The six practical considerationq are shown in Table VII.

Table VII -- Practical Considerations In Allocating Surplus

1.	The allocation must consider each function that surplus is performing
2.	The sum of the amounts of surplus allocated to the various sections of the insurer's book must be exactly equal to the insurer's total surplus,
3.	The amount of surplus allocated to any section of the insurer's book that presents an exposure to loss must be positive
4.	Among sections, the amount of allocated surplus, less amounts that will fund underpriced business or unfunded dividends, must increase as the section's exposure to unfunded losses increases.
5.	The allocated amounts must not change substantially due to small changes in the capital structure of the insurer, or of its results over the near term, and
6.	The formulas used to make allocations must be explicit, objective and justifiable.

Having considered several possible methods of allocating surplus and establishing minimum standards for allocation methods, we can now draw

CONCLUSIONS

None of the allocation methods presented in this essay satisfy the practical considerations. For example, most of the methods do not consider that surplus must serve both as a buffer against windstorm catastrophes that will exceed the unearned premiums and as a buffer against adverse liability reserve development. The method that does consider both, the NYCB method, doesn't reflect any difference between the two functions. None of the methods considers the potential of asset values falling. None consider the differences between certain losses and contingent ones. No method is developed in such a way that, in general, it will allocate more surplus to a section of the book that presents a greater exposure to unfunded losses. An equally serious concern is that none of the methods addresses the philosophical questions that underlie any attempt to allocate surplus.

Does this mean that the actuary is left without sound, practical analytical tools for comparing performance, for pricing and for analyzing profitability? No.

The concept of the insurance operating profit margin can be used to answer the same questions as an allocation of surplus is intended to answer. The insurance operating profit margin is the contribution to the insurer's annual profits from a section of the book (earned premiums less incurred loeses, expenses and dividends plus investment income) compared to the annual earned premiums for that portion of the book:

The insurance operating profit margin can be calculated on a calendar, accident, or policy year basis. The use of the insurance operating profit margin in decision-making depends only on knowing the value that the open marketplace currently puts on insurance coverage.

To develop a price for an insurance contract that reflects the value of the use of the insurer's surplus, the price should be set to make a fair operating profit. That profit margin can be derived from industry or insurer results, adjusted for later changes in market conditions, or from corporate objectives. This calculation is certainly more simple, objective and empirically based than any analysis of risk, beta, returns on net worth and premium-to-surplus ratios. It is therefore more likely to produce stable and accurate prices.

If management believes that investment income opportunities are fairly stable, an additional complication can be eliminated. Pricing can be determined by using a marketplace underwriting profit or loss as a target. This analysis requires no allocation of investment income to sections of the book.

Management performance can also be evaluated using operating or underwriting profit margins. If the various underwriting management centers write books of business that are similarly distributed, and make similar demands on the insurer's capabilities, then the total insurance operating profit margin can be directly compared between centers. If there are differences between the profit center's various books, their relative performance can be compared on separate sections. Perhaps Homeowners to Homeowners, and Medical Malpractice to Medical Malpractice, etc. A different approach is to calculate a single result over all portions of a center's book by setting a company-wide target operating profit margin for each line of insurance, and comparing each center's results against what it would have produced if each section of its book had earned the company-wide target. In symbols, for profit center #j, for line of insurance #i:

(24)

The insurance operating profit margin can be used in economic decision- making whenever an allocation of surplus could be used. It also brings a parsimony and understanding that formal allocation techniques lack.

If for some reason a method of pricing or performance appraisal that uses an allocation of surplus in its calculations is essential, it is sensible to use an analytical tool that is fairly insulated from the vagaries of the allocations. One such tool is the Myers-Cohn pricing model that has been employed by the Massachusetts Auto Rating Bureau.

The MARB described the model in a recent paper (16) as:

"The basic premise underlying the Myers-Cohn model can be stated this way: a fair premium must be equal to the expected losses and expenses, discounted to present value at a risk-adjusted rate, plus the present value of the federal income taxes on underwriting and investment income, discounted at a risk-free rate. Premiums calculated this way preserve the equity invested in the company and give the investor a fair reward for the risk of underwriting.

Myers-Cohn Formula

"The discount factor applicable to losses and expenses first reflects the investment income on the cash flow at current risk-free rates. The Myers-Cohn model thus was consistent with prior models which included investment income at a risk-fuse rate of return. Although the model assumes that investment income can be earned at the risk-free rate, the company and its stockholders take the risk and receive the reward for any alternate risky strategy. Additionally, the discount factor applicable to losses and expenses reflects a risk adjustment that is chosen to yield a reasonable compensation for the uncertainty in both the estimates of losses and expenses and in their realization -- or in other words, for the risk of underwriting. The fair premium can then be calculated by including the present value of the federal income taxes on investment and underwriting income. The inclusion of the present value of income taxes on investment income requires the use of some method of allocating surplus to each line. The Myers-Cohn paper suggests allocating the surplus roughly in proportion to total outstanding reserves...

"In the Massachusetts applications to date the risk adjustment was chosen from among CAPM estimates but, unlike the Fairley models, nothing in the model requires the use of the CAPM or any other specific model of risk."

The allocated surplus is only important to develop the amount of taxes incurred as a result of investing the surplus. While the treatment of surplus has varied in applications of the Myers-Cohn Model, results are relatively stable. Calculations presented at ISO's Actuarial Research Committee in 1985 showed that for one set of parameters, a sixty point change in the premium-to-surplus ratio created a change of less than five points in the indicated Auto BI profit provision.

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(15) The operating profit margin can be seen in careful, practical application as the Argonaut Return in David Skumick’s Measuring Division Operating Profitability, 1985 GAS Discussion Paper Program.

(16) Taken from "The Use of Investment Income in Massachusetts Private Passenger Automobile and Workers' Compensation Ratmaking" by Richard Derrig.

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