Definition — what a day-count convention is
A day-count convention is a rule that standardizes how you count days between two dates when calculating interest, accrued interest, or discount factors. The convention defines (1) how many days are considered to have passed between two calendar dates and (2) the denominator used to turn that count into a fraction of a year. That fraction determines the money owed for the period.
Why it matters
Different conventions give different day-count fractions for the same two dates. That changes:
– accrued interest due on bond trades,
– cash flows and present value (PV) calculations in swaps and loans,
– rate calculations for money-market instruments.
Common conventions (short definitions)
– Actual/Actual (actual/actual): Use the true number of calendar days in the period and the actual length of the year (often the actual number of days in the coupon period or year). Common for U.S. Treasury securities.
– Actual/360: Use the real count of days between dates but divide by 360. Widely used for money-market deposits and many floating-rate notes.
– Actual/365: Count actual days and divide by 365. Used for some currencies (notably British pound denominated instruments).
– 30/360: Assume every month has 30 days and each year has 360 days. Common for many fixed-rate bonds and the fixed leg of swaps.
– 30/365: Like 30/360 but the year denominator is 365; used for some markets (e.g., GBP and JPY swaps).
Where each is typically used (practical guide)
– U.S. Treasury bonds and notes: actual/actual.
– Most money-market deposits and many floating-rate notes: actual/360 (exception: GBP instruments use actual/365).
– Fixed-rate leg of many swaps and fixed-rate bonds: 30/360 or 30/365 depending on currency/market.
– Floating leg of swaps: often actual/360 if fixed leg is 30/360; actual/365 where fixed leg uses 30/365.
Step-by-step checklist when you encounter a contract or trade
1. Identify the instrument (bond, swap, deposit, loan).
2. Check the contract or market convention for the day-count convention.
3. Confirm coupon/payment frequency and whether rates are fixed or floating.
4. Determine the exact start and end dates for the accrual period.
5. Apply the convention’s rule for counting days between those dates.
6. Compute the day-count fraction = (counted days) / (denominator as specified).
7. Calculate interest or accrued interest = principal × nominal annual rate × day-count fraction.
8. Document assumptions (leap-year treatment, business-day adjustments) and save the source of the chosen convention.
Worked numeric example
Scenario: You hold a bond with face value 1,000, annual coupon rate 6% (paid annually or as an annualized rate). You need accrued interest from Jan 1 to Mar 1 in a non-leap year (Jan 1 → Mar 1).
Basic formula:
Accrued interest = Principal × Annual coupon rate × (day-count fraction)
Compute days between dates:
– Actual days: Jan (31) + Feb (28) = 59 days.
a) Using actual/365:
Day-count fraction = 59 / 365
Accrued interest = 1,000 × 0.06 × (59 / 365) = 60 × 0.16164 ≈ $9.70
b) Using actual/360:
Day-count fraction = 59 / 360
Accrued interest = 60 × (59 / 360) ≈ 60 × 0.16389 ≈ $9.83
c) Using 30/360 (every month assumed 30 days):
Counted days = 30 (Jan) + 30 (Feb) = 60
Day-count fraction = 60 / 360 =
= 60 / 360 = 1/6 ≈ 0.1666667
Accrued interest = 1,000 × 0.06 × 0.1666667 = 60 × 0.1666667 = $10.00
Quick comparison (same inputs):
– Actual/365 → ≈ $9.70
– Actual/360 → ≈ $9.83
– 30/360 → $10.00
Why the results differ
– Actual/365 and actual/360 use the true day count between the two dates but divide by different denominators (365 vs 360), so actual/360 gives a slightly larger fraction and therefore more accrued interest.
– 30/360 forces each month to be 30 days. In this example Jan+Feb count as 60 days (vs 59 actual), so the 30/360 convention produces the largest accrual.
Practical checklist — how to know which convention to use
1. Read the bond prospectus, indenture or trade confirmation — the day-count convention is usually specified there.
2. Follow market convention for the instrument:
– U.S. Treasury securities: typically actual/actual (ACT/ACT).
– Money-market, commercial paper, many bank loans: often actual/360.
– Many corporate and municipal bonds: often 30/360 (but check documentation).
3. Watch for variants: e.g., ACT/365 vs ACT/365L (le