accounting.

To use the model, one needs to know the ratio of prepaid expenses to net income and the rate of increase in the volume of premiums. I presume that the model works as well for the entire mix of business of the firm or the industry as it does when applied to a given line of insurance because the terms of the equations can embrace premiums, losses, expenses, prepayments, income, and other variables, irrespective of lines of insur

ance.

In illustrating the model, Dr. Plotkin concludes that if, for example, the premium volume increases 6 percent in a given year, the adjusted rate of return resulting from accruing the prepayments would be 1.2 percent (not percentage points) greater than the unadjusted (mixed cash/accrual) rate of return. In a footnote in the text, Dr. Plotkin mentions that (for the period) the effect "of the mixed cash/àccrual statutory system is to understate the total rate of return by less than 10 percent (not percentage points) in typical cases."

In the summary of Appendix B, Dr. Plotkin reports that the "actual distortion on actual total income for the entire period 1955-1965" (according to figures in Best's Aggregates and Averages) amounted to 5.9 percent. The distortion is a percentage of the actual total income. While the point is not made expressly clear, I presume from the context that the 5.9 percent figure results from using the model which is presented in the same Appendix. If such is the case, I cannot see why the 5.9 percent figure was not cited in the text or in the footnote referred to earlier. If the 5.9 percent figure arose from some other calculation, an additional explanation should have been provided.

of the "equity” latent in the unearned premium reserve account. Norgaard and Schick, for example, mention (on page 3) that, according to page IX of the 1967 edition of Best's Digest of Insurance Stocks, the unearned premium reserve account is overstated 40 percent on the average. Mr. Goddard, in the study cited earlier, brought up through 1966 for stock companies the illustration in the "McCullough Report" 10 where the rate of return is expressed as a fraction, the denominator of which is policyholders' surplus plus estimated prepaid expenses. His estimate of prepaid expenses, as a percentage of policyholders' surplus, ranged from a low of 11.4 percent in 1964 to a high of 18.9 percent in 1957. The average for the 1956-1966 period was 14.0 percent.

Using the Goddard estimates of prepaid expenses, I expressed estimates for the respective years for the same companies as percentages of the unearned premium reserve and found the figures to range from a low of 20.9 percent in 1964 to a high of 23.8 percent for 1956. The average Goddard-estimated prepaid expenses in the unearned premium as a percentage of the unearned premium reserve was 22.1 with the trend downward.

In an effort to compare the Goddard estimates with the Plotkin estimates I under took a crude reconciliation of the estimates for the years 1957-66. The accompanying Table 1 shows the results to be a sort of mish-mash which do not suggest that the Plotkin-Little model and the Goddard estimates have much in common. My use in column 4 of 6 percent (as suggested in the Plotkin-Little Appendix B) as the average for adjusting the mixed cash/accrual income figure to an accrual

10 Second Report of The Special Sub-Committee of The Fire and Marine Committee, National Association of Insurance Commissioners, Re Un

1921 Standard Profit Formula, including report by Roy C. McCullough (October, 1947).

OF

Col. 4 Product of Col. 3 times .06.

Col. 6 Col. 4 less Col. 5.

income figure, probably was not warranted. The year-to-year increase in premium volume was erratic enough to negate the use of an average adjustment figure for the period. Since premiums increased even in the years for which the table indicates a loss, I did not attempt to adjust income for these years. If the adjustment percentages for the respective years were applied, perhaps the results would be more informative. My abortive effort at reconciliation of the two estimates leaves me uncertain about the year to year importance on insurer income of the prepayment of expenses.

11. Treatment as an Industry

The Little report has been criticized for treating the property-liability data on an industry, as opposed to a company-bycompany basis. Critics point to the diversity of underwriting and investment activities and results among insurers. Cer

tainly, diversity exists within the property-liability insurance, but it also exists in other "industries" such as drugs, automobile, steel, pre-fabricated housing, limestone, mining, to mention only a few. Despite the intra-industry diversity, scholars, managers of business firms, government regulators, and others need industry data to gauge absolute and relative efficiency and profitability of groups of generally related firms. Therefore, I do not endorse the criticism of the industryaverage approach. Rather, I find it useful for convenient, albeit carefully qualified, generalizations.

On a related point, I would have liked to see a more detailed statement of the rationale for selecting the 43 actively traded groups of stock companies plus the nine subsidiary groups of stock companies whose figures were studied. Since they constituted (by total assets, I presume) only 53.0 percent of the industry,

more information about the means of their selection was in order.

