industry segmentation and predictor motifs for solvency

©The Journal of Risk and Insurance, 1999, Vol. 66, No. 1, 99-123.

Industry Segmentation and Predictor Motifs forSolvency Analysis of the Life/Health Insurance Industry

Etti G. Baranoff Thomas W. Sager

Robert C. Witt

ABSTRACT

This paper contributes one principal idea to the methodology of solvency studies for the lifeinsurance industry. The idea is grouping, which is applied in two different ways. First,companies are grouped into industry segments by insurer specialization or by size. Second,predictor variables are grouped into thematically related motifs. The primary benefits of groupingare improved solvency prediction and improved interpretation of predictors. Improved predictionresults from industry segmentation; improved interpretation from predictor motifs. The models aredeveloped by the technique of cascaded logistic regression, which forecasts solvency status onthe basis of motifs, rather than of individual variables. A key finding is that the segments differ intheir significant motifs in anticipated ways. For example, investment motifs are important forsolvency in the Life and Annuities segments, but not in the Health segment. A similar patterncharacterizes the difference between large and small insurers. The study covers the 1990 through1992 time period, when there were a historically high number of troubled companies.

INTRODUCTION

The financial condition of life and health insurance firms received substantialattention in the early 1990’s as a result of several prominent insolvencies andincreases in the number of troubled insurers generally. During the 1980’s, theNational Association of Insurance Commissioners (NAIC) created an automateddatabase covering most regulated insurers in the United States. The annual NAICcompilations extended previous databases by including small carriers.1

The advent of such large-scale databases has created both opportunities andchallenges for solvency studies. For example, the opportunity to extend solvencymodels to most firms in the entire industry, but the challenge of modeling anindustry heterogeneous in size and product specialty. The opportunity to discoverif a thorough combing of extensive accounting data can improve the

Etti G. Baranoff is Assistant Professor of Insurance at Virginia Commonwealth University. Thomas W.Sager is Professor of Statistics at the University of Texas at Austin. Robert C. Witt (deceased) was the GusS. Wortham Chairholder in Risk Management and Insurance at the University of Texas at Austin.1 Prior to the NAIC database, the most extensive data compilation was by A. M. Best, which excludes smallinsurers.

mailto:[email protected]

mailto:[email protected]

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understanding of insolvency, but the challenge of avoiding over-fit models thatwill not validate on new data.

This paper contributes one principal idea to the methodology of solvencystudies based on large-scale databases. The idea is grouping, which is applied intwo different ways. Envisioning the NAIC database as a spreadsheet in which therows represent insurers and the columns represent financial variables extractedfrom annual statements, we group the rows into industry segments by insurerspecialization or by size. We also group the columns by thematically relatedmotifs. Our purpose is to determine if grouping can improve solvency prediction,either in terms of improved prediction rates, or in terms of enhancedinterpretability. We find that it does both.

Grouping companies facilitates testing whether insolvency models vary acrossrecognizable industry segments. Grouping predictor variables by motifsimultaneously facilitates predictor selection and also adds an enhancedinterpretability feature. With a very large number of financial variables nowavailable to monitor solvency, the selection of predictors by automatic (stepwise)procedures runs a risk of selecting a predictor set with little logical inter-relationship and spuriously high success rate. Motifs help control these problems:Financial variables can be grouped into motifs by their logical relationships witheach other on a priori, non-computational grounds. The vector of variables ineach motif is then processed nonlinearly into a scalar. The computer theneffectively selects (stepwise) among the motifs, rather than among the variables.The number of motifs to select from is far less than the number of variables. Anda selected motif represents a set of variables that necessarily are logically inter-related. The motifs play a role analogous to that of the factors in a principalcomponents regression. The analyst can match the motifs that emerge assignificant for a segment with distinguishing characteristics of the segment tobetter understand the suites of characteristics important for solvency in thesegment. For example, we show that the motif of investment ratios -- rather thanspecific individual ratios -- is important for solvency in life and annuityspecialists.

It is shown that segmenting the industry by specialization or by size adds tothe explanatory power of solvency models. Moreover, it is also shown thatsegmentation results in improved insolvency prediction, compared with unitarymodeling of the entire industry, and that the models differ in anticipated waysamong segments. The implication for regulation is that a given financial behavioror condition may not be equally significant for solvency signaling across the entirelife/health insurance industry. For example, as discussed above, investment-related motifs are very important solvency predictors for life insurers specializingin life and annuity products, but are not at all important for health productspecialists. These motifs are also important for the segments of larger companies,but not in the solvency models of the very small insurers.

The study uses pooled data for the period of 1990 through 1992, when the lifeinsurance industry experienced a relatively large number of insolvencies and

Industry Segmentation and Predictor Motifs 101

troubled companies.2 The data regarding troubled companies was obtainedthrough a special call to the insurance departments in the various states for theyears 1991 and 1992.

