I’m writing this blog on 8/27/2018, the day my third grandchild was born. Dates are important in life. But, they are also important for actuaries, both on the job and for passing the exams. On the surface, it may seem like managing dates is easy because usually it only involves finding the time difference between two dates. Since this is essentially subtraction, or counting, it seems pretty easy. However, it’s easy to make a silly mistake. Or, even if you calculate the difference correctly, it’s important to calculate efficiently so it doesn’t take valuable exam time. So, if you’re struggling with dates, perhaps I can help.
Usually, the goal in working with calendar dates involves either counting the number of months or years between dates. Let’s assume the goal is to calculate the months between 1/1/2018 and 12/31/2018. This is easy because we know this is one year, or 12 months. But, how would calculate this? The key is to make sure the two dates are consistent: either both beginning of month (BOM) or both end of month (EOM). Notice, we’re given the first date as BOM and the second date as EOM. So, change one date to the other format. We could change the first date to EOM. Thus, change 1/1/2018 to 12/31/2017. When counting months for the exam, there is no difference between the two. Even though the starting date changed by one day, they both represent a 12-month difference. Now, compare 12/31/2017 to 12/31/2018 and it’s clear there is one-year difference. So, if the two dates are 4/1/2018 and 12/31/2018, then change the first date to EOM to be consistent with the second date. That means we compare 3/31/2018 to 12/31/2018. Now, because both are EOM, we can simply subtract months: 12-3 to get 9. Notice if we didn’t change the first date and used 4/1/2018, then when we subtract months, 12-4, we get 8, which is not correct. It’s not correct because the two dates are not in a consistent format.
Another way to compare 4/1/2018 and 12/31/2018 is to change the second date to BOM, which is 1/1/2019. Here, you can think of Jan 2019 as the 13th month in 2018. So, 13-4=9. In other words, if the second date is one year after the first year (2019 vs. 2018), then add 12 months to the month of the second date.
OK – try another. How many months are between 4/1/2018 and 1/31/2019? The first date is BOM and the second date is EOM. So, let’s change the second date to BOM 2/1/2019. Recognize there is a one-year difference. So, the month count is 2+12-4=10. Of course, if the second date is 1/31/2020 and we compare 4/1/2018 and 1/31/2020, then there is a 2-year difference. Thus, the month count is 2+(2*12)-4=22.
Let’s summarize what we do in 3 steps:
One final thought. You may be wondering if can we always convert between EOM and BOM. For example, is there ever a time when we should not convert April 1 to March 31 or April 30 to May 1? As mentioned before, if the purpose is calculating interest between dates, then this conversion is safe. The only time you need to be careful with this conversion is if you’re wondering whether a cash flow exists within a given time period.
Let’s say you’re given a savings fund and you’re calculating the balance as of 12/31/2018. If there is a deposit on 1/1/2019, for the purpose of calculating interest, you can assume the deposit occurs on 12/31/2018. However, since the deposit occurs one day after the valuation date, you do not consider the 1/1/2019 deposit in the accumulated savings as of 12/31/2018. So, the caution when converting between BOM and EOM is this should not change whether a cash flow occurs within a valuation period.
This same concept applies to other time periods, such as quarters and years. How many years are there between 1/1/2008 and 12/31/2018? The first date is beginning of year (BOY) and the second date is end of year (EOY). Make them consistent: either both BOY or both EOY. So, if we choose to make both EOY, then change 1/1/2008 to 12/31/2007. Now that both are EOY, we can subtract years: 2018 – 2007 = 11 years between the two dates.
Working with dates is a common issue in exams FM and LTAM and you may find it in other exams but not as common. So, I recommend you incorporate the concepts you’ve learned here into your exam prep as soon as possible.
We shouldn’t view math just as numbers, formulas, and problems. Math is much more.
I’ve been helping aspiring actuaries for more than 20 years. When I’m not teaching, I like to read, run, and listen to good math stories. When I was preparing for the actuarial exams, there was nothing like Coaching Actuaries. Now, we combine teaching and technology to guide the next generation of actuarial students.