# An analysis of life insurer retention limits.

This study examines the relationship between ceding life
insurers' retention limits on an insured life basis and certain
operational and financial characteristics of the companies. Analysis is
performed using 97 major U.S. insurers with 1987 assets ranging from
$108 million to $32 billion. Retention limits for these insurers vary
from $25,000 to $20,000,000 per insured life. Five factors are shown to
have the greatest impact on life insurer retention limits. Not
unexpectedly, firm size is found to be the most important factor. Four
other explanatory factors, each statistically significant at the 0.01
level, provide important additional insight into this relationship.
These factors are (1) form of insurer organization (i.e., mutual or
stock), (2) the firm's emphasis on new business, (3) average policy
size, and (4) the company's emphasis on term insurance.
Collectively, the principal components regression model explains nearly
90 percent of the total variation in retention limits for the sample
insurers.

The life reinsurance decision centers on the establishment of retention limits. Retention is the amount of any insured loss to be borne by the primary (or ceding) company. Life retention limits normally are expressed as an amount per insured life. Claim amounts in excess of the insurer's retention are the responsibility of its reinsurers. This study examine the relationship between the size of ceding companies' retention limits and certain insurer characteristics.

The setting of an appropriate retention limits is a non-trivial decision for an insurer. It ultimately affects both the risk exposure and the profitability of the ceding company. It establishes the maximum individual claim amount that the insurer believes it can tolerate, given its financial and operating characteristics. Further, the dollar retention limit is directly related to other elements in the total reinsurance process. For example, an automatic binding limit (i.e., the maximum amount for which the ceding insurer binds the reinsurer under an automatic reinsurance treaty) is usually expressed as a multiple of the retention limit. Second, a subsequent increase in the retention limit affects the amount of previously ceded insurance that the primary insurer can recapture.

It can be expected, a priori, that different financial and operational characteristics of life insurers, together with differences in their products and markets, will lead to varying motives for establishing retention limits. This study seeks to shed light on insurer characteristics that may account for differences in these retention limits.

Literature Review

The literature describing the various forms of reinsurance agreements is extensive. In the life insurance area, the works of Dowsley (1982), Dukes (1982), and Gold (1978) may be noted.

Prior work on the analysis of both life and property-liability reinsurance (and insurance) decision processes can be classified into three major categories: (1) objectives of reinsurance, (2) normative methods, and (3) empirical studies. Each category is discussed below.

Objective of Reinsurance

A review of the literature suggests numerous objectives of reinsurance. The following listing of the primary uses and objectives of life reinsurance can be considered representative and reasonably exhaustive (if not redundant): (1) risk spreading-minimizing the concentration of risk, (2) surplus relief-reducing surplus strain caused by new business writings, (3) stabilization of overall mortality experience, (4) stabilization of operating results, (5) reduction in the probability of insolvency, (6) minimization of the potential for catastrophic losses, (7) transfer of investment or lapse risk, (8) take advantage of reinsurers' underwriting expertise, (9) transfer (or sell) certain classes of business (e.g., substandard issues), (10) increase the ceding company's capacity for growth, (11) tax minimization-in specific situations reinsurance may reduce the ceding company's tax liability, and (12) assist the ceding company when experimenting with a new market.

Normative Methods

Optimal reinsurance coverage was examined by Beliveau (1984), Mossin (1968), Samson and Thomas (1983), and Wiser (1985). Signaling equilibrium, expected utility, and simulation methodologies were used in determining optimal reinsurance levels.

Pareto optimal risk exchanges between insurers and the design of Pareto optimal reinsurance contracts were examined by Borch (1962, 1974), Benktander (1975), and Verbeek (1966). The equilibrium conditions necessary for reinsurance have been analyzed by Borch (1974) and Pressacco (1979).

The normative studies cited focused on the risk retention decision in property-liability insurance. Few published studies exist on the selection of life reinsurance retention limits, and none deal directly with the question of retention selection on a per insured life basis or relate the retention decision to an insurer's financial or other operating characteristics. Rosenthal (1947) examined the random portion of total mortality fluctuations and provided a simple method for determining the retention limit. His approach involved an application of the law of large numbers to the reinsurance decision. As expected, the number of insured lives and the variation in insurance amounts are the two important factors in his formula.

Pentikainen (1952) applied the concept of collective risk theory to the retention limit problem. Setting a probability of ruin of 1.0 percent, he provided a formula for retention limit establishment. The collective risk theory approach may be criticized both for its arbitrary nature in establishing the ruin probability and for its emphasis on "safety first."

Empirical Studies

Mayers and Smith (1990) examined the relationship between a property-liability insurer's overall level of reinsurance and selected financial and operating characteristics. The Mayers and Smith study focused on aggregate reinsurance demand for all insured exposures, while the current study examines reinsurance demand per insured exposure. This leads to the use of a different dependent variable (i.e., a ratio of aggregate reinsurance premiums ceded to total premiums vs. a per insured dollar retention limit) and the use of somewhat different regression methodology.

