Etti G. Baranoff
Associate Professor of Insurance
Virginia Commonwealth University
School of Business
1015 Floyd Avenue
Richmond, Virginia 23284-4000
(804) 828-3187 ebaranof@vcu.edu
Thomas W. Sager
Professor of Statistics
Department of Management Science and Information Systems
The University of Texas at Austin, CBA 5.202
Austin, Texas 78712-1175
(512) 471-3322
Thomas S. Shively
Professor of Statistics
Department of Management Science and Information Systems
The University of Texas at Austin, CBA 5.202
Austin, Texas 78712-1175
(512) 471-1753
Risk Theory Seminar 2004,
New York City
*This is work in progress. Please, do not quote without permission from the authors.

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ABSTRACT
We study the functional interrelationship between the capital ratio and asset risk (endogenous) and a set of categorical and continuous predetermined variables for the life insurance industry in the U.S. for the years 1994, 1997 and 2000. We introduce a flexible, non-linear simultaneous equations model, based on semiparametric splines (SSEM), new to such studies, as a tool for managerial discretion and regulatory forbearance. SSEM has both a linear component and a nonlinear component that utilizes stochastic splines. Two versions of the asset risk measures are considered in two separate models: regulatory asset risk and opportunity asset risk. The insurers’ regulatory asset risk is based on the school of thought that emphasizes the default risk of the asset portfolio. The insurers’ opportunity asset risk is based on the potential for both gain and loss resulting from volatility of returns of the asset portfolio. The theoretical backdrop includes two competing hypotheses. One predicts a positive interrelationship between capital and asset risk and the other predicts a negative interrelationship. Theoretical support for a positive interrelationship is found in agency theory, transaction cost economics (under monitoring), and regulatory and bankruptcy costs hypotheses. We term this set of theories the finite risk hypothesis because of the constraints they impose on total risk taking. Theoretical mechanisms that support a negative interrelationship include the risk subsidy generated by the existence of guarantee funds. The set of theories that predict an expansion of total risk taking we term the hypothesis of excessive risk taking.
The results of the semiparametric models tend to favor the finite risk hypothesis. However, the interrelationships between the capital ratio and asset risks are often not linear – and not always even monotone. They also vary by year in a way that may reflect effects of the market boom of the 1990’s. Leverage plots for some of the predetermined variables are strikingly nonlinear. Our results suggest that the interplay of economic and financial forces may be more complex than assumed by the linear models in common use. For example, firm behavior may depend on which range of predictor values the firm occupies.
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This is the first academic study in the capital structure literature to compare the simultaneous effects of two different measures of asset risk on the capital-to-asset ratio using a new, flexible, non-linear simultaneous equations model based on semiparametric splines (SSEM model) in two separate models. The study is done for the life insurance industry in the U.S. for the years 1994, 1997, and 2000. One asset risk measure is regulatory asset risk , which is based on the school of thought that emphasizes the default risk of the asset portfolio. The second is opportunity asset risk , which is based on the potential for both gain and loss resulting from volatility of returns of the asset portfolio. As summarized in Table 2, the regulatory asset risk tracks the C1
1
component of the current life risk-based capital measurement of asset risk (as in
Baranoff and Sager, 2002 and 2003). The regulatory objective behind this measure is to protect against insolvency by assessing the downside risk of the asset portfolio. Regulatory asset risk is essentially a weighted average of the asset portfolio, with higher weights assigned to riskier asset categories. The opportunity asset risk, on the other hand, reflects potential for gain as well as loss. It measures the potential variability of returns on the firm’s allocation of assets. Given the importance of variability in portfolio theory, opportunity asset risk has a natural role in the firm’s drive to maximize value.
