Day Count Conventions

These are the day count conventions available in TS, with how each one counts days and what else it is called. Six more conventions are not available in TS; they are listed at the end.

In the formulas and rules below, Date1 is the start date and Date2 the end date.

Quick reference

Conventions in TS

Act/Act ISDA

Also called: actual/actual, act/act, actual/actual (ISDA), actual/actual (Historical), ISDA actual/actual (Historical), actual/365, act/365

Counts the actual days and years, splitting the period into the part in a leap year and the part in a non-leap year. Days are counted as a Julian day difference: the first day of the period is included and the last day is excluded.

DayCountFactor = Days not in leap year / 365 + Days in leap year / 366

Example: 2019-12-31 to 2020-01-31 gives 1/365 + 30/366.

The coupon factor uses the same formula, with Date3 in place of Date2. Coupon payments vary from period to period, because the periods have different numbers of days. The formula applies to both regular and irregular coupon periods.

Act/Act ICMA

Also called: actual/actual (ICMA), act/act (ICMA), act/act ISMA, ISMA-99, ISMA Actual/Actual (Bond)

Counts the actual days and years according to the act/act ICMA convention.

DayCountFactor = Days(Date1, Date2) / (Freq × Days(Date1, Date3))

Freq is the number of coupon payments a year.

For regular coupon periods, where Date2 and Date3 are the same:

CouponFactor = Days(Date1, Date3) / (Freq × Days(Date1, Date3)) = 1 / Freq

This method makes every coupon payment the same amount. It also values all days in a coupon period equally, but the coupon periods themselves can differ in length. With semi-annual payments on a 365-day year, one period can be 182 days and the other 183. Each day in the first period is then worth 1/182 of the payment, and each day in the second 1/183.

For irregular coupon periods, the period is divided into one or more quasi-coupon periods (also called notional periods) that match the normal payment frequency. The interest for each such period, or part period, is calculated, and the amounts are added up.

For example, a broken first interest period from 2015-09-11 to 2016-02-29 has 171 days. Without the broken period, it would have been 182 days (2015-08-31 to 2016-02-29). The day count is then 171/364.

A fixing period of 1M does not work with the days in February. Fixing periods of 6M or 1Y work fine.

Act/365 F

Also called: actual/365 fixed, act/365 fixed, actual/365F, A/365 fixed, A/365F, English

Counts the actual days and always divides by 365. Each month is treated normally and the year is taken to be 365 days.

DayCountFactor = Days(Date1, Date2) / 365

Example: 1 February 2005 to 1 April 2005 gives 59/365.

The coupon factor uses the same formula, with Date3 in place of Date2. Coupon payments vary from period to period, because the periods have different numbers of days. The formula applies to both regular and irregular coupon periods.

Act/360

Also called: actual/360, A/360, French

Counts the actual days and always divides by 360. Each month is treated normally and the year is taken to be 360 days.

DayCountFactor = Days(Date1, Date2) / 360

Example: 1 February 2005 to 1 April 2005 gives 59/360.

The coupon factor uses the same formula, with Date3 in place of Date2. Coupon payments vary from period to period, because the periods have different numbers of days. The formula applies to both regular and irregular coupon periods.

30/360 ISDA Bond Basis

In TS: D30/360 ISDA Bond Basis

Also called: 30/360 ISDA, 30/360 U.S. Municipal, Bond basis

Counts days by the 30/360 ISDA convention. It works exactly like 30/360 US below, except for the first two rules. The order of the calculations matters:

1. D1 = MIN(D1, 30).
2. If D1 = 30, then D2 = MIN(D2, 30).

This gives the same result as ISDA's definition of 30/360 Bond Basis:

• If DAY1 is 31, set D1 to 30. Otherwise set D1 to DAY1.
• If DAY2 is 31 and DAY1 is 30 or 31, set D2 to 30. Otherwise set D2 to DAY2.

At month end, accrued interest is calculated as 28 days for February if you run month end on 28 February, and as 30 days if you run it on 30 April, 30 June, 30 September or 30 November. If you run month end on the last day of a 31-day month, that month is calculated as 31 days.

