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Table III-A -- Total Squared Error (in 10¹² 's) From Regressing Quarterly Losses
Table III-B -- Chi-Square Statistics From Regressing Quarterly Losses
These results show substantial instability, as well as the problems noted
with using one-year flows to allocate surplus.
Other allocation methods have avoided using one-year flows by examining
ratios of surplus to unpaid losses, total reserves or total
liabilities (10). Table IV shows an allocation on loss reserves.
Table III-C -- December 31, 1985 Surplus ($000's)
Allocated on
Unpredicability of Losses
Table IV -- Surplus Allocated On Loss and Loss Expense Reserves
 |
Line |
December 31, 1985 Reserves |
Allocated
December 31, 1985 Surplus |
|
| Auto Liability |
$ 40,583,226 |
$19,847,726 |
| Auto Physical Damage |
3,357,221 |
1,641,890 |
| Homeowners |
5,168,457 |
2,527,697 |
| Other Property |
3,510,750 |
1,716,975 |
| Workers' Compensation |
33,330,445 |
16,300,664 |
| Medical Professional |
10,074,143 |
4,926,884 |
| Other Liability |
26,123,56 |
12,776,050 |
| Miscellaneous |
32,252,599 |
15,773,530 |
 |
| Total |
$154,400,404 |
$75,511,417 |
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These methods have reversed the problems of growth and runoff that the other
methods pose. A growing line presents an exposure to catastrophic loss that
may be out of proportion to its reserves or other liabilities that arose
earlier. A short-tailed line will be similarly under-represented even if
the potential for very large losses is significant. In short, the
volatility of a dollar of expected paid losses is not uniform among lines.
Khury pointed this out for reserves in his paper, "Loss Reserves:
Performance Standards" (PCAS, LXVII, 1980).
Clearly, the uncertainty in a dollar of windstorm unearned premiums, or
casualty excess-of-loss loss adjustment expense reserves is higher than that
of a dollar of automobile collision loss reserve. However, the principal
difficulties in using these methods to make informed business decisions is
the lack of support for these allocations. This is summarized in the NYCB
Report.
"The hardest choices facing anyone wishing to evaluate insurance
profits are those associated with returns on invested capital.
- "It is not possible to satisfactorily determine how much capital is
associated with a particular group of policies.
- "It is even harder to determine how much capital should be
associated with such a group of policies.
- "It is hardest of all to determine whether an observed rate of
return on capital is satisfactory or not.
"..Any prospective method must deal with expected capital requirements
and expected rates of return on that capital. Thus, the prospective
approach adds its own set of significant estimation problems to the
problems inherent in both methods." [Emphasis in original.]
Attempts to rationally allocate a risk margin to unpaid losses on the basis
of expected variability cannot solve these problems. This is because the
observed variability is neither constant in time, (as shown above) nor
uniform among lines (as noted by Khury).
Without downplaying the specific problems of each at these allocation
methods, there are general, practical problems that any method must
address. Three problems deserve mention here. Sections of an insurer's
book are often tied together in the marketplace, such as a piece of
accommodation business written to obtain other, desirable business. In any
adversarial decision there is an incentive to make the most favorable
allocation, which may not be the most accurate. Finally, surplus is not in
itself relevant. Equity is. While surplus is the key component of equity,
pre-paid expenses, tax loss carry forwards, Schedule P excess reserves,
non-authorized reinsurance, other non-admitted assets, and sunk costs such
as training or software development costs have value and need to be
reflected in any informed economic decisions, in addition to surplus. These
other quantities are less subject to analysis.
Tables I, II, IIIc and IV each allocated the industry's surplus. The
results, which are summarized in Table V, are substantially different. That
is because, while each of these four methods reflected an allocation based
on one variable that is associated with increased exposure, each method
based its allocation on a different variable. Each method reflects some of
the limitations on the insurers' capacity: none reflects all of them.
We have seen several practical concerns which would limit the usefulness of
each allocation method for economic decision-making. But this is not to
conclude that every allocation method must be impractical. However, before
practical allocation methods can be discussed, there is a need to understand
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(10) See for example the 1984 New York Compensation Board Report to the
New York Insurance Department , or Model D in Report of the NAIC
Investment Income Task Force, Section III. The NYCB allocates
surplus, first to fund any unearned underwriting losses, and the
remainder in proportion to the sum of loss reserves and the
expected loss component of the unearned premium reserves. The NAIC
approach , which has been used in Texas, allocates surplus in
proportion to estimated total liabilities.
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