12. Importance of Outside Capital

The Plotkin paper emphasizes the potential capacity problem which may arise in the property-liability insurance industry unless the rate of return is increased so as to attract more outside capital. This emphasis has been questioned because of the ability of insurers to generate capital internally by collecting premiums in advance of paying losses and expenses.

Certainly, the unearned premium reserve and the loss and loss adjustment expense reserves represent a part of the capital structure. During periods of expanding premium volume these liability accounts are likely to represent increasing proportions of the total capital structure. Yet, to infer that managers of stock property-liability insurance companies can be indifferent about the cost of and rewards to outside capital is to overstate a case.

The unearned premium reserve, the loss reserve, and related accounts, as of the end of 1966, for the 792 stock companies reported in Best's Aggregates and Averages offset only about 55 percent of the assets of these companies, leaving the other 45 percent to be financed either through retained earnings or outside capital. For the mutual sector, the comparable figure was about 62 percent. It is easy to see that, except for a purely postassessment type of operation, the industry cannot each year generate enough capital to support its premium volume with much if any margin of assets out of which to meet extraordinary demands for funds.

The crucial point, therefore, is that the rate of return has to be sufficiently high to keep the capital in the property-liability insurance industry, whatever the source of the capital or the time of its generation. Capital will flow from the industry if the long-range rate of return drops below the proper risk-adjusted

these comments show the behavior of policyholders' surplus of stock companies and mutuals, expressed as a percentage of liabilities and as a percentage of total

assets.

A rationale for examining such percentages is that sustained profitability, especially for the mutual sector, would cause the ratios to rise over the long run. Over about a 20-year period, relative policyholders' surplus for the mutuals has trended downward and for stock companies has trended upward only slightly if at all. This behavior, especially in the absence of inordinate dividends to stockholders 11 or stock redemptions, might be taken as support of the point of view that the property-liability insurance industry has not been sufficiently profitable to permit the growth of relative surplus. The argument is strengthened if one assumes that insurance accounting practices have not changed not changed significantly during the period. Whatever the understatement or overstatement of equity in policyholders' surplus, it can be assumed to have remained relatively the same throughout the period. The tables and charts in the Appendix show (by the way) the effect of adding back to policyholders' surplus the unrealized losses and of subtracting from policyholders' surplus the unrealized gains.

The analysis, however, needs to be pursued further. Considerable profit might have been taken out of the stock sector through dividends to stockholders or through redemption of shares of stock. On the other hand, external generation of new capital during the period, for all we know, might have been the only condition preventing the ratios from declining grossly. The case deserves further study through an attempt to adjust aggregate policyholders' surplus to reflect inputs

"Since dividends to policyholders are simply refunds of premiums, they can be ignored in such an analysis.

and outputs over the period. If the account could be adjusted to neutralize the effects of dividends to stockholders, stock redemptions, and flotations of new capital, the results would be considerably more useful. If the long-range behavior of policyholders' surplus is to be cited in convincing support or refutation of the Plotkin-Little findings, much work remains to be done.

14. Need for a General Theory

Finally, I would like to mention that I was impressed by an observation made in a recent paper by Dr. Bob A. Hedges.12 Dr. Hedges observed that the Little approach, as described in the Plotkin paper, is an "ad hoc" approach to an old and continuing problem, namely, the pricing of insurance so that the rates are adequate but not excessive nor unfairly discriminatory. As Dr. Hedges commented, the Little report (as well as the Plotkin paper) is carefully worded to say, in effect, merely that there is no evidence that any excessive property-liability insurance industry profit exists to warrant lowering rates by making explicit provision in the ratemaking formula for investment income. I agree with this conclusion but I endorse Dr. Hedges' statement that what is needed is a general theory which can be widely used by the industry, by regulatory officials, and by others to assure that insurance prices are adequate, not excessive, and not unfairly discriminatory. Dr. Hedges' paper indicates that he is at work on such a theory. We look forward to the early publication of his studies.

In the meantime, we can find numerous matters of substance on which to contemplate a general theory by restudying the excellent report which Dr. Plotkin has prepared.

12 "Rationale of Property and Liability Insurance Finance-Studied and Unstudied," 1968 Risk Theory Seminar of the American Risk and Insurance Association and to be published later.