Day Count Convention

A day count convention is a rule for turning a period of time into a fraction of a year for the purpose of calculating interest. Every interest-bearing instrument, whether a bond, a loan, a deposit or a swap, quotes an annual rate, but interest is paid for periods shorter or longer than a year. The convention says how many days are treated as falling in the period and how many in the year, and the ratio of the two, the day count fraction, is multiplied by the rate and the principal to give the amount due.

Different markets settled on different conventions long before computers, some favouring simple arithmetic and others exact calendars, and the differences have persisted. The convention is stated in the terms of each instrument and stored in its instrument reference data. It works together with the business day convention, which moves dates that fall on non-working days.

The general calculation is:

• $P$ is the principal or nominal amount.
• $r$ is the annual interest rate, written as a decimal.
• $D$ is the number of days in the interest period, counted as the convention directs.
• $B$ is the day count basis, the number of days the convention assigns to a year.

Take 1,000,000 at 6% for the period from 1 March to 1 September. The actual number of days is 184. Under a 30/360 convention each month counts as 30 days, giving 180 days, and interest is $1{,}000{,}000 \times 0.06 \times 180 \div 360 = 30{,}000$. Under Actual/360 it is $1{,}000{,}000 \times 0.06 \times 184 \div 360 \approx 30{,}666.67$. Under Actual/365 it is $1{,}000{,}000 \times 0.06 \times 184 \div 365 \approx 30{,}246.58$. The same rate therefore produces three different payments.

• 30/360. Every month is treated as 30 days and the year as 360. Variants differ in how they handle the 31st of a month and the end of February. The United States version, often called the bond basis, is usual for US corporate, agency and municipal bonds; a European version, 30E/360, appears in older issues in the Eurobond market.
• Actual/360. The real number of days is divided by 360. This is the standard for money markets in US dollars and euros, for most floating-rate instruments and for rates such as SOFR. Because a full year contains 365 days, the borrower pays slightly more than the quoted rate over twelve months.
• Actual/365 Fixed. The real number of days is divided by 365, even in a leap year. It is used in sterling money markets and in several other currencies.
• Actual/Actual (ICMA). The real number of days in the period is divided by the real number of days in the full coupon period, multiplied by the number of coupons a year. Each regular coupon is therefore exactly equal. It is used for US Treasury notes and bonds and for most European government bonds, including UK gilts.
• Actual/Actual (ISDA). Days falling in a leap year are divided by 366 and the rest by 365. It is found mainly in swap documentation.

The convention determines each coupon payment where periods are irregular, and it always determines bond accrued interest, the amount a buyer pays the seller for interest earned since the last coupon date. Two bonds with the same coupon and dates but different conventions will have different accrued amounts on most days of the year.

In an interest rate swap the two legs commonly use different conventions, for example 30/360 on the fixed leg and Actual/360 on the floating leg, and the difference must be allowed for when rates are compared. Loan agreements state the convention in their interest clause; syndicated loans in most currencies use Actual/360, with Actual/365 for sterling. Yield calculations such as yield to maturity also depend on the day count used to discount each cash flow, so yields quoted on different bases are not directly comparable without conversion.

A wrong day count in a system produces small but persistent errors: payments that do not agree with the paying agent's figures, breaks in reconciliations and mispriced trades. Operations and data teams therefore check the convention against the offering document when a security is set up, along with the coupon schedule, any stub periods and the rule for month-end dates. Particular care is needed around February, at the end of months with 31 days and for a floating rate note whose periods change with each adjustment for holidays.

Convention names are not fully standardised. The same rule may be written as Actual/365 Fixed, A/365F or Act/365, and the label 30/360 covers several slightly different methods. Standard definitions are published by the International Capital Market Association (ICMA) for bonds and by the International Swaps and Derivatives Association (ISDA) for derivatives, and those legal definitions, not the short names, decide the calculation in a dispute.

• International Capital Market Association
• International Swaps and Derivatives Association