [x] 30/360
 [ ] Actual/Actual
 [ ] 30/365
 [ ] Actual/360
> **Explanation:** The 30/360 daycount convention assumes each month has 30 days and a year has 360 days, simplifying interest calculations.
### What is the dirty price of a bond?
 [x] The clean price plus accrued interest
 [ ] The clean price minus accrued interest
 [x] The total amount paid by the buyer
 [ ] The price at which the bond was issued
> **Explanation:** The dirty price is the clean price plus accrued interest, representing the total amount the buyer pays to the seller.
### Why is understanding settlement procedures important?
 [x] To ensure fair transactions and prevent settlement errors
 [ ] To calculate the bond's yield
 [ ] To determine the bond's maturity date
 [ ] To assess the bond's credit risk
> **Explanation:** Understanding settlement procedures is crucial for ensuring fair transactions and preventing errors that could lead to financial losses.
### How is accrued interest calculated?
 [x] Using the coupon payment, number of days accrued, and number of days in the coupon period
 [ ] Using the bond's maturity date and yield
 [x] Using the bond's face value and coupon rate
 [ ] Using the bond's credit rating
> **Explanation:** Accrued interest is calculated using the coupon payment, number of days accrued, and number of days in the coupon period.
### What does T+2 settlement mean?
 [x] The transaction is settled two business days after the trade date
 [ ] The transaction is settled on the trade date
 [ ] The transaction is settled two weeks after the trade date
 [ ] The transaction is settled two months after the trade date
> **Explanation:** T+2 settlement means the transaction is settled two business days after the trade date.
### What is the purpose of the daycount convention?
 [x] To calculate the number of days accrued for interest calculations
 [ ] To determine the bond's maturity date
 [ ] To assess the bond's credit risk
 [ ] To calculate the bond's yield
> **Explanation:** The daycount convention is used to calculate the number of days accrued for interest calculations, affecting the accrued interest and dirty price.
### True or False: The clean price includes accrued interest.
 [ ] True
 [x] False
> **Explanation:** False. The clean price does not include accrued interest; it is the price of the bond excluding any accrued interest.