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All about Data

In order to understand the different aggregation methods (CY, AY, PY), we will use a concrete example so that its crystal clear.

Data

Policy Effective Date Expiration Date Initial Policy Premium
1 June 1, 2012 May 31, 2013 480
2 July 1, 2012 December 31, 2012 125
3 March 1, 2013 February 28, 2014 225
4 August 1, 2013 March 31, 2014 300

Also, six months after the policy expires, the initial policy premium on every policy increases by 8% due to the final audit.

Calculate

  1. CY 2013 EP a.o. Dec 31, 2013
  2. CY 2013 WP a.o. Dec 31, 2013
  3. PY 2013 EP a.o. Dec 31, 2013
  4. PY 2013 WP a.o. Dec 31, 2014

Principles

  • CY aggregation means to include all the transactions made in that given calendar year.
    • Meaning, it could be from policies which are not written/effective that year. And when I say "all the transactions", it includes any movement of money that happened in that year.
    • Which means for Policy 2, the final audit happens on Jul 1, 2013 (six months after expiration, check table above) and so even though none of Policy 2 premium is earned in CY 2013, its audit amount has to be included in CY 2013 (which is \(125 \times 8\% = 10\)).
  • PY aggregation means to include the transactions of all the policies effective in that given policy year.
    • Meaning, we only look at the effective date of the policy, underlying the transaction and use that blindly to decide whether to include or exclude that transaction.
    • If the policy reopens and has the same policy effective date, then also it has to be included in the original policy year.
  • WP means all the premium that was written in that particular aggregation (CY/PY).
    • You have to put the full term premium amount.
    • Think of this story, you go to an UW and buy a policy. He bills you with some money, you pay it to him. He records/writes it in the company's policy database. That "act" has to be included in the written premium aggregation.
    • This also means that if you go back and decide to cancel the policy at some later date, he will deduct the amount that you have already earned from that premium and return you some money (which gets "unwritten" from the company database). This "act" has to be recorded as unwriting of premium (negative written premium) in the database.
    • Now, you think of WP in terms of CY or PY, just check whether the transaction of writing or unwriting premium has to be included in that CY/PY based on the definition of CY/PY and just add or subtract (in case of cancellation).
    • A question: Should premium audits be included in WP? Of course! You can think of it as "new money" which needs to be added to that policy. Note that you never go back and edit the old records in the database, you create new transactions to audit.
  • EP refers to the amount for which coverage to the insured has already been provided.
    • To illustrate this, imagine you bought an annual policy today (6/19/2025) for $1000. The company is then obligated to provide you with coverage if something happens to you tomorrow (6/20/2025). It is also obligated to to provide you with coverage if something happens to you one day before the policy expires (6/18/2025). But there is a difference between the two dates.
    • Tomorrow, if you decide to cancel the policy, the company is not obligated to provide you with coverage thereafter. However, it has to pay you almost the full amount since it effectively gave you coverage for only one day (today, virtually negligible).
    • However, if you decide to cancel the policy one day before it expires, company will not provide coverage thereafter. BUT, it will only pay you a very little bit of money (the amount that it charged you for one day of coverage). Why? Because it provided you with coverage for the 364 days that has already passed. They have to charge you for it, because if anything would have happened to you in those 364 days, they really would have protected you. And so, charging you for those days makes sense.
    • This is the concept of earning premium. How do we know how much we are paying for each day? The answer is however you assume it to be. If you decide that the premium should be earned uniformly (split all premium equally between all days of coverage) and just calculate a fraction of the total premium.
    • So, if you understood correctly, EP for a PY will naturally contain the full premium amount as of the given date. In this case the only calculation you need to do is IF an "as of (a.o.)" date exists. (Note again that you should only include the policy if its effective date lies in the PY)
    • Where as, EP for a CY will be calculated by taking the end point as the end of the calendar year. So just consider the end of the CY as the "as of" date.

Answers

Now use the following principles to find out the answers to the above

  1. \(\$\ 623.4\)
  2. \(\$\ 573.4\)
  3. \(\$\ 375\)
  4. \(\$\ 576\)

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