Introduction

Day count conventions play a crucial role in determining the interest earned or paid on financial instruments, including bonds, loans, and derivatives. These conventions establish a standardized method for calculating the interest accrued over a specific period. In this chapter, we will delve into the most commonly used day count conventions, explore the markets in which each convention is typically employed, and provide practical examples of how to apply these conventions to interest calculations.

Common Day Count Conventions

Day count conventions define how the number of days between two interest payment dates is calculated. Some of the most widely used conventions include:

• Actual/Actual (Act/Act): This convention calculates the actual number of days in the interest period and the actual number of days in the year. It is commonly used in government bonds, corporate bonds, and mortgage-backed securities.

• Actual/360 (Act/360): Here, the actual number of days in the interest period is divided by 360, which is a typical denominator for a year. This convention is frequently used in money markets and short-term instruments.

• 30/360 (Bond Basis): This convention assumes each month has 30 days and each year has 360 days. The interest period is calculated based on these assumptions. It’s prevalent in the bond market and simplifies interest calculations.

Markets for Each Convention

The choice of day count convention depends on the specific financial instrument and the market it belongs to:

• Actual/Actual (Act/Act): This convention is popular in markets where precision is critical, such as government bond markets. It accurately reflects the number of days in both the interest period and the year.

• Actual/360 (Act/360): Money markets and instruments like commercial paper often employ this convention due to its simplicity, making it suitable for short-term calculations.

• 30/360 (Bond Basis): The bond market often uses this convention as it simplifies calculations for fixed-income securities. It’s a pragmatic approach for bonds with semi-annual or annual interest payments.

Application to Interest Calculation

Let’s apply each convention to a hypothetical scenario:

Consider a 5-year corporate bond with a 6% annual coupon rate. The bond pays interest semi-annually.

• Actual/Actual (Act/Act): Suppose we are calculating the interest accrued for the first semi-annual period. If the interest period spans from January 1 to June 30, and the bond has a face value of USD 1,000, the interest accrued using Act/Act would be: $Interest = 6\% \times 1,000 \times \frac{182}{365} = \text{USD 30.41}$

• Actual/360 (Act/360): Using the same scenario, the interest accrued for the first semi-annual period using Act/360 would be: $Interest = 6\% \times 1,000 \times \frac{182}{360} = \text{USD 30.33}$

• 30/360 (Bond Basis): Continuing with the example, the interest accrued for the first semi-annual period using 30/360 would be: $Interest = 6\% \times 1,000 \times \frac{180}{360} = \text{USD 30}$