Gottheimer (1983) hypothesized a positive linear relationship between the retention limit selected by a property-liability insurer and its assets, policyholders' surplus, premium volume, and loss ratio. Using stepwise regression, he concluded that the two most significant factors to consider in selecting an appropriate retention level were assets and premium volume. Although restricted to the retention decision in property-liability insurance, Gottheimer's approach is somewhat similar to that used in this study. No published empirical study on life retention limits exists, except some documentation of reinsurance and retention data on a limited scale.(1)

Research Methods

Specific Research Issues

The focus of this study is on the determinants of retention limits established by life insurers in proportional reinsurance transactions. The retention limit is defined as the amount of ordinary life insurance retained by the ceding insurer on the life of any insured individual (under all policies, collectively). For the companies included in the study, the retention limits varied from $25,000 to $20 million.

Although the major purpose of the study is to identify the various determinants of individual life retention limits and their relative importance, the final model can also be used to forecast retention limits in terms of specific company financial and operating characteristics. The primary hypothesis to be tested is that a linear relationship exists between the size of a ceding insurer's per insured life retention limit and selected insurer financial and operating variables.

Variable Selection and Specification

The defendant variable examined in this study is the ceding company's per insured life retention limit in dollars. The insurance literature suggests numerous possibilities for explanatory independent variables. Black and Skipper (1987, p.431) indicate that the size of the individual retention limit is a function of several economic and operational factors including insurer surplus, quality of the insurer's agents and underwriting staff, average policy size, distribution of insurance in force (e.g., by amount, grouping by age and sex), and distribution of new business.

Conceptually, other factors including amount of insurance in force, amount of new business written, premium volume, lapse rates, organization form (mutual vs. stock), asset size, profitability, and term/whole life mix potentially may affect the retention decision. Unquestionably, the prices that ceding companies pay for reinsurance should be a major factor in the ceding company's establishment of its retention limit.

Some of these variables cannot be (or have not been) measured quantitatively (e.g., quality of underwriting department). Also, publicly available data do not exist for other potential explanatory variables (e.g., reinsurance prices).

Ultimately, 17 independent variables were selected for analysis. Many of these variables probably measure the same (or similar) insurer characteristics. For example, company size can be measured in many ways, including admitted assets, capital and surplus, and premium volume (i.e., direct premiums written).

Selection of Sample and Data Sources

Several criteria were used in selecting the life insurer sample. Because the data needed for the study were obtained from the annual editions of Best's Insurance Reports, the first criterion, of necessity, is that information on the insurer is available in these annual reports. The 1988 life-health edition contains selected 1987 financial statement information, including retention limits, on approximately 1,600 U.S. and Canadian life and health insurers.

To avoid possible distortion in the results by very small life insurers, only those insurers with at least $100 million in total assets (less separate accounts) at the end of both 1986 and 1987 were selected. Further, relatively new companies (i.e., those commencing their operations after 1976) were omitted from the sample. Because Canadian insurer regulation differs from U.S. regulation, Canadian insurers were deleted from the sample. Also, fraternal benefit societies and savings bank life insurers were omitted because of their special structure and regulation.

Many life insurers are heavily engaged in the sale of annuities or health insurance. Because this study examines ceding company retention limits in ordinary life insurance transactions, only those insurers whose business is primarily the marketing of individually issued life insurance are examined. Thus, if a company's ratio of life reserves to net policy reserves equaled or exceeded 70 percent in both 1986 and 1987, the company was retained. Otherwise, the insurer was removed from any further analysis.

A few additional companies were omitted from the sample because of data insufficiency or other data problems. The resulting sample consisted of 97 life insurers whose admitted assets (including separate accounts) range from $108 million to $31.8 billion. The necessary data were collected for each of these insurers, their retention limits, and selected other data. the sample insurers, their retention limits, and selected other data.

Research Results

A cross-section multiple regression model was initially estimated. However, as noted above, several of the 17 selected independent variables that a priori might affect the level of retention limit were believed to measure similar insurer characteristics.

Diagnostics applied to the initial multiple regression model strongly suggested the possibility of multicollinearity. Principal components regression was employed to address the multicollinearity issue and to fully utilize information derived from the correlated variables.

Principal Components Analysis

Based on the Scree diagram and mineigen criterion,(2) six components (factors) were retained in the model. Table 1 shows the initial factor loadings matrix whose elements are correlation coefficients between the original 17 variables and the six factors.

[TABULAR DATA OMITTED]

The six factors account for 87 percent of the total variance in the 17 explanatory variables. Using the varimax rotation method, the six factors were rotated again to improve result interpretability.(3) Table 2 shows the varimax factor loadings matrix.

[TABULAR DATA OMITTED]

A principal components regression model using the six varimax rotated factors as explanatory variables is estimated through ordinary least squares (OLS).(4) Table 3 shows the tentatively named factors, their regression coefficients, and t-statistics (in parentheses below the corresponding coefficient). The overall model is statistically significant at a p-value of 0.0001. The coefficients of five of the factors (or insurer characteristics) are significant at the 0.01 level, with the profitability coefficient significant at the 0.10 level.

[TABULAR DATA OMITTED]

As seen in Table 3, the dependent variable is the square root of the dollar retention limit. This transformation was performed to better meet the homeskedasticity assumption that underlies the OLS model.

