Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles Part 3

 Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles Part 3

Naturally, one should consult with qualified accounting professionals
to decide how to properly record the financials of complex or difficult contracts.
1.1 What is unearned premium?
According to the glossary of the IASA Property-Casualty Insurance Accounting text [5], “Unearned
Premium [is] the portion of the premium applicable to the unexpired period of the policy”.  What is the
Unearned Premium Reserve (UEPR)?  Again from the glossary, “The sum of all premiums
representing the unexpired portions of the policies or contracts which the insurer or reinsurer has on its
books as of a certain date….”  So, the UEPR is a liability that represents the premium for the unexpired
risks on the insurer’s books.
The Statement of Principles Regarding P&C Insurance Ratemaking [4] states that ratemaking is
prospective, and that a rate is an estimate of the expected value of future costs.  Also, a rate provides
for  all costs associated with the transfer of risk.  This paper is concerned primarily with the pure
premium portion of the rate – i.e. the expected loss and loss adjustment expense, not including other
expenses.
Combining these two concepts, we see that the UEPR consists of the pure premiums and the other
expenses for the  unexpired portion of the risks that are currently on the insurer’s books.   From one
valuation date to another, the amount of unexpired risk on an insurer’s books changes: new risks may
be written, and the  unexpired portion of those risks that were on the books at the beginning of the
period generally decreases.  This is captured in the familiar accounting identity:EP = WP + UEPRbegin – UEPRend
where:  EP is the premium earned during the period,
WP is the premium written during the period,   and
UEPRbegin and UEPRend are the UEPR at the beginning and end of the period, respectively
One can see that, ceteris paribus, if the UEPRend is made smaller, then the amount of premium earned
is larger; and, conversely, if the UEPRend is made larger, then the amount of premium earned is smaller.
Should it happen that the UEPRend for a certain policy is larger than the UEPRbegin  without any new
premium being written (we shall see below how this might happen), then the above identity forces us to
conclude that the premium earned on this policy during this period was negative.
Much of the history and a survey of traditional estimation techniques for the UEPR can be found in
James L. Morgan’s Chapter 5 of the IASA text.  Morgan reports that early in the 19
th
 century the usual
practice was that written premium was fully earned at policy inception, and that in 1848 the State of
New York required insurers to carry a liability equal to an amount needed to reinsure all outstanding
risks safely.  Ignoring frictional costs and risk loads (as in the “Frictionless World” described below),
this amount is the pure premium portion of the UEPR.  A modern codification of this statutory
requirement is section 1305 of the New York State Insurance Code.

http://insurance-links.blogspot.com/2011/07/premium-earning-patterns-for-multi-year_02.html

Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles Part 2

Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles Part 2

appeared on CASNET.  Ruy Cardoso of Ernst & Young asked a hypothetical  question which I will
paraphrase here: Losses are certain at $10 per month.  You cover $20 excess $100 in aggregate.  The
contract begins 7/1/xx.  What is the loss reserve at 12/31/xx (ignore investment income)?
After a short section defining unearned premium, the bulk of this paper consists of several examples
that illustrate some of the consequences of taking the “adequate pure premium reserve” approach to
establishing the unearned premium reserve (UEPR).  The examples in this paper have been designed to
illustrate how the experience early in a multi-year contract affects the expected losses (to the contract,
not ground-up) that occur later in the contract, and how this in turn should affect premium reserving
and earning patterns.  While the examples could be made more “realistic”, it was felt that this would
introduce complications not relevant to the central issue. For example, in our simplification of Ruy
Cardoso’s question above, we have assumed that there are certain losses of $20 per month.  If the
losses are certain, there are questions of risk-transfer.  Similarly, in Section 4, the single premium
policy has an indefinite term –  even though such a policy would be highly unusual.  Despite the
simplifications, the examples and the technical considerations they illustrate are relevant.
After these examples, Section 7 provides some comments on Practical Considerations, including
remarks relevant to the new requirement that an actuary opine on the adequacy of the unearned
premium reserve under certain circumstances.
The author would like to thank the reviewers and colleagues  who  read and commented on early
versions of this paper.  The views and examples contained in this paper are those of the author. In some
cases, the approach contained herein might result, for example, in earning premium faster than somestate’s regulations would allow.

http://insurance-links.blogspot.com/2011/07/premium-earning-patterns-for-multi-year.html

Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles

Premium Earning Patterns for Multi-year Policies with Aggregate Deductibles

Section 1: Introduction
Statutory accounting requires that reserves be established for covered losses that have occurred but are
unpaid (loss reserves) and – effectively – for losses that have not yet occurred, but will be covered by
policies already on the books (unearned premium reserves).  Furthermore, these reserves need to be
separate.
A problem can arise when a multi-year contract has a large aggregate deductible.  If losses depleting
the deductible occur faster than expected, the premium reserve at some point in time may be
inadequate.  Of course, it is also possible that those losses occur slower than anticipated in which case
the premium reserve may be redundant.  The approach taken in this paper is that at each point in time
(or at the end of each accounting period) the pure premium portion of the unearned premium reserve
should be exactly adequate.  This, in turn, implies a certain earning pattern for the premium that, in
some cases, requires that negative premium be earned.
This paper was inspired by a discussion in my workplace on capital allocation for second-event covers
and similar types of transactions.
1
  Shortly after this conversation, a very interesting discussion thread
                                                      
1
 Do you need more capital to write a second-event cover than to write a first-event cover, because its results are more
volatile?  Do you need less because the probability of a loss to the cover is more remote?  (If so, once the first event occurs,
you are now effectively on a first-event cover.  Do you at this point allocate more capital?  What if you don’t have it?