List of Day Count Conventions

Q

Where can I find a list of commonly used day count conventions?

✍: FYIcenter.com

A

Here is a list of commonly used Day Count Conventions and their rules to calculate DiR(), and DiY() functions as defined in previous tutorials.

30/360 (30U/360, 30US/360, 30/360 US, 30/360SIA) - Mainly used by US agency/corporate bonds.

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    If T1 is End of Month, set D1 = 30,
    If T2 is End of Month and D1 = 30, set D2 = 30,

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30/360 US (NASD)

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    D1 = min(D1,30), 
    If D2 = 31, 
      If D1 < 30, set T2 = T2 + 1 day 
      Otherwise, set D2 = 30  

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30A/360 (30/360 Bond, 30/360 ISDA) - Mainly used by US municipal bonds.

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    D1 = min(D1,30), 
    If D1 = 30, set D2 = min(D2,30).

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30E/360 (30S/360, 30/360 European, 30/360 ICMA, 30/360 ISMA)

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    D1 = min(D1,30),
    D2 = min(D2,30).

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30E/360 ISDA (30/360 German)

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    If T1 is End of Month, set D1 = 30, 
    If T2 is End of Month, 
      unless it's End of February and the Maturity Date, set D2 = 30.

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30E+/360 Not widely used.

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    D1 = min(D1,30), 
    If D2 = 31, set T2 = T2 + 1 day, 

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30IT/360 US

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
  where D1 and D2 are adjusted sequentially as below:
    If M1 = 2 and D1 > 27, set D1 = 30, 

DiY(Y1, M1, D1, Y2, M2, D2) = 360

30/365

Day_Count_Factor(Y1,M1,D1,Y2,M2,D2)
   = DiR(Y1,M1,D1,Y2,M2,D2) / DiY(Y1,M1,D1,Y2,M2,D2)

DiR(Y1, M1, D1, Y2, M2, D2) = 360×(Y2-Y1) + 30×(M2-M1) + (D2-D1)
DiY(Y1, M1, D1, Y2, M2, D2) = 360

Act/360 - This convention follows the concept of a year has 12 months with 30 days in each month. DiY() is fixed to 360, 5 to 6 days less than days in a calendar year. So you are getting 5 to 6 days extra interest in a calendar year.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 360

Act/364 - This convention follows the concept of a year has 52 weeks with 7 days in each week. DiY() is fixed to 364, pretty close to 365/365 days in a calendar year.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 364

Act/365 (Act/365F, Act/365 Fixed) - Mainly used by banks in US for their savings and CD (Certificate Deposit) accounts. This convention fixes FiY() to 365, so it is easier to calculate. It is very accurate for regular years, and less accurate for leap years.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 360

Act/365A

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 
  366, if a leap day is in [T1,T2)
  365, otherwise

Act/365CA - Mainly used by Canadian bonds.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 
  366, if a leap day is in [T1,T2)
  365, otherwise

Act/365L

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = 
  366, if Frequency=1 and the accrual range has a leap day
  366, else if Frequency>1 and (Y2,M2,D2) is in the leap year
  365, otherwise

Act/Act (Act/Act ISDA) - This convention tries to follow the calendar accurately.

                          Days_in_Regular_Year   Days_in_Leap_Year
Day_Count_Factor(T1,T2) = -------------------- + -----------------
                                   365                  366 
Or: 
  Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
  DiR(T1,T2) = 366×Days_in_Regular_Year + 365×Days_in_Leap_Year
  DiY(T1,T2) = 365×366

Act/Act AFB (Act/Act Euro)

Day_Count_Factor(T1,T2) = Full_Years + Partial_Year_Factor
  Full_Years are counted backward

Partial_Year_Factor = Days_in_Partial_Range/Days_in_Year 
Days_in_Partial_Range = Calendar days in the partial range 
Days_in_Year = 
  366, if a leap day is in the partial range 
  365, otherwise

Act/Act Bond (Act/Act ICMA, Act/Act ISMA) - Mainly used by US treasury bonds. This convention ensures that every accrual period generates the same amount of interest. And every day generates the same amount of interest in the same accrual period.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2)
DiY(T1,T2) = Accrual_Frequency × Calendar_Days(T1,T3)

Bus/252BR (Act/252, ActW/252, BD/252, BU/252) - Mainly used in Brazil.

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = # of business days in the range in Brazilian calendar
DiY(T1,T2) = 252

NL/365

Day_Count_Factor(T1,T2) = DiR(T1,T2) / DiY(T1,T2)
DiR(T1,T2) = Calendar_Days(T1,T2) - Leap_Days
DiY(Y1, M1, D1, Y2, M2, D2) = 365

Related abbreviations

ICMA - International Capital Market Association.
IPMA - International Primary Market Association.
ISDA - International Swaps and Derivatives Association.
ISMA - International Securities Market Association. Formed after the merger of ICMA and IPMA.

References: