Day Count Conventions
Understanding how interest is calculated: Actual/365 and other key conventions
What is a Day Count Convention?
A day count convention is the "language" or rule used to determine how interest accrues over time. It answers the question: "How do we measure a 'year' and a 'month'?"
This seems trivial, but the answer determines how accrued interest is calculated. Different bond markets use different rules, and using the wrong one will result in an incorrect price.
A day count convention is expressed as a fraction:
\[\frac{\text{Days in Month}}{\text{Days in Year}}\]Common Conventions
Here are the most important conventions you will encounter in fixed income:
| Convention | What It Means | Used For |
|---|---|---|
| Actual/365 (or Act/365F) |
|
Japanese Government Bonds (JGBs), JPY markets, Sterling (GBP) markets. |
| Actual/Actual (Act/Act) |
|
US Treasury Bonds, and many other government bond markets. |
| 30/360 |
|
US Corporate Bonds, Municipal Bonds, and many types of swaps. This is a simplification from pre-computer days. |
Why It Matters: JGBs (Act/365) vs. US Treasuries (Act/Act)
The difference between Act/365 and Act/Act lies in the denominator (how we measure the year), not the numerator. Let's see how this impacts daily accrual calculations for a 2% coupon bond with ¥100,000,000 face value over a semi-annual period.
1. JGB (Actual/365) - Fixed Denominator
For a semi-annual period of 184 actual days, the semi-annual coupon is ¥1,000,000.
\[\text{Daily Accrual} = \frac{¥1,000,000}{365 \div 2} = \frac{¥1,000,000}{182.5} = ¥5,479.45\]The denominator is always 365 ÷ 2 = 182.5 days, regardless of the actual length of the coupon period. This is simple and consistent.
2. US Treasury (Actual/Actual) - Variable Denominator
For the same period, the denominator uses the actual number of days in that specific coupon period.
\[\text{Daily Accrual} = \frac{¥1,000,000}{184} = ¥5,434.78\]The denominator changes based on the actual period length (181, 182, 183, or 184 days), making each period's daily accrual rate unique.
The JGB market's Act/365 convention simplifies calculations by using a fixed denominator. The US Treasury's Act/Act convention is more precise but results in different daily accrual rates for each coupon period. Understanding these conventions is essential for accurate bond pricing—we'll explore why accrued interest matters in later chapters.
When pricing a JGB, you *must* use the Actual/365 convention to match the market's standard for calculating accrued interest and correctly arriving at the dirty price.
📌 Important Note: JGB Repo Markets Use Different Conventions
While JGBs themselves use Actual/365 for bond pricing and accrued interest, the JGB repo market uses different day count conventions:
- International JGB repo transactions: Use Actual/360
- Domestic JGB repo transactions: Use Actual/365 Fixed
Key Takeaway: Always confirm which market you're working in. Bond pricing uses Act/365, but repo financing may use Act/360 depending on the counterparty and market convention.
Next Chapter
Congratulations on completing Chapter 1. You now have a solid foundation in the "what" and "why" of JGBs. In the next chapter, we will explore the "who" and "how" of the JGB market itself.
Next: Chapter 2 - The JGB Market Structure