Interpretation of the Regression Relationship

As is common in studies using factor and component analysis, a certain amount of judgment must be used in explaining the results. Factor 1 has been identified as the mutuality dimension. This is because high correlations were found between Factor 1 and the ratios of participating insurance to total insurance (both new and in-force business), mutual form of organization, and the ratio of policyholder dividends to direct premiums written. Participating life insurance and policyholder dividends are characteristic of mutual life insurers. The expected sign for this factor was positive because, in general, premiums for participating life insurance have built-in margins for dividends and, hence, result in a larger premium inflow, ceteris paribus. This fact should provide some additional margin to absorb unusual fluctuations and, therefore, should result in larger retentions.

The model sign for Factor 1 is positive. Thus, higher retention limits are associated with the mutuality dimension. Because the mutuality dimension is orthogonal to the "firm size" dimension (factor), these findings are not explained by the fact that, in general, mutual life insurers are of substantial size. Other reasons might also underlie the observed relationship. Many stock life insurers reinsure significant amounts of their direct writings with a parent insurer or other members of a controlled group of insurers. Since mutual companies cannot be owned by another entity, no possibility exists of a pass-through of insurance (through reinsurance transactions) to an insurance company parent. This difference in ownership may partly account for a lower retention limit for stock insurers.

Factor 2 indicates a ceding company's concentration of its product lines in term insurance. This conclusion is evidenced by high loadings between Factor 2 and the four variables that represent ratios of term insurance to aggregate insurance amounts. It was believed that insurers specializing in term insurance would have lower retention limits because term life products, carrying proportionately larger net amounts at risk over time and smaller premium rates, were thought to represent more risk to the insurer, ceteris paribus.

However, the model sign for Factor 2 is positive. It may be that insurers concentrating in term insurance sales may be more aggressive in risk-taking and, therefore, may be more inclined to retain larger amounts. Additionally, because term premium rates are lower and margins smaller than those for whole life, it may also be that insurers with large proportions of term insurance desire to retain much of the face amount to maximize the available cash flow for investment purposes.(5) Again, since Factor 2 and the "average policy size" dimension are orthogonal, the larger policies typically sold in the term market do not explain the positive sign of Factor 2.

The positive sign observed in the model for Factor 3, firm size, is consistent with the expected sign. Firms with large admitted assets, capital and surplus, and premium volume would reasonably be expected to retain greater amounts of insurance. Insurers with large amounts of statutory capital and surplus can retain greater amounts per insured because they are less affected by surplus strain caused by the writing of new business.

The sign for average policy size (Factor 4) also is as expected. The positive relationship between average policy size and retention limit simply indicates that as average policy size increases, insurers show a greater willingness to retain larger amounts per insured life. This appears to be consistent with the use of reinsurance to minimize the potential adverse effects on a ceding company's financial and operating results arising from one or more large death claims - large in relation to the average death claim.

The negative sign observed for the profitability dimension (Factor 5) contradicts the study's a priori expectation. The empirical finding suggests that higher profitability is associated with lower retention limits. Profitable insurers might utilize reinsurance for tax purposes to the extent that reinsurance may reduce taxable income. However, restraint should be exercised in attaching too much importance to this finding for several reasons. First, the coefficient is not statistically significant at the conventional level (i.e., 0.05 or less). Second, profitability was measured for a single year only. Insurers usually do not change their retention limits yearly, yet insurer profits may fluctuate widely from year to year. Also, this dimension measures the profitability of the total operations (i.e., group, individual, annuity) of the ceding company, whereas the retention limit is only for the insurer's ordinary product line. Further, the two variables most highly correlated with profitability (i.e., return on equity and the ratio of net operating gain to net premiums written) are measured on a statutory basis. Statutory profitability may be a poor indicator of an insurer's profitability when measured according to generally accepted accounting principles.

Factor 6 has been labeled " Concentration on new business." The two variables that exhibit the highest correlation with this dimension are lapse ratio and the ration of commissions to direct premiums written. The observed sign indicates that a negative relationship exists between an insurer's average lapse ratio and the size of its retention limit. A similar relationship exists between size of retention limit and the commissions ratio. These results are consistent with the contention that ceding companies with high lapse ratios and high commission expenses seek to transfer a portion of these costs to reinsurers through the use of smaller retention limits. High lapse rates and high commission expenses are often a direct result of a large volume of new sales, and in this event ceding insurers are likely using reinsurance for surplus relief.

Factor scores used to derive the regression equation have been standardized to a mean of zero and unit standard deviation. Further, since the factor scores are uncorrelated because of orthogonality, it is reasonably safe to address the relative influence of each factor on retention limits through examination of the [R.sup.2,s] and the regression coefficients.(6)

Table 3 shows that firm size is the most important factor, accounting for approximately 75 percent of the total variation in the retention limits. The other five factors are statistically significant, and they collectively explain slightly more than 14 percent of total variation. The most important of these factors are mutuality and concentration on new business. The profitability factors accounts for only a nominal amount of the total variation in retention limits.

Summary and Conclusions

This study analytically examines life reinsurance retention limits on a per insured basis relationships to specific ceding company financial and operating characteristics. A principal components regression model applied to a sample of 97 U.S. life insurers shows that five factors (dimensions) are highly significant in explaining a ceding company's retention level. Of these five factors, firm size (measured by admitted assets, direct premiums written, and capital and surplus) appear to have the greatest impact on insurer retention limits. Collectively, the model explains nearly 90 percent of the total variation in retention limits for the sample insurers.

