An ACT/365 swap is a type of interest rate swap, which is a financial contract where two parties agree to exchange interest payments on a certain amount of money (called the principal) for a fixed period of time. One party pays a fixed interest rate, while the other pays a variable interest rate that changes according to a market benchmark (such as LIBOR).
The name ACT/365 comes from the way the interest payments are calculated. The fixed interest rate is applied to the actual number of days between each payment date, divided by 365. This means that the fixed interest payments are the same regardless of whether the payment dates fall on leap years or not. The variable interest rate is applied to the actual number of days between each payment date, divided by 360. This means that the variable interest payments are slightly higher than if they were calculated using 365 days.
The advantage of an ACT/365 swap is that it is easier to compare the fixed and variable interest rates, since they are both based on the same year length of 365 days. The disadvantage is that it does not reflect the actual number of days in a year, which can cause some discrepancies in the cash flows. For example, a 10-year swap that starts on January 1, 2024 and ends on January 1, 2034 will have 10.139 years of fixed interest payments, but only 10 years of variable interest payments. This means that the fixed interest payments will be slightly higher than the variable interest payments over the life of the swap.
Basic Theory:
In an ACT/365 swap, interest is calculated based on the actual number of days in a month and a year, with the year assumed to have 365 days. This contrasts with other day count conventions, such as 30/360, where a month is assumed to have 30 days, and a year has 360 days. The ACT/365 convention is considered more precise and is commonly used in financial markets.
Procedures:
The general procedure for calculating interest in an ACT/365 swap involves the following steps:
- Determine the Actual Days: Calculate the actual number of days between interest payment dates using the ACT/365 convention.
- Calculate the Interest: Use the formula:
Interest = (Principal * Rate * Actual Days) / 365
Scenario:
Suppose you have a notional amount of $1,000,000 in an ACT/365 interest rate swap with a fixed rate of 3%. The interest is paid semi-annually, and the actual days between payment dates are as follows:
- From January 1st to July 1st: 182 days
- From July 1st to January 1st of the next year: 184 days
Calculation in Excel:
- Create an Excel table with the following columns:
- Payment Date
- Actual Days
- Interest Calculation
- Enter the payment dates and actual days for each period.
- Use the following formula for each row in the “Interest Calculation” column:
= (Principal * Rate * Actual Days) / 365 - Sum up the interest calculations to get the total interest for the swap.
Results:
| Payment Date | Actual Days | Interest Calculation |
|---|---|---|
| July 1st | 182 | =($1,000,000 * 0.03 * 182)/365 |
| January 1st | 184 | =($1,000,000 * 0.03 * 184)/365 |
Total Interest = Sum of the “Interest Calculation” column
Other Approaches:
If you prefer a more automated approach, you can use the built-in Excel functions. For example, you can use the COUPDAYSACT function to calculate the actual days and then apply the interest formula:
=($1,000,000 * 0.03 * COUPDAYSACT(start_date, end_date))/365
This function directly calculates the actual days based on the ACT/365 convention.