30E/360 Eurobond

In TS: D30E/360 Eurobond

Also called: 30E/360, 30/360 ISMA, 30/360 European, 30S/360 Special German, Eurobond Basis, Special German

Counts days by the 30E/360 convention, often called Eurobond Basis, as included in ISDA 2006:

1. If D1 is 31, change D1 to 30.
2. If D2 is 31, change D2 to 30.

This is the same as 30/360 TRUE in Excel.

At month end, accrued interest is calculated as 28 days for February if you run month end on 28 February. Every other month is calculated as 30 days.

30/360 US

In TS: D30/360 US

Also called: 30/360 US, 30U/360, 30US/360, US/NASD method

Counts days by the 30/360 US convention. Apply these date rules in order. More than one can apply, and a date changed by one rule is used in the rules after it:

1. If Date1 is the last day of February and Date2 is the last day of February, change D2 to 30.
2. If Date1 is the last day of February, change D1 to 30.
3. If D2 is 31 and D1 is 30 or 31, change D2 to 30.
4. If D1 is 31, change D1 to 30.

This convention is used for US corporate bonds and many US agency issues. It is usually just called "30/360", though "30/360" can also mean any of the other conventions in this group, depending on the context.

At month end, accrued interest is calculated as 30 days for February if you run month end on 28 February, and as 30 days if you run it on 30 April, 30 June, 30 September or 30 November. If you run month end on the last day of a 31-day month, that month is calculated as 31 days.

30E/360 ISDA

In TS: D30E/360 ISDA

Also called: 30/360E ISDA, 30E/360 (2000, outdated), 360/360, Eurobond Basis (2000, outdated), German Master

Counts days by the 30E/360 ISDA convention, the Eurobond Basis from before 2000:

• If DAY1 is 31, or the last day of February, set D1 to 30. Otherwise set D1 to DAY1.
• If DAY2 is 31, or the last day of February but not the termination date, set D2 to 30. Otherwise set D2 to DAY2.

TS does not currently make any adjustment for the termination date.

At month end, accrued interest is calculated as if every month has 30 days. For example, if you run month end on 28 February, February is counted as 30 days. Months with 31 days are treated the same way: if you run month end on 31 July, every month since the last payment date is counted as 30 days.

Not available in TS

These conventions are not available in TS. They are very rare in the Nordics, and we don't know of any customers who have used them.

30E+/360

Also called: 30E+/360, 30Eplus/360 ISMA

Counts days by the 30E+/360 convention:

1. If D1 is 31, change D1 to 30.
2. If D2 is 31, change D2 to 1 and M2 to M2 + 1.

Act/Act Euro

Also called: actual/actual (Euro), actual/actual (AFB), actual/365 (actual)

Counts the actual days and years according to the Euro convention, which uses a set of rules to find the days in the year (DiY). The basic rule: if 29 February falls between Date1 (included) and Date2 (excluded), DiY is 366; otherwise it is 365.

If the period from Date1 to Date2 is more than a year, the calculation is split in two:

• the number of complete years, counted back from the last day of the period
• the remaining stub at the start, calculated with the basic rule

For example, a period from 1994-02-10 to 1997-06-30 is split into:

• 1994-06-30 to 1997-06-30: 3 whole years, counted back from the end
• 1994-02-10 to 1994-06-30: 140/365

The result is 3 + 140/365.

This convention was first written in French. In translation, "Période d'Application" became "Calculation Period", and because ISDA gives "Calculation Period" a specific meaning (Date1 to Date3), this can cause confusion. In the original French, the period is Date1 to Date2, not Date1 to Date3.

Act/365 A

Also called: actual/365A

Counts the actual days and divides by 365, or by 366 if the period includes a leap day.

Act/365 L

Also called: actual/365 leap, actual/365L, Actual/Actual AFB/FBF Master Agreement, AFB Actual/Actual (Euro)

Counts the actual days and divides by 365, or by 366 if the period includes a year with a leap day.

NL/365

Also called: actual/365 no leap, actual/365NL

Counts the actual days minus any leap days, and always divides by 365.

30/360 German

Also called: 30/360 German, 30E/360 ISDA, German

Counts days by the 30/360 German convention.

Further reading

• Day count convention (Wikipedia)