PRIOR RESEARCH AND FOCUS OF THE STUDY

Prior Research

Statistical models for insolvency prediction began with the seminal work ofAltman (1968) and the work of Trieschmann and Pinches (1973) for theproperty/casualty (P/C) industry. Barniv and McDonald (1992) provided acomprehensive review of the entire solvency detection literature through 1992.More recent P/C solvency studies include the neural network approach ofBrockett, Cooper, Golden and Pitaktong (1994). Additionally, a comparisonbetween the logit models and hazard models of Lee and Urrutia (1996), both withmatched-pair samples; the whole-database studies of Cummins, Harrington, andKlein (1995) on risk-based capital and insolvency; and Barniv and Hathorn(1997) on mergers and insolvency.

Most life/health solvency studies have appeared after 1990 and also show amigration from matched-pairs samples to whole-industry analyses with the adventof the NAIC databases. Barniv and Hershbarger (1990) used matched-pairsampling of pooled data from 1975 to 1985 to correctly classify the insolvencystatus of between eighty-two and ninety-one percent of life insurers one and twoyears in advance. More recently, Ambrose and Carroll (1994) used matched-pairsampling of pooled data from 1969 to 1986 to predict life insolvencies for 1987 to1991. They attribute their finding of relatively low predictive power to temporalchanges in the factors responsible for insolvency over long time spans.3 Using theNAIC database for 1986 through 1991, Carson and Hoyt (1995) compared logisticregression, recursive partitioning, and discriminant analysis for predicting lifeinsolvencies. Although they did not analyze segments, they conjectured that“models segregated by insurer size and product line also may yield additionalinsights into the problem of insurer insolvency.”

Focus of the Study

The primary aim of this study is to determine whether segmentation of thelife/health insurance industry by product specialty or size can improve solvencymodels. Improvement may be assessed quantitatively by an increase in power topredict insolvency and/or qualitatively through new insight-generating tools (byrelating the unique characteristics of a specialty or size segment to the significantmotifs of the solvency models.) Even if it was not possible to improve insolvency

2 The advantage of a short pooling period is a built-in control for dynamic changes in the industry. If theinsolvency count had been much lower, a longer pooling period might have been necessary.3 The first major work to utilize the unaudited NAIC life database was the dissertation of Cheong (1991),who recognized the desirability of segmenting the industry, but did not achieve high predictive power.


prediction, the creation of tools (such as the two-stage cascaded logisticregression) for generating new insights about insolvency may justify the exercise.

The advent of the NAIC files extends database coverage to small insurers,which not only are more heterogeneous in specialty, financial behavior andcondition, but also suffer more insolvencies than larger insurers. Additionally, theelectronic availability of large portions of annual statement data provides a muchlarger pool of financial and accounting variables for analysis. Careful exploitationof this vast data resource requires new approaches to realize its opportunities andavoid its pitfalls.

This study organizes the NAIC annual statement data into large-scalestructures in order to exploit its potential in an intuitive, but systematic manner.A large number of financial ratios were developed to represent many pages of theannual statement. These ratios were sorted into categories by common functionalmotif. For example, the investment motif was the largest category; other motifcategories included assets, liquidity, expenses, etc. To build solvency predictionmodels using motif categories, this study adopts the cascaded logistic regressionmethodology explained later.

DATA AND METHODOLOGY

Data

For this study, the solvency status of life insurers was determined by a special-purpose survey of all insurance regulation agencies in the fifty States. Aninsolvent insurer was defined as a company that was placed in supervision,rehabilitation, conservatorship or liquidation during 1991 or 1992.4 Theclassification of a company as insolvent was limited to these official actions forthe sake of consistency of definition across the fifty States. This definitionresulted in ninety-one life insurers classified as insolvent: forty-nine in 1991, andforty-two in 1992 (see Table 1). With such historically high counts, it was notnecessary to pool insolvencies across many years to accumulate statisticallypowerful sample sizes, as in several other studies. Two years of pooling weresufficient. Longitudinal pooling potentially runs the risk of losing power due todynamic changes in the causes of insolvency. By using data from a short periodof time, this study therefore mitigates the effects of any such temporal trends.Moreover, the set of available predictor variables will also be consistent for thestudy years.

For each insurer classified as solvent or insolvent in 1991, predictor variableswere obtained from the NAIC life insurer database for 1990. Similarly, for eachinsurer classified as solvent or insolvent in 1992, predictor variables wereobtained from the NAIC life insurer database for 1991. By “1990 data” we meanthe 1990 predictors and 1991 solvency status. Similarly, “1991 data” means 1991predictors and 1992 solvency status. We shall therefore examine one-year-ahead

4 Supervision includes confidential supervisions. Thus, our data included information not readily availablefrom public information sources.


forecasting of solvency status. In a version of this research done earlier for theTexas Department of Insurance, two-year-ahead forecasting was studied, withsomewhat comparable results (Baranoff 1993).

