What is Day Count Convention for Bonds and how does it impact the trading prices of a Bond?
Most market regulators pre-define the Day Count Convention in Bond Market that will be followed in the region. This is particularly important to calculate the accrued interest between two dates, and to determine the fair trading price of bonds.
An important aspect for these calculations of accrued interest is the number of days between the previous interest payment date, and the current date. But there is no formal and universally accepted method to count days.
To simplify the calculations in Bond market, some assumptions have to be made related to the counting of days between any dates. After that, it will be possible to get the amount of accrued interest. This standardized method of day counting is also known as the Day Count Convention in bonds.
Popular Day Count Conventions
It is possible that different financial instruments within the same country, might be following separate methods of day counting. For example, Bank Loans might be using a particular method, and other debt securities might be following a different method.
One of the most popular Bond Market Day Count Convention is the 30/360 convention. In simple terms, this method assumes that each month is made up of 30 days, and that each year is made up of 360 days (12 months x 30 days).
The assumption of 360 days in a year can significantly ease the calculations, because the number is highly divisible. For example, in a 360-day Financial Year:
Monthly Coupon is paid every 30 days
Quarterly Coupon is paid every 90 days
Half-yearly Coupon is paid in 180 days
Etc.
(To learn more about the frequency of Coupon Payments, refer: What is Coupon frequency in bonds?)
Whereas if we had used the actual number of days in the year (365 / 366 days), then the calculations would have become very complex. Although it is now possible to quickly do advanced calculations through technology, the process of using 360-day year was popularized in earlier days, when similar calculations had to be largely done manually.
Important dates in Day Count Convention
In the process of counting the number of days, one of the given dates will be the Start Date, and the other will be the End Date. When using Day-Count Convention for bonds, we are usually trying to find the interest accrued till the present date, from the most recent Coupon payout date in the past.
So, let us assume that the 2 dates that we are using for the Interest Day Count in Bonds are defined in the below-mentioned format.
\(D_1\), \(M_1\), \(Y_1\): Refers to the day, month and year in the ‘Start Date’, from which the interest has started to accrue. For Bonds, the Start Date is usually the date on which the last Coupon was given. If no Coupon has been paid so far, then the Bond Issue date is usually treated as the Start Date.
\(D_2\), \(M_2\), \(Y_2\): Refers to the day, month and year in the ‘End Date’ or ‘Valuation Date’. This is usually the present date on which the calculations are being made.
Day Count Factor
After the number of days in the accrual period have been measured, the applicable interest amount for the defined period can be calculated by adjusting the interest rate. The concept of ‘Day Count Factor’ is used to adjust the annual Coupon Rate, to the applicable interest rate for the defined time period.
The structure/layout of this factor is also used to communicate the Day Count Convention in Bond Market. In general, the format looks like this:
Days in accrual period / Days in the year
But many times, some assumptions have to be made about the number of days. The most popular Day-Count Convention in Bonds have been mentioned below.
Actual/Actual: (also known as Act/Act) This is measured by dividing the actual number of days between a time period, and the actual number of days in the year. No standardization and assumptions are applied in this case.
Actual/365: (also called Act/365) In this case, the number of days in a year are fixed at 365 days (even in case of a Leap Year). So, the measurement is done by dividing the exact number of days in the time period, by 365 days.
30/360: Refers to the method where the number of days in each month is fixed at 30 days, and the days in a year are assumed to be 360 (12 months x 30 days = 360 days). There are multiple variants of the 30/360 Bond Day Count Convention, where different adjustments have to be made to the values of \(D_1\) and \(D_2\). The European method and the US method of 30/360 convention are the most widely used techniques.
Using Day Count Convention in Bond Market
The concept of counting days is universal, and it could be applied to any type of interest accruing instruments. Some of the most popular reasons and situations in which the Bond Interest Day Count could be measured, have been mentioned below.
Fair Market Value on any given date
The most common need for counting days in a bond is to measure the Fair Market Value of the Bond, on any given date. This fair value is used as a reference price between a buyer and a seller of the bond. It could even be used for accounting purpose, where a company holding some Bonds would like to capture the latest value of the Bonds on the statements.
Example: Suppose that a Bond pays interest on 01 April of every year, and an investor would like to sell this on 10 July. Although the next payout date is 01 April of next year, but some interest has already been earned on this bond till 10 July. So, the seller is entitled to receive this accrued amount, and the Bond Price should reflect that. This is also known as the Dirty Price of the Bond.
To get the accrued interest amount, we would first need to count the number of days that have passed since the latest Coupon payment. So, the last Coupon payment date becomes the Start Date, and the current date becomes the End Date.
Determine Coupon Amount
Another popular use of Day Count Convention for Bonds is to measure the Coupon amount, by using the exact time period. The Coupon Rate of a Bond is usually fixed in advance, but the Coupon amount will have to be calculated.
Example: Suppose that a Bond pays a monthly Coupon on the last working day of every month. This means that if the last calendar day in a month falls on a weekend or a holiday, then the Coupon will be paid on the immediately preceding business day. So, the Coupon might be paid on 29th of a particular month, whereas it could be paid on 31st of another month.
It is important to decide the day count for Bonds, because the number of days in the month is not fixed in this case. If the bond follows an Act/365 convention, then the actual number of days between the last payment date (of previous month) and the last day of the current month will need to be measured. This will be divided by 365 to get the Day Count Factor, and to get the exact Coupon amount.
Early redemption of Bonds
In some cases when the Bond is Callable, the Bond Issuer might decide to redeem the Bonds before the maturity date. This early redemption could even happen on a date that is different from the Coupon payment date. So, the Day Count Convention in Bond Market can help to decide the accrued Coupon amount till the early redemption date.
Example: Suppose that a Callable Bond pays an annual coupon on 01 June of every year. The Bond issuer decided to use the Call option, and redeem the Bonds on 06 November. Now, when the settlement amount is being distributed on 06 November, the Bond Issuer will pay the Face Value of the Bond, and the accrued Coupon.
So, the first step would be to measure the number of days between 01 June (last Coupon date) and 06 November (Call date / redemption date). This can then be used to calculate the adjusted Coupon amount that has to be paid at settlement time.
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