The authors have not addressed important questions such as: (1) Are primary insurers establishing their per insured retention levels in the most appropriate manner? (2) Are primary life insurer retention limits higher or lower than they should be? (3) What should be the relationship between overall insurer demand for reinsurance and individual insured retention limits? Further research is needed on these questions, especially the last.

(1) Cardinal (1984) reports that retention limits vary generally from a low of 0.5 percent of capital and surplus to a high of 2.0 percent. He recommends a retention limit equal to 2.0 percent of capital and surplus but provides no justification for this recommendation. Taylor, et al. (1967/1968) report the results of a survey of 104 life insurers that shows retention limits of 1.0 to 1.5 percent of capital and surplus, with the percentage decreasing as capital an surplus increase. Munich American Reassurance Company (1988) summarizes its survey results on ordinary life retention limits according to insurer distributions by total assets, capital and surplus, and the amount of ordinary business in-force, each a variation of insurer size.

(2) The Cattell's Scree Test plots the variance accounted for by each principal component on the characteristic roots and principal components space, and it deletes all components that lie beyond a "bendpoint' in the curve. The Kaiser's mineigen criterion retains principal components with eigenvalues exceeding unity. for the rationale of these criteria, see Cattell (1966) and Cattell and Vogelmann (1977).

(3) See Green (1978) for a discussion of various rotation methods, including the varimax method.

(4) The authors believe that a principal components regression model is the appropriate model to use here. It is acknowledged, however, that the results when projected back in terms of the original variables are sensitive to some methodological details (e.g., the number of components retained).

(5) Due to smaller margins available, term insurance may be subject to more stringent underwriting. If priced accordingly, term rates may not support reinsurance rates based on more liberal underwriting.

(6) It is reasonably safe to assess the relative importance of the six factors in the sense that while a multicollinearity problem is not present, the standardized regression coefficients are still sensitive to the spacings of the observations on the independent variables. See p. 262 of Neter, et al. (1985).

References

Beliveau, Barbara C., 1984, A Signalling Model of Reinsurance, Journal of Insurance, 7: 69-83. Benktander, Gunnar, 1975, A Note on Optimal Reinsurance, Astin Bulletin, 8: 154-63. Best's Insurance Reports, annual, Life and Health edition (Oldwick, NJ: A.M. Best Company, Inc.). Black, Kenneth, Jr. and Harold D. Skipper, Jr., 1987, Life Insurance, Eleventh edition (Englewood Cliffs, NJ: Prentice-Hall, Inc.). Borch, Karl, 1962, Equilibrium in a Reinsurance Market, Econometrica, 30: 424-44. _______, 1974, The Mathematical Theory of Insurance, (Lexington, Mass.: Lexington Books). Cardinal, Clayton A., 1984, On Life Reinsurance, Best's Review: Life-Health, (October): 76-80 and 151. Cattell, Raymond B., 1966, The Scree Test for the Number of Factors, Multivariate Behavioral Research, 1: 245-76. _______, and S. Vogelmann, 1977, A Comprehensive Trial of the Scree and KG Criteria for Determining the Number of Factors, Multivariate Behavioral Research, 12: 289-325. Dowsley, Gordon, 1982, The Explosion of Reinsurance in Financial Planning, Best's Review: Life-Health, (August): 22, 24, 94, and 96. Dukes, Jeffrey T., 1982, The Revitalization of Reinsurance, Best's Review: Life-Health, (July): 20, 22, and 98. Gold, Melvin L., 1978, Reinsurance: Why and How? Best's Review: Life-Health, (November): 16, 18, and 74-6. Gottheimer, George M., 1983, A Strategy for Reinsurance Management, CPCU Journal, 36: 206-18. Green, Paul E., 1978, Analyzing Multivariate Data, (Hinsdale, IL: The Dryden Press). Mayers, David and Clifford W. Smith, Jr., 1990, On the Corporate Demand for Insurance: Evidence from the Reinsurance Market, Journal of Business, 63: 19-40. Mossin, Jan. 1968, Aspects of Rational Insurance Purchasing, Journal of Political Economy, 76: 553-68. Munich American Reassurance Company, 1988, Life Insurance Company Ordinary and Group Retention Survey, (Atlanta, GA: Munich American Reassurance Company). Neter, John; William Wasserman; and Michael H. Kunter, 1985, Applied Linear Statistical Models, Second edition (Homewood, IL: Richard D. Irwin, Inc.). Pentikainen, T. "On the Net Retention and Solvency of Insurance Companies." Skandinavisk Aktuarietidskrift, 35 (1952): 71-92. Pressacco, F., 1979, Value and Prices in a Reinsurance Market, Astin Bulletin, 10: 263-73. Rosenthal, Irving, 1947, Limits of Retention for Ordinary Life Insurance, The Record, AIA, 36:6-22. Samson, Danny and Howard Thomas, 1983, Reinsurance Decision Making and Expected Utility, The Journal of Risk and Insurance, 50:249-64. Taylor, R. H.; J. C. Wooddy; H. G. Verbeek; and A. Jacob, 1967/1968, Panel; Retention Limits and Stop-Loss Reinsurance, Proceedings, CAPP, 17:70-94. Verbeek, Henry G., 1966, On Optimal Reinsurance, Astin Bulletin, 4:29-38. Wiser, Ronald F., 1985, To Buy or Not to Buy Reinsurance, Best's Review: Property-Casualty, (February): 70-9.