The Journal of Risk and Insurance

TABLE 1Sample Data Sets for Creating the Solvency Prediction Models

Entire Data Set a

1990 1991Estimation Data Set:

Pooled 1990/91 SubsetValidation Data Set:

Pooled 1990/91 SubsetSpecialty Segment b Insolvent Solvent Insolvent Solvent Insolvent Solvent Insolvent Solvent

Life & Annuities 10 590 10 596 10 315 9 316Health 13 252 11 252 12 135 12 136Reinsurance 4 370 5 389 4 218 5 217Combination 13 617 3 587 8 267 7 266Not assigned 9 6 13 6

Total 49 1835 42 1830 34 935 33 935Size Segment c

Large & Medium 18 849 4 847 11 437 11 436Small 10 414 7 408 8 212 8 213Very Small 12 570 18 574 15 286 14 286Not assigned 9 2 13 1

Total 49 1835 42 1830 34 935 33 935

a Before elimination for missing datab A company was assigned to a given specialty segment by product line if the company derived over seventy percent of its direct premium writing from that line. Initially, fourspecialty segments were defined: annuities, life, health, and reinsurance.c Large/Medium companies have assets exceeding $25 million; small companies have assets between $25 and $5 million; and very small have less than $5 million.


Predictor motifs. To identify appropriate predictor variables, we combedprior research and consulted regulatory analysts to identify more than 200 relevantfinancial ratios and variables that could be calculated from NAIC annualstatement data. More than 100 remained after eliminating variables with toomany missing values. To bring some order to this array of predictors, eachpredictor was reviewed manually and assigned a unique motif based on the themeof the annual statement page where the predictor is found or on the perceivedrelevance of the predictor to a given functional category. The functional motifcategories are: Affiliated, Assets, Capitalization, Cash Flow, Leverage Related toPremium, Expenses, Investments, Liquidity, Results from Operations, Persistencyof Business, Reinsurance Activities, Reserves, Returns on all Business, SurplusChanges, Underwriting Results, and Product Mix. The large class of Investmentpredictor ratios was subdivided into three motifs on the basis of divisor of theratio: total assets, invested assets, or policyholders surplus. Descriptions ofpredictors used in the final models are shown in the appendix.5 It is not claimedthat the sorting of predictors into motifs is optimal in any theoretical or statisticalsense -- only that it groups variables that are clearly related on intuitive grounds,and therefore may provide explanatory power and/or qualitative insights intoimportant influences on insolvency.6

Segmentation. Segmentation is done by company specialty line and by size.A company was assigned to a given specialty segment by product line if thecompany derived over seventy percent of its premium writing from that line.Initially, four specialty segments were defined: annuities, life, health, andreinsurance. But since only three companies were insolvent in the annuitysegment, the annuities segment was combined with the life segment companies.Insurers unassigned by the seventy percent test were placed into a “combinationspecialty.”7 Size segments were defined on the basis of total insurer assets.Large/Medium companies have assets exceeding $25 million; Small companieshave assets between $25 and $5 million; and Very Small have less than $5million.8

5 The appendix breaks down the specific ratios of each motif that appears in any of the models. Theappendix also provides the actual sign of all surviving financial ratios represented in the final insolvencymodels. Because of the large number of ratios used in this study, the analytical procedures emphasize themotifs rather than the individual ratios.6 One line of evidence provides some statistical justification for the motifs: All pairwise correlationsbetween the variables in a given motif were calculated and squared (excluding the correlation between avariable and itself). The mean of these squared correlations is an index of the degree of coherence amongthe predictors in a given motif. Then all correlations between variables in the motif and variables not in thegiven motif were calculated and squared. The mean of the latter should be smaller than the mean of theformer if the motifs are successful in grouping related variables. The average “between” R-square was0.03; the average “within” R-square was 0.12.7 In general, the product specialties become more distinctive and homogeneous if the seventy percentcriterion is raised, and they become less distinctive and more heterogeneous if the criterion is lowered. Theprediction models also become more successful at higher levels, and less successful at lower levels (thelower the level, the less differentiated the segment is, hence the more the models resemble a unitary model.)However, at higher levels the number of insolvencies is reduced, thus making model validation moreproblematic.8 The Large/Medium segment consolidates four size segments in order to obtain sufficient insolvencies.


Expectations. We expect that the Investment motifs will play a moreimportant role for the Life/Annuity and the Large/Medium segments than for theHealth, Small and Very Small segments since Life/Annuity and Large insurersare exposed to greater investment risks than underwriting risk (Baranoff 1993).9

Methodology

The models pooled the 1990 and 1991 data into one data set and divided it into anestimation sample and a validation sample.10 The pooled 1990 through 1991 datacontain hundreds of companies appearing twice, once in 1990 and again in 1991.To avoid statistical problems arising from correlated observations, the estimationand validation samples were randomly selected in such a manner as to insure thatan insurer appears in one or the other sample, but not both. Furthermore, therandom selection was stratified so that the distribution of insolvencies by specialtyand size segments in the estimation sample would closely match thecorresponding distribution in the validation sample. A similar randomizationstrategy was employed by Barniv and Hathorn (1997). Table 1 shows thedistribution of insurers for the models. Of the original ninety-one insolvencies,sixty-seven remained after eliminations due to missing predictor values.

