Understanding Duration Options

Decimal Date Subtraction

With decimal date subtraction, the date endpoints are converted to decimal values before the subtraction; the result is therefore a decimal.

Raw Date Subtraction

Raw date subtraction subtracts days from days, months from months, and years from years. The raw dates are formatted as yyyy/mm/dd. The following example illustrates this method:

 1995/12/11

- 1988/09/05

  __________

  0007/03/06 or seven years, three months, and six days.

Consider, however, the following subtraction:

 1990/11/06

- 1977/12/13

You cannot subtract 13 days from 6, so you have to convert one of the months to days. But when you change the 11 month to 10, how many days do you carry to the days column? When you set up raw date subtraction methods, you choose whether to use the actual number of days per month or an assumed number days per month.

If you use the actual number of days per month, the number of days depends on the month in question. In this case, the tenth month (October) is the most recent full month that you can convert to days. October has 31 days, so 1990/11/06 becomes 1990/10/37. You still have to convert one year to months to complete the subtraction, but you know there are always 12 months per year. You end up, then, with a date of 1989/22/37 and your equation yields:

 1989/22/37

- 1977/12/13

  __________

  0012/10/24 or 12 years, 10 months, and 24 days.

If you assume 30 days per month, 1990/11/06 becomes 1990/10/36, and after you again convert 1 year to 12 months, you end up with 1989/22/36. Your equation is now:

 1989/22/36

 - 1977/12/13

  __________

  0012/10/23 or 12 years, 10 months, and 23 days.

Period Counting

Period counting measures a duration by starting with the later date, then subtracting defined periods (years, months, and days) until reaching the earlier date. You choose the period or periods to count.

You will likely use period counting durations to measure the difference between the normal and actual retirement dates. You use this information to determine early retirement penalties. For example, if your plan's early retirement reduction is 3 percent per year, you use period counting to determine the number of years between the normal and actual retirement dates.

You're also likely to use period counting durations for measuring elapsed time service or PRSA coverage periods.

Let's calculate the duration between 1977/12/13 and 1990/11/06. (These are the same dates used for the second example under "Raw Date Subtraction.") You count years, months, and days. Period counting methods always start with the later date and count backwards.

First you count years, and you find 12 complete years in the interval. This takes you from 1990/11/06 back to 1978/11/06. When you count months, you find 10 complete months in the interval. This brings you to 1978/01/06. When you count the days, you always use actual days per month. Your last count includes 6 days in January and 18 days in December, for a total of 24 days. The result is 12 years, 10 months, and 24 days.

Although it appears that period counting always gives the same result as raw date subtraction, there is a difference. Period counting counts actual days for the first full month between the two dates, whereas raw date subtraction counts actual days for the last full month between the two dates.

For example, consider the duration from February 15 to August 10 of the same year. If you use period counting, you end up with 5 full months from August 10 back to March 10, plus 23 additional days between February 15 and March 10. If you use raw date subtraction, you end up with 5 full months between February 15 and July 15, plus 26 days between July 15 and August 10. The difference occurs because February only has 28 days, whereas July has 31 days.