Day Convention

[skoh]

Hi David,

How can we correctly count the number of days in for Day Count Convention?

For example in Hull's Drill practice question page 149,

A US Treasury bond pays a 7% coupon on January 7 and July 7. How much interest accrues
per $100 of principal to bondholder between July, 2004, and August 9, 2004? How would
your answer be different if it were corporate bond?

Ans:
06.01 There are 33 calendar days between July 7, 2004 and August 9, 2004. There are 184
calendar days between July 7, 2004 and January 7, 2005. The interest earned per $100 of
principal is therefore 3.5 x 33/184 = $0.6277. For a corporate bond we assume 32 days
between July 7 and August 9, 2004 and 180 days between July 7, 2004 and January 7, 2005.
The interest earned is 3.5 x 32/180 = $0.6222.
See this spreadsheet for calculations.
b. 8.031%
c. 7.953%
d. 7.969%
e. 8.048%

What I calculated was 181 days from Jan to Jul (24 days in Jan +28 in Feb +31x2+30x2 + 7 days in Jul).

Is there a method to calculate without knowing the actual number of days in a particular year?

Thanks!

 

[chiyui]

I think not, you must count the actual number of days straightly.
BTW, 2004 is a leap year. So from Jan/2004 to Jul/2004 should be 182 days instead of 181 days.

About the question, it said the interests are paid every 07/Jan and 07/Jul.
And it asked the interest between 07/Jul/2004 and 09/Aug/2004. (33 days, as you've known)
So, you should not use 07/Jan/2004 ~ 07/Jul/2004 as the base. (182 days as I said before)
You should use 07/Jul/2004 ~ 07/Jan/2005 as the base. (There are 184 days)

I think you've just misunderstood the denominator but that's no big deal. If you think about the interest period carefully then it'll be okay.

 

[bball8530]

Does the exam expect us to know how many days are in each month when doing day counts for Accrued Interest?

 

[chiyui]

I think yes, because it's common sense to know there're 31 days in August, and there're 29 days in February every 4 years from 2000 on.
It's not a problem of finance, but a problem of how one understands something as ordinary as the calender......