The cascaded two-stage stepwise logistic regression methodology. We used acascaded two-stage logistic regression11 to develop the solvency predictionmodels.12 For a given segment of companies, the first stage is a set of ordinary(stepwise) logistic regressions, each of which is specific to one of the motifcategories of the thematically related financial predictors. The stepwise process isemployed to reduce the number of predictors in a motif by eliminating thosewithout discriminatory power and by purging redundant predictors. Additionally,an entire motif category is eliminated if the category generally lacks

9 Larger companies enjoy the ability to compete in the lucrative financial intermediation markets and writea large portion of their product portfolio in annuities. Annuities do not pose as large an insurance risk ashealth insurance products (Baranoff 1993). However, annuities participation entails an aggressiveinvestment strategy in order to compete in the aggressively competitive financial intermediation market.Large insurers also have sufficient size to invest in private placements and own mutual investmentcompanies. We therefore expect the annuities segment and larger size segments to invest more aggressively.For more complete analysis of the comparison of risk exposure of the segments, see Baranoff’s dissertation(1993), chapters 1 and 3.10 Due to change in the distribution of insolvencies between 1991 and 1992 across the segments, estimationof the model with one year’s data and validation with the subsequent year’s was not possible for allsegments.11 Apparently the first to use the term "cascaded logistic regression" was Timothy B. Bell, Scott Szykownyand John J. Willingham (1991), where it was used in auditing to estimate the probability of fraudulentfinancial reporting.12 Because the number of insolvent companies is small relative to the number of solvent companies and thenumber of initial predictor variables is rather large in this study, there is a possibility that the nonlinearmaximum likelihood estimation procedures used in our logistic regression methodology may suffer fromestimation bias and distortions due to extreme outliers, skewed distributions, and a relatively small numberof insolvencies. In an attempt to address some of these concerns we supplemented the usual logisticregression analyses with a more robust non-parametric form of logistic regression in which the values of theoriginal predictor variables were replaced by their ranks. Results from the later analyses were similar tothose reported in Tables 4A and 4B. Nevertheless, in spite of these checks there may remain some bias incoefficient estimates due to the approximate nature of the asymptotic distribution theory for relatively smallsamples of insolvencies.


discriminatory power. For each company, the result of the first stage is a set of upto, but usually less than seventeen estimated probabilities, one probability for eachmotif with discriminatory power. The second stage is an additional logisticregression, in which the estimated probabilities from stage one become predictorsof insolvency. The result of stage two is a predictive equation that weights theprobabilities from stage one in an overall summary estimate of insolvencyprobability. The profile of motifs that emerge at stage two may help the analystunderstand which thematic categories contribute most to insurer insolvency andmay provide further insights into areas needing regulatory attention. The two-stage cascaded logistic regression bears some resemblance to ordinary two-stageleast squares regression,13 which can be viewed as the use of estimated dependentvalues from a first regression as independent predictors in a second stage.14 It isalso similar to the non-iterated version of the neural net model of Brockett, et al.(1994), which also re-weights logit probabilities.

Although the cascaded technique provides a more flexible model thanordinary logistic regression, its adoption in this paper is not for the purpose ofimproving solvency prediction. Rather, its role is two-fold: to facilitate automaticscreening of predictor motifs, and to generate new insights about insolvencies.Stage one primarily screens predictors; stage two screens motifs. By examiningthe motifs that emerge, an analyst or regulator can easily gain appreciation andinsight into the relative importance of behavioral motifs that are associated withinsolvency -- an appreciation facilitated by the fact that the scale for eachpredictor motif is measured in the same common unit (probability). Asimplemented in this study, the two-stages of the cascaded process are entirelyautomatic, although manual intervention is permitted. In this study, the automaticprocess is used to screen all of the constructed financial indicators. This permitsthe models to seek otherwise overlooked sources of explanatory power and ifnecessary to adapt dynamically to future changes in the set of motifs associatedwith insolvency. But the danger is that models fit on so large a set of initialpredictors may fail to predict insolvency through over-fitting. Thus, we give extraattention to validation issues.

EMPIRICAL RESULTS

Empirical Evidence for Industry Segmentation

For industry segmentation to be useful for solvency prediction, it is logicallynecessary that segmentation be an effective stratifier of the industry with respectto the predictors of solvency. Effective stratification necessitates that thesegments be heterogeneous from one segment to another but homogeneous withinsegments. Table 2 provides empirical evidence that this is the case. For

13 Theil (1971), pp 444-458. Also see in Econometrics Methods by J. Johnston (1984).14 There are also parallels between the cascaded approach and a two-step multivariate logit estimationprocedure proposed by Domencich and McFadden (1975) and further investigated by Amemiya (1978).Their two-step model is less efficient than the one-step model but computationally simpler. The form of thetwo-step model investigated by Amemiya is somewhat different from the cascaded model used here.


illustrative predictors, means and standard deviations are provided both byspecialty and by size segment. The non-parametric Kruskal-Wallis test rejectsequality of both specialty and size segments for all predictors shown. Weconclude that the segments are generally different from each other with respect tothe predictor set. Segmentation also increased homogeneity. For the completepredictor set, we calculated standard deviations both at industry level and atsegment level. For each segment about eighty percent of the predictors hadsmaller standard deviations within the segment than at industry level. The meanreduction in standard deviation from industry level to segment level averagedabout twenty-three percent.

