This means that the adjusted rate of return is 1.2% greater than the reported rate.

would equal 0.05 x 1.0116 = 0.0506, or 5.06%. See Figure B-1

for other values of a 1, given g and F

Should the rate of growth go to infinity (or as high as one can imagine), the maximum increase in adjusted rate of return would be the percentage of prepayments to net income,

For both annual (I) and average (II) rates of return, adjusted ratios are related to reported ratios by a; a has the following properties:

The best place to make refinements in any economic model is in its assumption. In eneral, we may state that the present set of assumptions reflects reality fairly well and that he results are robust and will not be materially altered by changing the assumptions.

One refinement that strengthens the results is the inclusion of interest, dividend, and other incomes in the operating income figure. This inclusion has the effect of raising net ncome (I* = 1, + Other Net Income), and thereby lowering the proportion f U is of net in

ome

This lowers a in all cases where it has any effect.

Different growth patterns and changing maturity structures may have some effect, ut reasonable shifts will have but minor impact on the size of a.

As previously stated, the results of the model are quite robust and not critically ependent on the particular assumption used. In fact, it can be shown that all the results folow with but one basic assumption. We must assume an unchanged distribution of policy maturity within individual years. This is not a very severe assumption, is roughly approxinated in reality, and has but slight numerical effect on our results if it is violated.

All other assumptions made about particular growth patterns and constancy of Expense ratios need not hold for the general results to be true. In short, the only assumpion that need be retained is:

This way of stating the assumption does not imply that P is solely of function It is important to realize that P is a function of the past writings (PW, t < T) as well as he current writings (PW t).

Further refinements can be made by breaking the various loss-related and underwriting-related expenses into a number of subitems. This refinement has no effect on the results, it does, however, underscore the generality of the model. We are really addressing a question of prepayment of any kind, be it underwriting, loss reserves, or depreciation. ThereTore, these results may be extended to the industry's complete accounting system. Such extensions might be most useful in evaluating the tax costs involved in changing accounting Systems.

APPENDIX C

DATA SOURCES ON INSURANCE INDUSTRY

In order to assemble a complete picture of the property and liability insura industry and its relationship to the rest of the economy, it was felt necessary to devel data on the financial affairs of that industry which would be comparable to other segme of the economy.

While there are some 3500 firms in the property and liability insurance indus today, 300 write in excess of 95% of the total property and liability business. A sufficier large sample of companies as to be representative of this industry was required in order perform subsequent detailed statistical analyses. Data were collected for the 11-year per 1955-1965 inclusive. In general, this industry can be divided into four segments, e representing varying portions of the entire industry (Table C-1).

Source: Best's Fire and Casualty Aggregates and Averages- 1966.

The stock companies can be subdivided into actively traded stock compar (those whose shares are quoted daily) and subsidiary stock companies (owned by such fir as Sears, General Motors, and C.I.T. Finance), of which the latter is much the smaller gro

From the above it will be seen that the major thrust in data collection should in the area of actively traded stock companies. In addition, a control group was crea using aggregate figures for the entire property and liability industry and its compon parts. Table C-2 is a summary of the data collected, and its percentage of the total indust

Through inter-company holdings, a number of stock companies are operated consolidated groups. Further, within the mutual group there are several instances (such the Kemper Group) where mutual companies operate together although they can exchange stock.

Within the insurance industry, Alfred M. Best Co. is a recognized source of financial data that has been gathering and organizing insurance data for the past 100 years. Its basic source of information is the so-called Convention Statement published annually and prescribed by the insurance commissioners of each state. An insurance company must fite one such statement each year, in each state in which it does business. In general, the statements are relatively similar from state to state.

The experience in gathering and organizing data indicates that there is work yet to be done in the rationalization of insurance data. In Best's own publication, Best's Insurance Report - Fire and Casualty, all figures given are for the individual companies and only in the most recent years have consolidated group statements been prepared. In the case of the mutuals and any non-consolidated stock companies, it is possible to abstract the necessary data. While these data might be relatively complete, neither terminology nor organization are comparable to standard accounting practices, but rather follow traditional insurance industry, convention statement reporting.

From Best's Aggregates and Averages, it is possible to derive a fairly complete picture of the property and liability insurance industry. Aggregates and Averages provides grand totals on each of the four parts, Stock-Mutual-Reciprocal-Lloyd's, in the form of a balance sheet, underwriting account, investment account, and policyholders' surplus account. The figures are straight additions of individual company convention statement figures, and do not take into account any inter-company eliminations due to consolidations. Nor do they include all the companies writing property and liability insurance, but a majority of them, including all the companies of national importance. Using this picture of the industry, we compare our sample to the overall industry in order to judge both the sufficiency and validity of our sample.

Best's has compiled consolidated work sheets for the major stock groups companies over the past 11 years. Accordingly, this became our base of financial data. The consolidated work sheets provide an accurate picture of the financial operations of sample, since all activities with the exception of fire, casualty, and related business excluded.

In addition, Standard Statistics of New York provided year-end stock mark information on each of the actively traded stock groups. All data used in these analyses ha now been compiled, organized, and put in machine-readable form.

ORGANIZATION OF DATA COLLECTED

Because of differences between insurance company statements and ot financial statements, it was necessary first to define items reported by insura companies in their statements and second to construct a modified statement for industry. This made it possible to rank asset items from liquid (cash) to less liqu (mortgages and real estate) and to create composite items, where necessary, for analytical work. A similar approach was taken with the liability section a policyholders; surplus (net worth) was also broken down to form more comparal groupings. These statements approximate an ideal approach to insurance compa reporting, and the coding enables rapid manipulation of the data by computer.

In certain instances the data collected and the modified statements do correspond, generally because the information was either unavailable or not comparable other data collected. Items such as "Other Receivables" in the asset section have been us as a catch-all for a number of small, miscellaneous accounts. Similarly, “Total Curre Liabilities" represent all other liabilities except "Losses and Loss Reserves" plus "Unearn Premium Reserves." On the income statement, "Underwriting Gain" differs fr "Statutory Underwriting Gain" by the occasional miscellaneous items which are charged this account. Policyholders' dividends were added in before creating an operating profit loss figure, and then realized capital gains, less all income taxes. It is thus possible to analy operating income and all income on which taxes have been paid, and later to look unrealized capital gains and estimates of equities in unearned premiums or combined l reserves. This approach offers comparability for analytical purposes, but it is by no mean the only possible approach.

Besides the problems of consolidating groups of companies, it was also necessary exclude those activities of groups in fields other than the writing of property and liabil insurance, such as real estate, life insurance, and financing activities. This was one reason investment analyst's figures could be used and also why it was necessary to rely, ultimate on Best's own worksheets. Finally, because of the vast quantity of information provid annually by the insurance industry to various interested parties, it was necessary to make number of decisions to exclude certain data, to consolidate other data, and to break dow still another group of figures. The result is a relatively complete view of the financ activities of a representative sample of insurance companies, comparable to standa accounting practices.