¹ Michaelson, and Goshay, , “Portfolio Selection in Financial Intermediaries: A New Approach,” Journal of Financial and Quantitative Analysis, Vol. 2 (1967).Google Scholar

² Hofflander, A. E. and Drandell, Milton, “A Linear Programming Model of Profitability, Capacity and Regulation in Insurance Management,” Journal of Risk and Insurance (March 1969). The analysis, however, did not consider the risk associated with either activity.CrossRefGoogle Scholar

³ Hammond, J. D., Shilling, Ned, and Melander, Eugene, “Investment Risk and Insurance Risk: An Empirical Study of Their Relations and Interactions for Property and Liability Insurers,” paper presented to the 1970 Risk Theory Seminar,New Orleans(April 18, 1970) Google Scholar. The paper also appears in Volume 17 of: The Insurance Industry; Hearings of the U. S. Senate Subcommittee on Antitrust and Monopoly (November 24, 25, 26, 1969); pp. 10622–10632.

⁴ This would not be true in a perfectly competitive market where additional funds could be obtained only through selling insurance at a discount where claims costs and operating expenses would exceed premiums, the difference simply being viewed as a cost of capital. The existence of state regulation and concomitant barriers to entry and to full price competition may assure the generation of zero cost funds for a long period of time.

⁵ Sizes of the insurers can be observed in Table 1.

⁶ The numerator of the investment rate of return ratio was defined as: net investment income plus realized capital gains or losses plus unrealized capital gains or losses and the denominator was defined as invested assets. Invested assets is defined in this study to be 85 percent of total admitted assets. The proportion of total admitted assets which are not invested amounts, for most insurers, to about 15 percent. For ease of calculation, we have assumed this proportion to be the same for all insurers over all years. In addition, we have estimated income tax effects by deflating capital gains by 25 percent and net investment income by 19 percent. The latter value is based upon calculations which reflect the presence of tax-exempt bonds. Tax-exempts were assumed to be about 30 percent of the total portfolio. These adjustments are applied to all companies over all years.

Net worth values were estimated by adding 29 percent of the unearned premium reserve to policyholder surplus for each year. Net worth values have also been defined to account for the accrued 25 percent tax on unrealized capital gains.

⁷ Sharpe, William F., “Risk-Aversion in the Stock Market: Some Empirical Evidence,” Journal of Finance (September 1965), pp. 416–422. Our values are subject to the caution as indicated by Sharpe; possible changes within the 16-year interval of σ and β-time and risk values.CrossRefGoogle Scholar

⁸ Individual examination revealed this insurer to have the highest insurance exposure of all; a 1.67 ratio of net premiums to net worth.

⁹ Our earlier study used the ratio of equity securities to assets as a measure of risk. Although a shorter time period was analyzed, the measure showed a stronger association between underwriting and insurance risk.

¹⁰ Investment risk was taken as the dependent variable since insurer management appears quite strong in its belief that underwriting and not investment is the primary activity of an insurer. A level of investment risk, in other words, is adopted according to the level of underwriting risk and not independently. Moreover, it is probably easier to make short-run risk adjustments in investments than in underwriting. Wholesale cancellations of insurance contracts create public and regulatory ill-will and reinsurance markets appear to be much less organized than securities markets.

¹¹ The scatter clearly shows the influence of a small number of extreme values and also suggests that an hyperbola would offer an improvement in fit. It did not.

¹² Underwriting profit is included in the overall evaluation. It is the difference between earned premiums and the sum of claims and expenses incurred. Investment income on premium related funds is not considered in insurance statutory accounting for underwriting profit determination.

¹³ Insurance accounting identifies this value as the unearned premium reserve. Since the reserve is calculated on the basis of gross premiums and statutory accounting procedures do not permit statement of prepaid expenses as an asset, the unearned premium reserve typically contains an equity which eventually accrues to stockholders.

¹⁴ Insurance accounting identifies this value as the loss reserve. It contains no equity which would accrue to stockholders unless “overreserving” exists; i.e., actual claims payments turn out to be less than expected.

¹⁵ Sharpe, “Risk Aversion,” p. 416.

¹⁶ To engage in underwriting is not totally costless. Certain start-up costs are required and underwriting activity per se may produce a loss. That is, claims and expenses may exceed premiums. In that event, the deficit can be viewed simply as a cost of capital; see Launie, J. J., “The Cost of Capital of Insurance Companies,” Journal of Risk and Insurance (June 1971), pp. 263–268. Also, it would not be costless under perfectly competitive conditions. See footnote 4.CrossRefGoogle Scholar

¹⁷ Equations (2) and (3) and the argument leading up to them follow a similar development in Chapter IV, “The Effects of Changing Capital Levels on Insurance Stockholders Return and Risk,” in Studies on the Profitability, Industrial Structure, Finance and Solvency of the Property and Liability Insurance Industry—Report to the Insurance Rating Board, Arthur D. Little, Inc., Case 71948 (June 15, 1970). The chapter is attributed to Dr. Emilio Venezian. A similar analysis by Dr. Venezian also appears in his statement before the Texas Board of Insurance; Austin, Texas (October 19, 1970).

¹⁸ The assumption is not implausible. The risk-return position of the insurer will be worst when the correlation is highly positive and best when it is highly negative. While we have not undertaken detailed studies to determine actual correlation coefficients, it is difficult to imagine a highly positive correlation. Policyholder funds are typically invested in bonds while stock-holder funds are more closely associated with equity investments. New York law, for example, permits a property and liability insurer to invest in common stocks only if it has cash and “reserve investment” (essentially high quality fixed commitment obligations) equal to 50 percent of the total amount of its policy-holder funds. The assumption of a zero correlation greatly simplifies the mathematical analysis and is not in great disharmony with reality. A detailed mathematical analysis of the effects of correlation coefficients and other parameters on the insurer operating positions is being developed in a separate paper.

¹⁹ Sharpe, “Risk Aversion,” pp. 416–422.

²⁰ The assumption generally is consistent with insurer investment practice. Bonds are typically traded very little and are generally held to maturity. Moreover, statutory insurance accounting, apparently reflecting practice, does not value bonds at market but at amortized value.

²¹ An analysis of industry aggregate data from Best's Aggregates and Averages for the years 1950 through 1967 showed the standard deviation of the combined loss and expense ratio to be approximately three percent. Since the variability for an individual insurer would likely be in excess of that, the value was increased to six percent. Perusal of individual insurer data indicates a six percent standard deviation to be quite reasonable. The assumed return of 2.5 percent on policyholder supplied funds is similarly conservative since it could be obtained with no underwriting profit at all and an investment return of 2.5 percent. A bond portfolio of a typical insurer over the 1950 to 1967 interval would likely have earned very close to 2.5 percent and easily could have exceeded it.

²² Conglomerates have not been unaware of this potential when considering insurer acquisitions.

²³ A great deal of work remains to be done in estimating probabilities of ruin associated with different values of premium to net worth ratios. One of the more promising approaches to estimating such ruin values appears to be through simulation. For example, Sugars, in simulating the underwriting activities of an insurer under certain rigid conditions found that a ratio of 28.0 was attained before probability of ruin values was significantly above zero (Edmund G. K. Sugars), Individual Risk Theory as the Basis of Solvency Analysis and Control in Non-Life Insurance Companies. Unpublished Doctoral Dissertation, The Pennsylvania State University (1967), p. 86–87.