Industry Segmentation and Predictor Motifs

TABLE 2Comparative Analysis of Specialty and Size Segments for Selected Ratios a

Specialty Segments Size SegmentsRatio c Statistic Life/Annuity Combine Health Reinsurance Large/ Medium Small Very SmallCAP01 Mean 68.96 74.94 64.76 47.12 81.37 59.05 43.18

Std 28.5 24.6 26.54 28.84 17.86 26.05 30.18CP02 Mean 1.22 3.35 8.14 2.95 4.31 3.33 1.37

Std 8.47 22.32 43.88 15.83 29.73 15.71 10.37INV01 Mean 5.46 4.84 5.31 7.6 6.82 6.14 3.28

Std 14.31 9.32 11.28 19.62 16.12 13.46 9.03INV03 Mean 7.89 10.29 3.63 1.35 9.65 4.75 2.82

Std 12.76 14.53 7.71 6.26 13.23 11.71 8.69INV06 Mean 0.36 0.34 0.16 0.05 0.3 0.27 0.18

Std 1.98 1.35 0.72 0.76 1 2.17 1.36INV07 Mean 0.52 0.82 0.89 0.21 0.62 0.76 0.44

Std 1.89 2.91 3.91 1.33 1.72 3.48 2.86INV18 Mean 20.46 30.8 31.87 30.25 33.98 35.74 8.48

Std 77.88 161.44 225.87 268.17 139.86 309.82 43.36INV33 Mean 3.41 4.2 1.63 1.59 4.76 1.85 0.83

Std 7.09 8.61 3.7 6.62 8.22 6.67 4.3INV54 Mean 3.19 12.11 0.71 0.23 9.14 1.42 0.33

Std 18.15 173.87 9.94 2.24 136.87 19.85 3.29


Table 2, cont.

MIXANN b Mean 0.23 0.18 0.01 0 0.23 0.06 0.03Std 0.37 0.22 0.03 0.02 0.31 0.19 0.15

MIXHLTH b Mean 0.05 0.25 0.92 0.01 0.23 0.29 0.2Std 0.08 0.21 0.1 0.04 0.31 0.37 0.34

MIXLIFE b Mean 0.71 0.42 0.06 0.01 0.4 0.37 0.36Std 0.36 0.19 0.07 0.06 0.34 0.37 0.43

OPE08 Mean -6.79 6.85 5.28 16.09 -3.86 14.33 8.96Std 381.51 32.81 39.2 98.2 317.58 34.46 81.37

UND01 Mean -5.12 -1.48 -1.09 2.13 -4.05 -1.42 1.47Std 15.56 35.05 21.37 14.16 5.84 15.25 42.47

a For all predictors, means are significantly different across specialty segments and across size segments by Kruskal-Wallis test at p < .0001.b The three MIX proportions sum to less than 100%. The balance is reinsurance activity, which is omitted to avoid creating a singularity in the models.c DESCRIPTIONS OF PREDICTORS FOR TABLE 2:CAP01 - Total liabilities as a % of total assets; CP2 - Total premiums and annuity and other fund deposits as a % of PHS; INV01 - Investments in common stocks as a % oftotal assets; INV03 - Investment in mortgage loans as a % to total invested assets; INV06 - Foreclosed real estate as a % of total invested assets; INV07 - Investment in realestate as a % to invested assets; INV18 - Investments in affiliates as a % of PHS; INV33 - Non-investment grade bonds (classes 3-6) as a % of total bonds; INV54 - Delinquentmortgages as a % of PHS; MIXANN - Written premiums in annuity products as a % of all written premiums; reinsurance assumptions and annuity considerations;MIXHEALTH - Written premiums in health products as a % of all written premiums; reinsurance assumptions and annuity considerations; MIXLIFE - Written premiums in lifeproducts as a % of all written premiums; reinsurance assumptions and annuity considerations; OPE08 - Net gain (excl. capital gains/losses) as a % of all sources of income;UND01 - Earning before investment income and taxes as a % of total assets.


As can be seen from the MIX variables in Table 2, the Large/Mediuminsurers wrote twenty-three percent of annuity business and thirty-nine percent oflife business (sixty-one percent for both), while only twenty-two percent of healthbusiness. In contrast, the Small segment wrote only six percent of the annuities,and the Very Small segment, three percent. The analyses of some investmentratios show that the Annuities/Life and Combination segments were on averagemore in foreclosed real estate and delinquent mortgages and in non-investmentgrade bonds (classes 3-6). The Very Small segment, on the other hand, held lessin these types of investments as compared to the larger companies.

The Models

Study of the segment models displayed in Table 3 reveals several noteworthyfeatures. First, we observe that the motifs represented in the models varyconsiderably among the segments. For example, among the specialty segments,only the Life/Annuity model involves investment motifs, as expected. On theother hand, the Health segment displays no investment motifs but the Liquiditymotif emerges, as expected, from the need for cash flow for this short-tail line.Similarly, for size segments, we find the models for the larger segmentsemphasize investment motifs: Large/Medium has two investment motifs; Smallhas one; Very Small has none.