1 Life RBC formula comprised four components related to different categories of risk: asset risk (C-1), insurance risk (C-2), interest rate risk (C-3), and business risk (C-4). Each of the four categories of risk is a dollar figure representing a minimum amount of capital required to cover the corresponding risk. In 1996, the National Association of Insurance Commissioners
(NAIC) added changes to C-1 risk. Some of these changes relate to derivative instruments. Another major change was the creation of C-0 risk for investment of affiliated companies. The risk-based capital formula combines these five components into a single composite measure called RBC authorized capital.
RBC Authorized Capital = (C-0)+(C-4) + Square Root of [(C-1 + C-3) 2 + (C-2) 2 ] x 50%
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In the era of extensive practical and academic developments in financial risk management for capital structure, the tools that are used have become critically important. If current measures of asset risk prove incapable of predicting the future, as suggested by Jackson and Perraudin
(2000), and Mitchell and Mester (2004),
2
neither regulators nor managers should feel confident that prescribed capital minima adequately respond to institutional risks. Some studies regarding the impact of asset risk on minimum capital were published by the Journal of Banking in Finance
(2004). These studies respond to issues that were raised especially with the new Basel Accord II.
(See Mitchell and Mester (2004) for a summary.) Insurance regulators are currently working on risk assessment changes at the National Association of Insurance Commissioners (NAIC)
3
to augment the current risk-based capital formulas for both the property/casualty and life/health industries.
This study presents two model analyses. In the first (“regulatory”) analysis, we study the interrelationship between the capital ratio and regulatory asset risk in the context of appropriate control variables, which include the business focus variables suggested by the business strategy hypothesis (see Baranoff and Sager, 2003). The theoretical backdrop for the regulatory analysis is dominated by two competing hypotheses regarding the interrelationship between capital structure and asset risk (see Baranoff and Sager, 2002 and 2003) that can be summarized in the phrases finite risk and excessive risk . On the one side, there are agency theory, transaction cost economics (under monitoring), and regulatory and bankruptcy cost theories that tend to predict a positive interrelationship between capital structure and asset risk. We term this set of theories
2 The January 2000 issue of the Journal of Banking and Finance is a special issue on credit risk modeling and regulatory issues. The overview paper by Jackson and Perradin therein provides a summary of the shortcomings of the main models in use by financial institutions and banks to measure credit risk. In April, 2004 that journal produced another special issue dedicated to retail credit risk management and measurement pursuant to Basel
Accord II.
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Working Paper – Draft the finite risk hypothesis . The name is suggested by the limiting of risk that occurs when a reduction in leverage (increased capital ratio) accompanies an increase in asset risk. On the other side, there are theories that predict a negative interrelationship between capital and asset risk. A major supporting mechanism for this prediction is the risk-subsidy generated by the existence of guarantee funds. We term this set of theories the hypothesis of excessive risk taking . The name is suggested by the expansion of risk that occurs when increased leverage (lower capital ratio) accompanies an increased asset risk. In earlier studies with different modeling contexts
(Baranoff and Sager (2002, 2003)), the authors found higher regulatory asset risk associated with higher capital-to-asset ratios, thus supporting the finite risk hypothesis. In this study, the semiparametric nature of the model reveals more complex interrelationships, suggesting a more complex financial and economic picture. In general, finite risk tends to prevail, but the nature of the relationship may vary by year and may even vary among different ranges of the predictor values.
The second model (“opportunity”) analysis parallels the first. We examine the interrelationship between the capital ratio and opportunity asset risk, again in the context of appropriate control variables. The only difference between the first and second analyses consists in swapping the regulatory asset risk measure with the opportunity asset risk measure. As noted, the opportunity asset risk measures the variability of potential returns on the insurer asset portfolio. This asset risk does not take the actual returns of a firm’s asset classes, but uses proxies of returns from parallel macroeconomic indices. For example, instead of applying the actual firm-specific yield to the firm’s high-quality corporate bonds, we apply the prevailing
AAA bond rate. The returns are therefore hypothetical – what the company could have earned if
3 For the Spring 2004 meeting of the NAIC, the Risk assessment Working Group created an agenda that suggests that insurance regulators are in the beginning stages of developing a more sophisticated approach to assessing risk
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Working Paper – Draft it had invested its assets in those instruments measured by the macroeconomic indices that we used.