The life reinsurance decision centers on the establishment of retention limits. Retention is the amount of any insured loss to be borne by the primary (or ceding) company. Life retention limits normally are expressed as an amount per insured life. Claim amounts in excess of the insurer's retention are the responsibility of its reinsurers. This study examine the relationship between the size of ceding companies' retention limits and certain insurer characteristics.

The setting of an appropriate retention limits is a non-trivial decision for an insurer. It ultimately affects both the risk exposure and the profitability of the ceding company. It establishes the maximum individual claim amount that the insurer believes it can tolerate, given its financial and operating characteristics. Further, the dollar retention limit is directly related to other elements in the total reinsurance process. For example, an automatic binding limit (i.e., the maximum amount for which the ceding insurer binds the reinsurer under an automatic reinsurance treaty) is usually expressed as a multiple of the retention limit. Second, a subsequent increase in the retention limit affects the amount of previously ceded insurance that the primary insurer can recapture.

It can be expected, a priori, that different financial and operational characteristics of life insurers, together with differences in their products and markets, will lead to varying motives for establishing retention limits. This study seeks to shed light on insurer characteristics that may account for differences in these retention limits.

Literature Review

The literature describing the various forms of reinsurance agreements is extensive. In the life insurance area, the works of Dowsley (1982), Dukes (1982), and Gold (1978) may be noted.

Prior work on the analysis of both life and property-liability reinsurance (and insurance) decision processes can be classified into three major categories: (1) objectives of reinsurance, (2) normative methods, and (3) empirical studies. Each category is discussed below.

Objective of Reinsurance

A review of the literature suggests numerous objectives of reinsurance. The following listing of the primary uses and objectives of life reinsurance can be considered representative and reasonably exhaustive (if not redundant): (1) risk spreading-minimizing the concentration of risk, (2) surplus relief-reducing surplus strain caused by new business writings, (3) stabilization of overall mortality experience, (4) stabilization of operating results, (5) reduction in the probability of insolvency, (6) minimization of the potential for catastrophic losses, (7) transfer of investment or lapse risk, (8) take advantage of reinsurers' underwriting expertise, (9) transfer (or sell) certain classes of business (e.g., substandard issues), (10) increase the ceding company's capacity for growth, (11) tax minimization-in specific situations reinsurance may reduce the ceding company's tax liability, and (12) assist the ceding company when experimenting with a new market.

Normative Methods

Optimal reinsurance coverage was examined by Beliveau (1984), Mossin (1968), Samson and Thomas (1983), and Wiser (1985). Signaling equilibrium, expected utility, and simulation methodologies were used in determining optimal reinsurance levels.

Pareto optimal risk exchanges between insurers and the design of Pareto optimal reinsurance contracts were examined by Borch (1962, 1974), Benktander (1975), and Verbeek (1966). The equilibrium conditions necessary for reinsurance have been analyzed by Borch (1974) and Pressacco (1979).

The normative studies cited focused on the risk retention decision in property-liability insurance. Few published studies exist on the selection of life reinsurance retention limits, and none deal directly with the question of retention selection on a per insured life basis or relate the retention decision to an insurer's financial or other operating characteristics. Rosenthal (1947) examined the random portion of total mortality fluctuations and provided a simple method for determining the retention limit. His approach involved an application of the law of large numbers to the reinsurance decision. As expected, the number of insured lives and the variation in insurance amounts are the two important factors in his formula.

Pentikainen (1952) applied the concept of collective risk theory to the retention limit problem. Setting a probability of ruin of 1.0 percent, he provided a formula for retention limit establishment. The collective risk theory approach may be criticized both for its arbitrary nature in establishing the ruin probability and for its emphasis on "safety first."

Empirical Studies

Mayers and Smith (1990) examined the relationship between a property-liability insurer's overall level of reinsurance and selected financial and operating characteristics. The Mayers and Smith study focused on aggregate reinsurance demand for all insured exposures, while the current study examines reinsurance demand per insured exposure. This leads to the use of a different dependent variable (i.e., a ratio of aggregate reinsurance premiums ceded to total premiums vs. a per insured dollar retention limit) and the use of somewhat different regression methodology.

Gottheimer (1983) hypothesized a positive linear relationship between the retention limit selected by a property-liability insurer and its assets, policyholders' surplus, premium volume, and loss ratio. Using stepwise regression, he concluded that the two most significant factors to consider in selecting an appropriate retention level were assets and premium volume. Although restricted to the retention decision in property-liability insurance, Gottheimer's approach is somewhat similar to that used in this study. No published empirical study on life retention limits exists, except some documentation of reinsurance and retention data on a limited scale.(1)

Research Methods

Specific Research Issues

The focus of this study is on the determinants of retention limits established by life insurers in proportional reinsurance transactions. The retention limit is defined as the amount of ordinary life insurance retained by the ceding insurer on the life of any insured individual (under all policies, collectively). For the companies included in the study, the retention limits varied from $25,000 to $20 million.