TABLE 3Cascaded Logistic Regression Models for the Specialty & Size Segments Based on the Estimation Sample:

Parameter Estimate (Standard Error) e, f

Unitary Specialty Segments Unitary Size SegmentsMotif (Excl. reinsurance) Life & Annuity Combination Health Large & Medium Small Very small

Intercept-8.0968*(0.9717)

-5.3589*(0.7145)

-4.2355*(0.4901)

-8.4137*(2.158)

-7.03*(0.6268)

-7.1971*(1.2682)

-12.16*(3.2479)

-5.11*(0.6431)

Affiliated18.6866*(6.5079)

Assets8.4238**(5.0265)

-0.00 d

(0.00)-35.6456*

(11.81)

Capitalization (leverage)6.7342*(2.8906)

11.643*(5.6552)

5.47*(2.1988)

6.38*(1.7796)

Capitalization (in relationto premiums)

9.5403*(3.0703)

12.9508*(5.0132)

Expenses7.16*

(2.3038)13.3870*(5.0667)

Investment Group A a21.5046**(11.700)

13.9244(9.3493)

11.4909**(6.288)

Investment Group B b8.4462*(2.4248)

7.34*(1.8895)

14.9953*(3.3751)

13.84*(6.3536)

Investment Group C c6.0751**(3.2913)

7.7983*(2.4076)

5.91*(2.6665)

Liquidity5.6403**(2.8818)

8.7683**(5.1533)

7.00*(3.0552)

3.93(3.3722)


Table 3, continued

Operations - Gains andLosses

5.6038*(1.4112)

5.4013*(2.3702)

5.07*(1.2986)

17.2531*(5.4202)

11.05**(6.5598)

4.40*(1.7651)

Reinsurance6.2026**(3.2136)

Reserves7.3*

(2.9168)

Surplus15.9310*(4.4590)

10.4364*(3.2331

8.2034*(2.9615)

22.64*(6.1114)

52.43*(0.0128)

Underwriting(Gains/Losses)

Mix of Writing18.4392*(8.1032)

21.57*(6.494)

56.69*(21.4479)

11.64*(4.6259)

Pseudo-R2 42.8% 40% 28.7% 77.9% 39.0% 74.2% 68.8% 37.2%

a Group A ratios have Total Assets as denominator.b Group B ratios have Total Bonds as denominator.c Group C ratios have Policyholders Surplus as denominator.d For the unitary size segment model, the asset variable was forced into the model, but had essentially zero coefficient.e * indicates significance at 5%.f ** indicates significance at 10%


We also observe that the leverage and real estate predictors that played amajor role in the solvency models of Barniv and Hershbarger (1990) and Carsonand Hoyt (1995) emerge here for some, but not all of the segments. In our study,leverage and real estate are represented in the capitalization and investmentmotifs, respectively (see the Appendix to identify the individual ratios involved inthe significant motifs shown in Table 3).

Among the specialty and size models, there is a considerable variation in theexplanatory power, as represented by pseudo-R2. A possible reason for lowerexplanatory power for some segments is the regulatory lag in mandating reportingof new investment instruments used by the industry. The early 1990’s time periodof our study marked a modern zenith in the number of life insurer insolvencies,which derived in many cases from problems with real estate and mortgages. It ispossible that contemporaneous lack of sufficiently detailed information aboutthese investments affected the explanatory power of some of the segment models.Since then, more detailed reporting on real estate and mortgage activities has beenrequired for life insurer annual statements along with reporting of collateralizedmortgage obligations (CMOs).

Finally, the continuous product mix variables used to define the segmentsplay a role in the unitary models. However, the product mix motif does not enterthe specialty models, but does enter two of the size models. This furtherreinforces our view that specialty product line does matter for insolvency studiesand that segmentation is an effective means to model it.

Classification and Validation Results

Table 4A displays modeling results for specialty segments. The cut-off point forclassifying a company as insolvent on the basis of estimated probability ofinsolvency was selected by the “ratio of errors” methodology of Barniv andMcDonald (1992) and Carson and Hoyt (1995).15 The segment models incolumns 2-4 are developed separately for each segment and classification resultsare summed in column 5. For comparison purposes, the results of an industry-wide unitary model are shown in column 1. The unitary model includes thecontinuous product-mix variables used to segment the industry. Thus comparisonof columns 1 and 5 understates the effectiveness of product specialty forinsolvency prediction. Nevertheless, comparison of columns 1 and 5 showsspecialty segmentation to be advantageous. On balance, results for the estimationsample (section B of Table 4A) are slightly better for the segmented model thanthe unitary model, but results for the validation sample (section C of Table 4A)

15 The method selects the probability cut-off that results in equating the ratio of incorrectly classifiedinsolvent insurers to incorrectly classified solvent insurers within the estimation sample to the correspondingratio within the validation sample. For the life and annuity segment model, this ratio was about 0.26; forthe combination model, 0.38; for the health model, 0.10; for the unitary model (without reinsurance), 0.25.The ratios necessarily differ among segments because of the different rates of occurrence of insolvenciesamong the segments. For size segments, the same “ratio of errors” methodology was used: Thus, the ratiofor the large/medium model is 0.43, for the small model it is 0.29, and the very small model about 0.15.For the unitary model the ratio is about 0.23.


are distinctly superior for the segmented model. Results for the full sample(modeling the combined estimation and validation samples -- section A of Table2A) show that the segmented model maintains its advantage over the unitarymodel.