4 Differences in opportunity asset risk among insurers thus reflect differences in insurers’ asset allocation decisions (see Table 2 for a summary). The measure provides a benchmark of opportunity asset risk available in the market.
The theoretical backdrop for the interrelationship between capital structure and opportunity asset risk parallels that of regulatory asset risk, but is augmented by the role of returns. Competing predictions of positive and negative interrelationships are again predicted by finite and excessive risk, respectively. But additional support for both predictions can be found in Berger (1995), who studied the relationship between capital and returns. We extend and apply
Berger’s theoretical discussion to deduce implied interrelationships between opportunity asset risk and capital through the link provided by returns. Those arguments augment, rather than supplant, the finite and excessive risk hypotheses. The effect of a change in earnings (returns) depends on whether the finite or the excessive risk regime prevails, whether markets are perfect or not, whether firms retain their earnings and the effects of the tax shield of debt relative to equity. If finite risk and the relaxation of perfect markets prevail along with retention of earnings, then we expect opportunity asset risk and capital to have positive interaction. If excessive risk, perfect markets and tax shield dominate, then we expect negative interaction.
As noted in Figure 1, opportunity asset risk may be considered to touch more broadly on the spectrum of insurer risks than the regulatory asset risk does. Opportunity asset risk is also an important managerial tool for a firm to benchmark its strategic capital structure and asset allocation decision, not for a minimum capital requirement, but in order to achieve value maximization. Opportunity asset risk assesses the variability in returns faced by a hypothetical above and beyond the risk-based capital requirements.
4 The idea is, in part, an adaptation from the Cummins and Sommer (1996) study for the property/casualty industry.
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Working Paper – Draft firm that makes the same asset allocation decisions as the actual firm. The actual firm can benchmark against this figure by recomputing opportunity asset risk using its actual rates of return, rather than rates from market indices. On the other hand, regulatory asset risk has its own use as a benchmark – for regulatory forbearance and advisory minimum for managerial decision.
Since the SSEM model is extremely complex and our version has not previously been applied to simultaneous equations, we analyze annual data separately for each year, rather than time-series panel data. This avoids the additional complexity of autocorrelation. We selected the 1994, 1997 and 2000 life insurers statutory data from the National Association of Insurance
Commissioner (NAIC) database. The selection of these years is to capture the pre-boom in the stock market in 1994, the height of the bubble in 1997 and the subsequent collapse in 2000. The
SSEM model includes the following key features:

Automatic choice of linear or nonlinear model form, as appropriate

Flexible adaptation to the data through a large class of semiparametric model forms

Simultaneous equation modeling for specifying the structural relationship among endogenous and exogenous variables
To present the model results in a visually compelling format, we provide leverage plots
(see Results section). A leverage plot shows the estimated relationship between an endogenous variable and one of the model variables. In the plots included in this paper, we illustrate the relationships for a hypothetical (benchmark) insurer having a profile of values at industry median levels. Both the extent of nonlinearity and differences in the effect on capital between opportunity and regulatory asset risks are readily grasped by a glance at the leverage plots. Thus the leverage plot is designed as a useful tool for managers and regulators.
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The paper is structured as follows: The next section explains the observable variables.
Section III discusses the hypotheses. Section IV introduces the SSEM model and its importance. Section V provides the empirical results, featuring the leverage plots with their implications for the hypotheses and as benchmarking tool for both regulators and management.
The paper concludes with a summary.
The Data
Data were obtained from the NAIC database of insurers’ annual statements for the years
1994, 1997 and 2000. Each year had over one thousand active life insurers, ranging from very small to very large. Insurers with missing variables and a few outliers with anomalous data values were deleted. Table 1 provides summary statistics on the resulting sample, by year. The insurers for each year were randomly split into two subsets for the analyses. The models were developed on the first subset (“in sample” – two-thirds of the firms) and tested on the second subset (“holdout” – one-third of the firms). Comparing model performance on separate datasets is the essence of cross-validation, results of which are discussed in section 4.