Although the major purpose of the study is to identify the various determinants of individual life retention limits and their relative importance, the final model can also be used to forecast retention limits in terms of specific company financial and operating characteristics. The primary hypothesis to be tested is that a linear relationship exists between the size of a ceding insurer's per insured life retention limit and selected insurer financial and operating variables.

Variable Selection and Specification

The defendant variable examined in this study is the ceding company's per insured life retention limit in dollars. The insurance literature suggests numerous possibilities for explanatory independent variables. Black and Skipper (1987, p.431) indicate that the size of the individual retention limit is a function of several economic and operational factors including insurer surplus, quality of the insurer's agents and underwriting staff, average policy size, distribution of insurance in force (e.g., by amount, grouping by age and sex), and distribution of new business.

Conceptually, other factors including amount of insurance in force, amount of new business written, premium volume, lapse rates, organization form (mutual vs. stock), asset size, profitability, and term/whole life mix potentially may affect the retention decision. Unquestionably, the prices that ceding companies pay for reinsurance should be a major factor in the ceding company's establishment of its retention limit.

Some of these variables cannot be (or have not been) measured quantitatively (e.g., quality of underwriting department). Also, publicly available data do not exist for other potential explanatory variables (e.g., reinsurance prices).

Ultimately, 17 independent variables were selected for analysis. Many of these variables probably measure the same (or similar) insurer characteristics. For example, company size can be measured in many ways, including admitted assets, capital and surplus, and premium volume (i.e., direct premiums written).

Selection of Sample and Data Sources

Several criteria were used in selecting the life insurer sample. Because the data needed for the study were obtained from the annual editions of Best's Insurance Reports, the first criterion, of necessity, is that information on the insurer is available in these annual reports. The 1988 life-health edition contains selected 1987 financial statement information, including retention limits, on approximately 1,600 U.S. and Canadian life and health insurers.

To avoid possible distortion in the results by very small life insurers, only those insurers with at least $100 million in total assets (less separate accounts) at the end of both 1986 and 1987 were selected. Further, relatively new companies (i.e., those commencing their operations after 1976) were omitted from the sample. Because Canadian insurer regulation differs from U.S. regulation, Canadian insurers were deleted from the sample. Also, fraternal benefit societies and savings bank life insurers were omitted because of their special structure and regulation.

Many life insurers are heavily engaged in the sale of annuities or health insurance. Because this study examines ceding company retention limits in ordinary life insurance transactions, only those insurers whose business is primarily the marketing of individually issued life insurance are examined. Thus, if a company's ratio of life reserves to net policy reserves equaled or exceeded 70 percent in both 1986 and 1987, the company was retained. Otherwise, the insurer was removed from any further analysis.

A few additional companies were omitted from the sample because of data insufficiency or other data problems. The resulting sample consisted of 97 life insurers whose admitted assets (including separate accounts) range from $108 million to $31.8 billion. The necessary data were collected for each of these insurers, their retention limits, and selected other data. the sample insurers, their retention limits, and selected other data.

Research Results

A cross-section multiple regression model was initially estimated. However, as noted above, several of the 17 selected independent variables that a priori might affect the level of retention limit were believed to measure similar insurer characteristics.

Diagnostics applied to the initial multiple regression model strongly suggested the possibility of multicollinearity. Principal components regression was employed to address the multicollinearity issue and to fully utilize information derived from the correlated variables.

Principal Components Analysis

Based on the Scree diagram and mineigen criterion,(2) six components (factors) were retained in the model. Table 1 shows the initial factor loadings matrix whose elements are correlation coefficients between the original 17 variables and the six factors.

[TABULAR DATA OMITTED]

The six factors account for 87 percent of the total variance in the 17 explanatory variables. Using the varimax rotation method, the six factors were rotated again to improve result interpretability.(3) Table 2 shows the varimax factor loadings matrix.

[TABULAR DATA OMITTED]

A principal components regression model using the six varimax rotated factors as explanatory variables is estimated through ordinary least squares (OLS).(4) Table 3 shows the tentatively named factors, their regression coefficients, and t-statistics (in parentheses below the corresponding coefficient). The overall model is statistically significant at a p-value of 0.0001. The coefficients of five of the factors (or insurer characteristics) are significant at the 0.01 level, with the profitability coefficient significant at the 0.10 level.

[TABULAR DATA OMITTED]

As seen in Table 3, the dependent variable is the square root of the dollar retention limit. This transformation was performed to better meet the homeskedasticity assumption that underlies the OLS model.

Interpretation of the Regression Relationship

As is common in studies using factor and component analysis, a certain amount of judgment must be used in explaining the results. Factor 1 has been identified as the mutuality dimension. This is because high correlations were found between Factor 1 and the ratios of participating insurance to total insurance (both new and in-force business), mutual form of organization, and the ratio of policyholder dividends to direct premiums written. Participating life insurance and policyholder dividends are characteristic of mutual life insurers. The expected sign for this factor was positive because, in general, premiums for participating life insurance have built-in margins for dividends and, hence, result in a larger premium inflow, ceteris paribus. This fact should provide some additional margin to absorb unusual fluctuations and, therefore, should result in larger retentions.