For size segments (Table 4B), the advantage of segmentation over the unitarymodel is even more pronounced than for specialty segmentation. The overallpercentage of correctly classified companies in the validation samples (Tables4A(C) and 4B(C)) is statistically significantly greater (p < .0001 chi-square test)for the segmented models in Column 5 of each Table than for the unitary model inColumn 1 of the corresponding Table.

The unitary and segmentation models shown here begin with the samepredictor set and apply the same model development process. Thus, thecontribution of segmentation can be judged here more clearly than in comparisonsbetween our segmentation models and other models that may not use the samepredictor set. For example, Carson and Hoyt (1995) also use the NAIC data, butfor a different time period and with different predictors to develop a unitarymodel. In general, their unitary model classifies and validates somewhat betterthan our unitary model, but somewhat less well than our segmentation models.

Since the purpose of our use of the cascaded methodology was not todemonstrate its predictive superiority over traditional one-stage logisticregression, we do not provide a detailed comparison. However, as might beexpected from the more general form of the cascaded model, the cascadedclassification and validation results in general are at least as good as those of one-stage logistic regression. But we do not claim statistically significantimprovement.


TABLE 4AClassification and Validation Results of the Cascaded Logistic Regressions for Specialty Segments:

Number(N) and Percent (%) Correctly Classified

(1) (2) (3) (4) (5)=(2)+(3)+(4)Unitary (Excl. Reinsurance) Life & Annuity Combination Health Specialty Segments Combined

A. Full Sample a N % N % N % N % N %Solvent 1022 74 409 68 444 85 217 82 1070 77Insolvent 42 72 15 79 12 80 21 88 48 83Overall 1064 74 424 68 456 85 238 82 1118 77

B. Estimation Sample N % N % N % N % N %Solvent 588 84 209 70 227 86 120 90 556 80Insolvent 25 83 8 80 6 75 12 100 26 87Overall 613 84 217 70 233 86 132 91 582 80

C. Validation Sample N % N % N % N % N %Solvent 478 69 235 74 212 80 100 74 547 76Insolvent 19 68 9 100 5 71 10 83 24 86Overall 497 69 244 75 217 79 110 74 571 77

a For the full sample (Section A), the counts are based on the Lachenbruch jackknife method of estimating probability of insolvency. For the estimation sample (Section B) andthe validation sample (Section C), the counts are based on the actual probability of insolvency, as calculated from the model, being above or below the probability cutoff.


TABLE 4BClassification and Validation Results of the Cascaded Logistic Regressions for Size Segments:

Number (N) and Percent (%) Correctly Classified

(1) (2) (3) (4) (5)=(2)+(3)+(4)Unitary Large & Medium Small Very small Size Segments Combined

A. Full Sample a N % N % N % N % N %Solvent 1240 69 773 89 384 93 384 73 1541 85Insolvent 54 81 18 82 13 81 26 90 57 85Overall 1294 69 791 89 397 93 410 74 1598 85

B. Estimation Sample N % N % N % N % N %Solvent 696 77 431 99 202 98 207 78 840 93Insolvent 29 85 10 91 7 88 13 87 30 88Overall 725 77 441 99 209 98 220 79 870 93

C. Validation Sample N % N % N % N % N %Solvent 607 65 343 80 177 83 208 73 728 78Insolvent 24 73 8 73 6 75 12 86 26 79Overall 631 65 351 79 183 83 220 73 754 78

a For the full sample (Section A), the counts are based on the Lachenbruch jackknife method of estimating probability of insolvency. For the estimation sample (Section B) andthe validation sample (Section C), the counts are based on the actual probability of insolvency, as calculated from the model, being above or below the probability cutoff.


CONCLUSION

The main focus of this research has been on the usefulness of product specialtyand size segmentation for studies of Life/Health insurer insolvency. But we havealso introduced an effective method for dealing with the vast number of variablesthat are now tracked to monitor firm solvency. Grouping the predictor set intothematically related motifs both facilitates variable screening and also adds aninterpretability feature to the resulting models. The models identify generalthemes of variables that are significant for solvency by segment. The analyst canmatch the themes to distinguishing characteristics of the segments to betterunderstand the origins of insolvency in specific segments. The technique ofcascaded logistic regression implements the screening of motif predictors in stage1, and constructs the insolvency models in stage 2. The technique worksautomatically, without break between stages and without user intervention, and isat least as successful at forecasting solvency status as ordinary one-stage logisticregression. The result at the end of stage 2 is a model for estimating the hazard ofinsolvency, with the pattern of motifs that emerge providing insight into thediffering roles of predictor themes among industry segments. It was found, forexample, that investment-related factors figured prominently in solvencypredictions for larger companies and for Life/Annuity insurers. The main findingis that segmentation improves upon whole-industry models. Models specializedby product line and by size estimate and cross-validate better than unitary models.Additionally, the motifs that emerge as significant for insolvency prediction areconsistent with our expectations.


APPENDIX

The Stage 1 Signs of Remaining Ratios Whose Motifs Survive Stage 2 a, b, c

Unitary SIZE SEGMENTS UnitarySPECIALTYSEGMENTS

(incl.Reins.)

Large&

Med. SmallVerySmall

(excl.Reins.)

