## What is the Day Count Convention?

Day count convention is a system used in the finance field wherein number of days are used as a basis to determine the interest component in investments such as bonds, mortgages, swaps and forward rate agreements; and forms a basis for determining the present value of future cash flows involved in any financial transaction.

### Explanation

- Convention basically means an assumption used to standardized a few processes. We usually say, “there are 31 days in the month of December, 28 days in the month of February”. Day count convention may say “a month means a period of 30 days,” irrespective of the actual number of days in the relevant month. Similarly, we normally understand that a year consists of 365 days (or 366 days in case of a leap year). It can be assumed that a year usually contains 360 days irrespective of the actual number of days.
- So, if you are guessing that they are made for the purpose of ease of calculations, then you are partially right. As I said earlier, conventions are standardized processes. Hence, the dual purpose of this convention is a) ease of calculations b) standardization of calculations/assumptions.

### How Does it Work?

Let’s say a US-based company issued bonds of $ 10,000 each on the 1^{st} of January, 2019 at a coupon rate of 12% with semi-annual payouts. It means the investor would get the coupon amount of $ 10,000 * 12% * 6/12 = $ 600 every six months. But the question arises, “what is the date of payment of coupons?”

There can be various possibilities:

- Six months from exactly 1
^{st}January 2019, we get 1^{st}June 2019. - On an actual basis, a year contains 365 days (non-leap year). Then half of 365 gives us 182.5 days. In this case, we get 2
^{nd}July as the date of payment of the coupon. - Another convention says that a month contains 30 days. In this case, we get 31
^{st}May 2019 as the date of payment of the coupon.

Which date of coupon should an investor rely on? Here, the day count convention comes into play. The issuer of the bond chooses one of either convention and communicates the relevant dates to investors.

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### Example of Day Count Convention

Let’s take an example.

Given:

- Principal Amount / Par Value = $ 1,00,000
- Periodicity of Payment of coupons = Semi-annual
- Rate of Interest = 9%
- Coupon Every 6 months = $ 4,500

Please refer to the above given excel template for detailed calculation of the day count convention.

#### Where is it Used?

#### Explanation

- The issuer has issued a bond of the face value of $ 100,000 at a coupon rate of 9% with semi-annual coupon payments on 1
^{st}January 2019. The first coupon falls due on 1^{st}July 2019. Since the coupon is payable semi-annually, we can easily compute the annual coupon amount as $100,000*9% = $ 9000. Hence, for six months, the coupon amount is $ 4,500. - We need to calculate the accrued interest till 31
^{st}March 2019. Hence, we find the number of days from the start of the coupon period till 31^{st}March 2019, i.e., 89 days in case (I). We also compute the number of days between the coupon date and start date, i.e., 181 days in case (I). We then compute the ratio of the number of days accrued to the total number of days. We get 89/181 = 49.17%. We apply this to $ 4500, and we get the amount of accrued interest = $ 2,212.71. Thus, the investor is entitled to receive this amount had the bond issuer paid it on 31^{st}March 2019. - But is the amount calculated correctly? Yes. Is any alternative answer possible? Yes. It’s all about which day count convention is applied. In the case of the case (ii), the accrued interest is $ 2,250, and in case (iii), the said amount is $ 2,225.

### Types of Day Count Convention

Basically, there are two methods which govern these conventions:

#### #1 – 30/360 Method

- This method ignores the actual number of days during the period. It assumes that a month means a period of 30 days and a year means a period of 360 days.
- It is used for ease of calculations.

#### #2 – Actual Method

- This method considers the actual number of days during the period.
- This merits the actual facts rather than assumptions.
**Actual/360:**Here, the actual number of days is used. However, the base assumes that the year contains 360 days.**Actual/Actual:**Here, the actual number of days is used. Also, the actual number of days in the year are considered.

### Conclusion

We can say that the 30/360 days convention is easiest in its form & allows simple calculations. On the other hand, the actual/actual convention gives value to each day in the period. But as said earlier, the day count conventions are not defined in any statute but are globally understood.

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