The model sign for Factor 1 is positive. Thus, higher retention limits are associated with the mutuality dimension. Because the mutuality dimension is orthogonal to the "firm size" dimension (factor), these findings are not explained by the fact that, in general, mutual life insurers are of substantial size. Other reasons might also underlie the observed relationship. Many stock life insurers reinsure significant amounts of their direct writings with a parent insurer or other members of a controlled group of insurers. Since mutual companies cannot be owned by another entity, no possibility exists of a pass-through of insurance (through reinsurance transactions) to an insurance company parent. This difference in ownership may partly account for a lower retention limit for stock insurers.

Factor 2 indicates a ceding company's concentration of its product lines in term insurance. This conclusion is evidenced by high loadings between Factor 2 and the four variables that represent ratios of term insurance to aggregate insurance amounts. It was believed that insurers specializing in term insurance would have lower retention limits because term life products, carrying proportionately larger net amounts at risk over time and smaller premium rates, were thought to represent more risk to the insurer, ceteris paribus.

However, the model sign for Factor 2 is positive. It may be that insurers concentrating in term insurance sales may be more aggressive in risk-taking and, therefore, may be more inclined to retain larger amounts. Additionally, because term premium rates are lower and margins smaller than those for whole life, it may also be that insurers with large proportions of term insurance desire to retain much of the face amount to maximize the available cash flow for investment purposes.(5) Again, since Factor 2 and the "average policy size" dimension are orthogonal, the larger policies typically sold in the term market do not explain the positive sign of Factor 2.

The positive sign observed in the model for Factor 3, firm size, is consistent with the expected sign. Firms with large admitted assets, capital and surplus, and premium volume would reasonably be expected to retain greater amounts of insurance. Insurers with large amounts of statutory capital and surplus can retain greater amounts per insured because they are less affected by surplus strain caused by the writing of new business.

The sign for average policy size (Factor 4) also is as expected. The positive relationship between average policy size and retention limit simply indicates that as average policy size increases, insurers show a greater willingness to retain larger amounts per insured life. This appears to be consistent with the use of reinsurance to minimize the potential adverse effects on a ceding company's financial and operating results arising from one or more large death claims - large in relation to the average death claim.

The negative sign observed for the profitability dimension (Factor 5) contradicts the study's a priori expectation. The empirical finding suggests that higher profitability is associated with lower retention limits. Profitable insurers might utilize reinsurance for tax purposes to the extent that reinsurance may reduce taxable income. However, restraint should be exercised in attaching too much importance to this finding for several reasons. First, the coefficient is not statistically significant at the conventional level (i.e., 0.05 or less). Second, profitability was measured for a single year only. Insurers usually do not change their retention limits yearly, yet insurer profits may fluctuate widely from year to year. Also, this dimension measures the profitability of the total operations (i.e., group, individual, annuity) of the ceding company, whereas the retention limit is only for the insurer's ordinary product line. Further, the two variables most highly correlated with profitability (i.e., return on equity and the ratio of net operating gain to net premiums written) are measured on a statutory basis. Statutory profitability may be a poor indicator of an insurer's profitability when measured according to generally accepted accounting principles.

Factor 6 has been labeled " Concentration on new business." The two variables that exhibit the highest correlation with this dimension are lapse ratio and the ration of commissions to direct premiums written. The observed sign indicates that a negative relationship exists between an insurer's average lapse ratio and the size of its retention limit. A similar relationship exists between size of retention limit and the commissions ratio. These results are consistent with the contention that ceding companies with high lapse ratios and high commission expenses seek to transfer a portion of these costs to reinsurers through the use of smaller retention limits. High lapse rates and high commission expenses are often a direct result of a large volume of new sales, and in this event ceding insurers are likely using reinsurance for surplus relief.

Factor scores used to derive the regression equation have been standardized to a mean of zero and unit standard deviation. Further, since the factor scores are uncorrelated because of orthogonality, it is reasonably safe to address the relative influence of each factor on retention limits through examination of the [R.sup.2,s] and the regression coefficients.(6)

Table 3 shows that firm size is the most important factor, accounting for approximately 75 percent of the total variation in the retention limits. The other five factors are statistically significant, and they collectively explain slightly more than 14 percent of total variation. The most important of these factors are mutuality and concentration on new business. The profitability factors accounts for only a nominal amount of the total variation in retention limits.

Summary and Conclusions

This study analytically examines life reinsurance retention limits on a per insured basis relationships to specific ceding company financial and operating characteristics. A principal components regression model applied to a sample of 97 U.S. life insurers shows that five factors (dimensions) are highly significant in explaining a ceding company's retention level. Of these five factors, firm size (measured by admitted assets, direct premiums written, and capital and surplus) appear to have the greatest impact on insurer retention limits. Collectively, the model explains nearly 90 percent of the total variation in retention limits for the sample insurers.

The authors have not addressed important questions such as: (1) Are primary insurers establishing their per insured retention levels in the most appropriate manner? (2) Are primary life insurer retention limits higher or lower than they should be? (3) What should be the relationship between overall insurer demand for reinsurance and individual insured retention limits? Further research is needed on these questions, especially the last.

