## ACT ACT(ICMA)

Subtype of Name

The ISMA and US Treasury convention, also known as Actual/Actual Bond and Actual/Actual ISMA
Note this convention requires the knowledge of a pair of reference dates beyond the start and end of the accrual period, which - in the bond case - correspond to the start and end of the respective coupon period.
It also leads to fixed coupon amounts for full accrual periods, even when the corresponding number of days are not constant.
Let [T₁,T₂) be the period between two dates T₁ and T₂, of which the length L in annual units must be calculated
Calculation rule:
Let N be the number of days of [T₁,T₂), with T₁ included and T₂ excluded.
Let [T₁',T₂') be the reference period, as defined by two additional optional dates T₁' and T₂' that by default (if omitted) equal the dates T₁ and T₂
Let N' be the number of days of [T₁',T₂'), with T₁' included and T₂' excluded.
Let f be frequency (coupons per year in the bond case) found by rounding the fraction 12N'/365 to the closest integer.
Then:
L = N/(fN')
Special cases:
Case 1:
In a context of a given schedule of consecutive accrual periods such as that of a bond or swap, the dates T₁', T₂' are implied by that schedule.
If the period [T₁,T₂) represents a front stub period of that schedule, the date T₁' is not part of the given schedule, but is nominally calculated by subtracting the regular schedule's period from T₂
If the period [T₁,T₂) represents a back stub period of that schedule, the date T₂' is not part of the given schedule, but is nominally calculated by adding the regular schedule's period to T₁
Case 2:
In a context where no coupon periods exist, the applicable algorithm may define some ad hoc period that often equals one year.
This is for example the case in the yield calculation of a single future bullet cash flow, such that paid at maturity of a zero bond.