Everything about Day Count Convention totally explained
In finance, a
day count convention determines how interest accrues over time for a variety of investments, including bonds, notes, loans, medium-term notes, swaps, and FRAs. This includes the amount transferred on interest payment dates, but also the calculation of
accrued interest for dates between payments. When a security such as a bond is sold between interest payment dates, the seller is eligible to some fraction of the coupon amount.
It is used in many other formulae in
financial mathematics as well.
Development
The need for day count conventions is a direct consequence of interest-earning investments. Different conventions were developed to address often conflicting requirements: ease of calculation, constancy of time period (day, month, or year), the needs of the Accounting department, and many others. This development occurred long before the advent of computers.
There is no central authority defining day count conventions, so there's no standard terminology. Certain terms, such as "30/360", "Actual/Actual", and "money market basis" must be understood in the context of the particular market.
The conventions have evolved, and this is particularly true since the mid-1990s. Part of it has simply been providing for additional cases or clarification.
There has also been a move towards convergence in the marketplace, which has resulted in the number of conventions in use being reduced. Much of this has been driven by the introduction of the euro.
Definitions
Interest: Amount of interest accrued on an investment.
; CouponFactor: The Factor to be used when determining the amount of interest paid by the issuer on coupon payment dates. The periods may be regular or irregular.
CouponRate: The interest rate on the security or loan-type agreement, for example, 5.25%. In the formulas this would be expressed as 0.0525.
; Date1 (Y1.M1.D1): Starting date for the accrual. It is usually the coupon payment date preceding Date2.
Date2 (Y2.M2.D2): Date through which interest is being accrued. You could word this as the "to" date, with Date1 as the "from" date. For a bond trade, it's the settlement date of the trade.
; Date3 (Y3.M3.D3): The coupon payment date following Date2.
Days(StartDate, EndDate): Function returning the number of days between StartDate and EndDate on a Julian basis (for example, all days are counted). For instance, Days(15 October 2007, 15 November 2007) returns 31.
; EOM: Indicates that the investment always pays interest on the last day of the month. If the investment isn't EOM, it'll always pay on the same day of the month (for example, the 10th).
Factor: Figure representing the amount of the CouponRate to apply in calculating Interest. It is often expressed as "days in the accrual period / days in the year". If Date2 is a coupon payment date, Factor is zero.
; Freq: The coupon payment frequency. 1 = annual, 2 = semi-annual, 4 = quarterly, 12 = monthly, etc.
Principal: Par value of the investment.
For all conventions, the Interest is calculated as:
»
30/360 methods
All conventions of this class calculate the Factor as:
»
The CouponFactor uses the same formula, replacing Date2 by Date3. In general, coupon payments will vary from period to period, due to the differing number of days in the periods. The formula applies to both regular and irregular coupon periods.
Other names:
ISMA-Year
Actual/Actual AFB
Sources:
ICMA Rule 251.1(i) (Euro-sterling)
Accrued Interest & Yield Calculations and Determination of Holiday Calendars
Discussion
Comparison of 30/360 and Actual/360
The 30/360 methods assume every month has 30 days and each year has 360 days. The 30/360 calculation is listed on standard loan constant charts and is typically used by a calculator or computer in determining mortgage payments.
The Actual/360 method calls for the borrower to pay interest for the actual number of days in a month. This effectively means that the borrower is paying interest for 5 or 6 additional days a year as compared to the 30/360 day count convention. Spreads and rates on Actual/360 transactions are typically lower, for example, 9 basis points. Since monthly loan payments are the same for both methods and since the investor is being paid for an additional 5 or 6 days of interest with the Actual/360 year base, the loan’s principal is reduced at a slightly lower rate. This leaves the loan balance 1-2% higher than a 30/360 10-year loan with the same payment.
Business date convention
Date rolling (business date) conventions are a common practice to adjust non-business days into business days.
Footnotes
Further Information
Get more info on 'Day Count Convention'.
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