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.

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