(1) Cardinal (1984) reports that retention limits vary generally from a low of 0.5 percent of capital and surplus to a high of 2.0 percent. He recommends a retention limit equal to 2.0 percent of capital and surplus but provides no justification for this recommendation. Taylor, et al. (1967/1968) report the results of a survey of 104 life insurers that shows retention limits of 1.0 to 1.5 percent of capital and surplus, with the percentage decreasing as capital an surplus increase. Munich American Reassurance Company (1988) summarizes its survey results on ordinary life retention limits according to insurer distributions by total assets, capital and surplus, and the amount of ordinary business in-force, each a variation of insurer size.

(2) The Cattell's Scree Test plots the variance accounted for by each principal component on the characteristic roots and principal components space, and it deletes all components that lie beyond a "bendpoint' in the curve. The Kaiser's mineigen criterion retains principal components with eigenvalues exceeding unity. for the rationale of these criteria, see Cattell (1966) and Cattell and Vogelmann (1977).

(3) See Green (1978) for a discussion of various rotation methods, including the varimax method.

(4) The authors believe that a principal components regression model is the appropriate model to use here. It is acknowledged, however, that the results when projected back in terms of the original variables are sensitive to some methodological details (e.g., the number of components retained).

(5) Due to smaller margins available, term insurance may be subject to more stringent underwriting. If priced accordingly, term rates may not support reinsurance rates based on more liberal underwriting.

(6) It is reasonably safe to assess the relative importance of the six factors in the sense that while a multicollinearity problem is not present, the standardized regression coefficients are still sensitive to the spacings of the observations on the independent variables. See p. 262 of Neter, et al. (1985).

References

Beliveau, Barbara C., 1984, A Signalling Model of Reinsurance, Journal of Insurance, 7: 69-83. Benktander, Gunnar, 1975, A Note on Optimal Reinsurance, Astin Bulletin, 8: 154-63. Best's Insurance Reports, annual, Life and Health edition (Oldwick, NJ: A.M. Best Company, Inc.). Black, Kenneth, Jr. and Harold D. Skipper, Jr., 1987, Life Insurance, Eleventh edition (Englewood Cliffs, NJ: Prentice-Hall, Inc.). Borch, Karl, 1962, Equilibrium in a Reinsurance Market, Econometrica, 30: 424-44. _______, 1974, The Mathematical Theory of Insurance, (Lexington, Mass.: Lexington Books). Cardinal, Clayton A., 1984, On Life Reinsurance, Best's Review: Life-Health, (October): 76-80 and 151. Cattell, Raymond B., 1966, The Scree Test for the Number of Factors, Multivariate Behavioral Research, 1: 245-76. _______, and S. Vogelmann, 1977, A Comprehensive Trial of the Scree and KG Criteria for Determining the Number of Factors, Multivariate Behavioral Research, 12: 289-325. Dowsley, Gordon, 1982, The Explosion of Reinsurance in Financial Planning, Best's Review: Life-Health, (August): 22, 24, 94, and 96. Dukes, Jeffrey T., 1982, The Revitalization of Reinsurance, Best's Review: Life-Health, (July): 20, 22, and 98. Gold, Melvin L., 1978, Reinsurance: Why and How? Best's Review: Life-Health, (November): 16, 18, and 74-6. Gottheimer, George M., 1983, A Strategy for Reinsurance Management, CPCU Journal, 36: 206-18. Green, Paul E., 1978, Analyzing Multivariate Data, (Hinsdale, IL: The Dryden Press). Mayers, David and Clifford W. Smith, Jr., 1990, On the Corporate Demand for Insurance: Evidence from the Reinsurance Market, Journal of Business, 63: 19-40. Mossin, Jan. 1968, Aspects of Rational Insurance Purchasing, Journal of Political Economy, 76: 553-68. Munich American Reassurance Company, 1988, Life Insurance Company Ordinary and Group Retention Survey, (Atlanta, GA: Munich American Reassurance Company). Neter, John; William Wasserman; and Michael H. Kunter, 1985, Applied Linear Statistical Models, Second edition (Homewood, IL: Richard D. Irwin, Inc.). Pentikainen, T. "On the Net Retention and Solvency of Insurance Companies." Skandinavisk Aktuarietidskrift, 35 (1952): 71-92. Pressacco, F., 1979, Value and Prices in a Reinsurance Market, Astin Bulletin, 10: 263-73. Rosenthal, Irving, 1947, Limits of Retention for Ordinary Life Insurance, The Record, AIA, 36:6-22. Samson, Danny and Howard Thomas, 1983, Reinsurance Decision Making and Expected Utility, The Journal of Risk and Insurance, 50:249-64. Taylor, R. H.; J. C. Wooddy; H. G. Verbeek; and A. Jacob, 1967/1968, Panel; Retention Limits and Stop-Loss Reinsurance, Proceedings, CAPP, 17:70-94. Verbeek, Henry G., 1966, On Optimal Reinsurance, Astin Bulletin, 4:29-38. Wiser, Ronald F., 1985, To Buy or Not to Buy Reinsurance, Best's Review: Property-Casualty, (February): 70-9.

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Author: | Lee, Kwangbong; Palmer, Bruce A.; Skipper, Harold D., Jr. |
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Publication: | Journal of Risk and Insurance |

Date: | Mar 1, 1992 |

Words: | 3913 |

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