Life&

Ann. Comb. HealthAffiliatedAFF23 (-)*AssetsASS03ASS07 (+)*ASS11 (+)*Capitalization (leverage)CAP01 (+)* (+)*CAP02 (+)**CAP04 (-)** (-)* (-)**Capitalization (in relation to premiums)CP02 (+)*CP06 (-)* (-)*CP07CP08 (+)* (+)*ExpensesEXP01 (-)*EXP02 (+)** (+)**EXP05 (+)* (+)*EXP07 (+)*EXP08Investment Group A (as a % of Total Assets)INV00 (+)* (+)**INV01 (+)INV11 (-)*Investment Group B (as a % of Total Bonds)INV03 (+)*INV05 (+)**INV06INV07 (+)* (+)* (+)* (+)*INV08 (+)*INV10 (+)*INV33 (+)* (+)* (+)*Investment Group C (as a % of PHS)INV14 (-)* (-)* (-)*INV17 (+)INV18 (+)** (+)**INV34 (+)*INV54


Appendix, cont.

LiquidityLIQ04LIQ08 (+)* (+)* (+)* (+)*Operations - Gains and LossesOPE06 (-)* (-)* (-)*OPE07OPE08 (-)* (-)*OPE28 (+)* (+)OPE29 (-)* (-)*ReinsuranceREIN28REIN32 (+)*ReservesRES03RES04RES10 (+)*SurplusSUR01 (-)*SUR11 (+)* (+)* (+)*SUR14 (+)* (+)*Underwriting (Gains/Losses)UND01 (-)*UND09 (-)*UND11 (+)**Mix Of WritingMIXANN (+)** (+)** (+)MIXHEALTH

(+)* (+)* (+)* (+)*

a The coefficient sign is in parentheses.b * indicates significance at 5% in stage 1.c ** indicate significance at 10% in stage 1.


Descriptions of Motif Predictors in the Appendix

AffiliatedAFF23 Affiliated investment income as a % of total investment incomeAssetsASS03 Federal income taxes recoverable as a % of PHSASS07 Aggregated write-ins for other than invested assets as a % of admitted

assetsASS11 Non-admitted assets as a % of admitted assetsCapitalization (leverage)CAP01 Total liabilities as a % of total assetsCAP02 Total liabilities as a % to PHSCAP04 Unassigned surplus as a % of total assetsCapitalization (in relation to premiums)CP02 Total premiums and annuity and other fund deposits as a % of PHSCP06 Total health premiums as a % of PHSCP07 Net life and annuity premiums as a percent of PHSCP08 Net written premiums as a % of total assetsExpensesEXP01 Net commission as a % of net written premiumsEXP02 Investment expense as a % of net invested assetsEXP05 Agents balance as a % of total admitted assetsEXP07 Salaries as a % of PHSEXP08 General expenses as a % of PHSInvestment Group A (as a % of Total Assets)INV00 Changes in asset mixINV01 Investments in common stocks as a % of total assetsINV11 Invested assets as a % of total assetsInvestment Group B (as a % of Total Bonds)INV03 Investment in mortgage loans as a % to total invested assetsINV05 Properties occupied by the company to total invested assetsINV06 Foreclosed real estate as a % of total invested assetsINV07 Investment in real estate as a % to invested assetsINV08 Collateral loans as a % of invested assetsINV10 Aggregate write-ins as a % of total invested assetsINV33 Non-investment grade bonds (classes 3-6) as a % of total bonds.Investment Group C (as a % of PHS)INV14 Investment in properties occupied by the company as a % of PHSINV17 Collateral loans as a % of PHSINV18 Investments in affiliates as a % of PHSINV34 Non-investment grade bonds (classes 3-6) as a % of PHSINV54 Delinquent mortgages as a % of PHSLiquidityLIQ04 Investment instruments maturing in less than a year as a % of total invested

assetsLIQ08 Last year’s benefits as matched to the liquid assets for the coming year

(asset-liability matching)


Operations Gains and LossesOPE06 Net income as a % of total revenuesOPE07 Gains from operations a % of PHSOPE08 Net gain (excl. capital gains/losses) as a % of all sources of incomeOPE28 Realized capital gain yieldOPE29 Unrealized capital gain yieldReinsuranceREIN28 Surplus relief (same as NAIC ratio)REIN32 Reinsurance recoverable as a % of PHSReservesRES03 Unearned premium for health reserves as a % of PHSRES04 Gross health aggregate reserves as a % of PHSRES10 Misc. Liabilities and aggregate write-ins for liabilities as a % of admitted

assetsSurplusSUR01 Unassigned surplus as a % of PHSSUR11 Number of decreases in the PHS in the past four yearsSUR14 Ceding commissions less assuming commissions as a % of PHSUnderwriting (Gains/Losses)UND01 Earning before investment income and taxes as a % of total assetsUND09 Net health underwriting gain/loses to PHSUND11 Underwriting gains/losses as a % of PHSMix Of WritingMIXANN Written premiums in annuity products as a % of all written premiums,

reinsurance assumptions and annuity considerations.MIXHEALTH

Written premiums in health products as a % of all written premiums,reinsurance assumptions and annuity considerations.

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industry segmentation and predictor motifs for solvency

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