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The analysis has shown that insurer investment performance parallels that of other investors; greater returns are associated with greater variability. However, with the acquisition of higher levels of investment risk insurers generally reduce the level of underwriting risk which is undertaken. Thus, insurer management apparently attempts to keep ruin probabilities within some undefinable but clearly present limits. In the process of trading off between investment and underwriting risk, a higher rate of return to net worth is sacrificed.The sacrifice of potentially higher rates of return to equity, however, does not place the insurer at a disadvantage relative to the capital market or make attractive the alternative of operating as an investment trust. Under reasonable conditions governing the risk and return associated with underwriting activities, the insurer return to net worth is in a more efficient position as the result of underwriting activities than that offered by the capital market alone. For a given risk position, the return to the insurer exceeds that available from the capital market alone. Thus, so long as marginal returns to underwriting are positive, the leveraging afforded by the expansion of premium volume produces a superior return over the traditional leveraging which might be employed by an investor in the capital market.

The extent to which economies of scale exist in the property and liability insurance industry is examined. The analysis centers upon operating expenses and loss or claim costs. The cost effects of principal non-size variables, such as the legal form of organization, type of distribution system used, business mix, and the amount of insurance written in relation to policyholder surplus are also considered. Economies generally exist with operating expenses, and diseconomies exist with loss costs. No evidence of U-shaped cost curves is present. Average costs for operating expenses appear to decline with size and to level out as larger premium volumes are achieved. The notion of economies of scale has long been established in the literature of economics,1 as well as in the minds of entrepeneurs. Although the concept is easily enough accepted, statistical measurement of possible economies must be carried out with caution. Cost reductions or revenue increments which appear to be attributable to large size may in fact be due to other related factors. Scale economies may accrue smoothly over the range of firm size, or there may be jumps in the various cost or revenue functions as firms reach (or surpass) a "critical" size, permitting markedly different ways of doing business. Further, the firms in the industry may be so heterogeneous that comparisons among firms, even of the same size, The authors are, respectively, Professor of Business, Associate Professor of Quantitative Business Analysis, and Professor of Quantitative Business Analysis in The Pennsylvania State University. This paper was presented at the 1970 Annual Meeting of A.R.I.A. 1"The law of increasing return may be worded thus: An increase in labour and capital leads generally to improved organization, which increases the efficiency of labour and capital." A. Marshall, Principles of Economics, Eighth edition, (Macmillan & Company, New York, 1949), p. 318. may be meaningless. Output may be relatively easy to identify for firms producing single homogenous products. It is less so for multiple-product firms. Althougah some studies have analyzed economies of scale in certain industries producing tangible products, few attempts have been made to isolate size effects for any segment of the service industry.2 It is the intent in this paper to analyze the effects of size on costs in the property and liability insurance industry, one of the largest and most important of the service industries.3 " One notable exception is a study by the Securities and Exchange Commission of the effects on financing costs of the size of the issuer, "Cost of Flotation of Small Issues, 1925-29 and 1935-38," Report of Research and Statistics Section of the Trading and Exchange Division to The Securities and Exchange Commission, May 1940. The study found cost savings exceeding fifty per cent when bond issues were handled by large issuers. See Chart 6, p. 232, Cost Behavior and Price Policy, National Bureau of Economic Research, New York, 1943. For reference to studies of cost functions in manufacturing, electrical generation, distribution, etc., see also pp. 243-261, ibid. 3Premium volume for property and liability insurers amounted to $23.9 billion in 1967, the year selected for the study of size effects.