ln04-day count conventions
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Day Count Conventions
Fixed Income Securities, Xiaohui Gao 1
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Why “Count” Differently?
Fixed Income Securities, Xiaohui Gao 2
In the capital markets, there are anumber of ways that days betweendates are computed for interest rate
calculations These conventions developed in
different markets in order to simplify
calculations (before the days of calculators and computers), but theyhave continued to persist
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Calculating Interest Earned
Fixed Income Securities, Xiaohui Gao 3
The day count convention is usually expressed as X / Y
When calculating the interest earned between twodates,
◦ X defines the way in which the number of days betweenthe two dates is calculated
◦ Y defines the way in which the total number of days in thereference period is measured
The interest earned between the two dates is
Number of days between dates Interest earned in reference periodNumber of days in reference period
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Five Basic Day CountConventions
Fixed Income Securities, Xiaohui Gao 4
Actual/360
Actual/365
Actual/Actual
30/360
30/360 European
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Actual/360
Fixed Income Securities, Xiaohui Gao 5
This calculates the actual number of days between two dates and assumesthe year has 360 days
Many calculations for money marketinstruments with less than a year tomaturity use this day count basis,
including Treasury bills
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Actual/360 – Example
Fixed Income Securities, Xiaohui Gao 6
What would the interest payment befor a $1 million six-month CD issuedon 01/31/04 and maturing on
07/31/04, and that has a 6% coupon?◦ Actual number of days between 01/31/04
and 07/31/04 = 182 days
◦
Interest = 0.06 × $1,000,000 × (182/360)= $30,333.33
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Actual/365
Fixed Income Securities, Xiaohui Gao 7
This calculates the actual number of days between two dates and assumesthe year has 365 days
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Actual/365 – Example
Fixed Income Securities, Xiaohui Gao 8
What would the interest payment befor the same $1 million six-month CDissued on 01/31/04 and maturing on
07/31/04, and that has a 6% coupon?◦ Actual number of days between 01/31/04
and 07/31/04 = 182 days
◦
Interest = 0.06 × $1,000,000 × (182/365)= $29,917.81
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Actual/Actual
Fixed Income Securities, Xiaohui Gao 9
This day count basis calculates the actualnumber of days between two dates andassumes the year has either 365 or 366days depending on whether the year is aleap year
◦ More precisely, if the range of the datecalculation includes February 29 (the leap day),the divisor is 366, otherwise it is 365
This day count basis is used for Treasurybonds
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30/360
Fixed Income Securities, Xiaohui Gao 11
This day count convention assumes that eachmonth has 30 days and the total number of days inthe year is 360◦ There are adjustments for February and months with 31
days
◦ Assume Date 1 is of the form M1/D1/Y1 and Date 2 is of the form M2/D2/Y2, with Date 2 being later than Date 1 If D1 = 31, change D1 to 30
If D2 = 31 and D1 = 30, change D2 to 30
Days between dates = (Y2 – Y1)×360 +(M2 – M1)×30 + (D2 –
D1) This day count basis is used for U.S. corporate and
municipal bonds
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30/360 – Example
Fixed Income Securities, Xiaohui Gao 12
What would the interest payment befor the same $1 million six-month CDissued on 01/31/04 and maturing on
07/31/04, and that has a 6% coupon?◦ Number of days between 01/31/04 and
07/31/04 = 0 + (6 × 30) + 0 = 180 days
◦
Interest = 0.06 × $1,000,000 × (180/360)= $30,000.00
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30/360 European
Fixed Income Securities, Xiaohui Gao 13
The 30/360 day count basis is differentoutside the United States, where thecalculation was further simplified
◦ Assume Date 1 is of the form M1/D1/Y1 andDate 2 is of the form M2/D2/Y2, with Date 2being later than Date 1 If D1 = 31, change D1 to 30
If D2 = 31, change D2 to 30
Days between dates = (Y2 – Y1)×360 +(M2 – M1)×30 +(D2 – D1)
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30/360 European – Example
Fixed Income Securities, Xiaohui Gao 14
What would the interest payment befor the same $1 million six-month CDissued on 01/31/04 and maturing on
07/31/04, and that has a 6% coupon?◦ Number of days between 01/31/04 and
07/31/04 = 0 + (6 × 30) + 0 = 180 days
◦
Interest = 0.06 × $1,000,000 × (180/360)= $30,000.00
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