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Table 1: Summary statistics for the sample of life insurers, by year
Year Variable Description
1994 CAP Capital / Total assets
RegARisk Regulatory asset risk
OppARisk Opportunity asset risk
Atotal Total assets
Wtotal Total writings
LiabTot
Phealth
Pannuity
Plife
Total liabilities
Health writings / Total writings
Annuity writings / Total writings
Life writings / Total writings
RBCratio 100*Mkt cap / (2*Auth cap)
RetOnCap Income / Mkt capital
Ntype
Ngroup
Org type (1=stock)
Indicator for member of group (1=yes)
1997 CAP Capital / Total assets
RegARisk Regulatory asset risk
OppARisk Opportunity asset risk
Atotal
Wtotal
LiabTot
Phealth
Total assets
Total writings
Total liabilities
Health writings / Total writings
Pannuity
Plife
Annuity writings / Total writings
Life writings / Total writings
RBCratio 100*Mkt cap / (2*Auth cap)
RetOnCap Income / Mkt capital
Ntype
Ngroup
Org type (1=stock)
Indicator for member of group (1=yes)
2000 CAP Capital / Total assets
RegARisk Regulatory asset risk
OppARisk Opportunity asset risk
Atotal
Wtotal
LiabTot
Total assets
Total writings
Total liabilities
Phealth
Pannuity
Plife
RBCratio
Health writings / Total writings
Annuity writings / Total writings
Life writings / Total writings
100*capital / (2*authorized capital)
RetOnCap Income / capital
Ntype Organizational type (1=stock, 0=mutual)
Ngroup Indicator for member of group (1=yes, 0=no)
N Mean Median Std Dev
1321
1321
0.3644
0.0226
0.2737
0.0093
0.2895
0.0415
1321 0.0256 0.0228 0.0120
1321 1,452,250,678 40,447,418 7,717,715,179
1321 272,578,358 14,814,432 1,211,709,683
1321 1,351,811,506 24,679,556 7,354,736,709
1321 0.2479 0.0244 0.3461
1321
1321
0.1557
0.3472
0
0.2279
0.2836
0.3604
1321
1321
1321
1321
1319.5
0.0858
0.9152
0.6344
397.6
0.0791
1
1
3785.2
0.2546
0.2787
0.4818
1125
1125
1125
1125
1125
1125
1125
1125
1125
0.3391
0.0243
0.0178
0.2480
0.0100
0.0180
0.2770
0.0431
0.0064
1125 2,202,854,897 73,463,689 10,739,313,981
1125 380,096,323 26,130,230 1,418,951,317
1125 2,044,269,016 51,036,528 10,239,664,493
1125 0.2771 0.0456 0.3663
0.1678
0.3605
1291.6
0.0627
0.9067
0.7271
0.0005
0.2278
382.9
0.0792
1
1
0.2987
0.3642
4866.7
0.3441
0.2910
0.4456
1013
1013
1013
1013
1013
1013
1013
1013
1013
1013
0.3462
0.0245
0.0228
0.2471
0.0101
0.0219
0.2898
0.0424
0.0097
1013 3,024,772,924 99,693,275 12,971,890,168
1013 566,117,376 37,849,527 1,898,110,477
1013 2,815,147,132 61,264,859 12,367,350,741
0.2917
0.1711
0.3615
1329.1
0.0462
0.9102
0.7542
0.0495
0.0002
0.2405
412.7
0.0708
1
1
0.3752
0.3042
0.3677
3831.0
0.3063
0.2861
0.4308
Additional variables include lagCAP, lagOppARisk, lagRegARisk, which are the values for the named variables in the preceding year, and logATotal, logWTotal, and logLiab, which are the natural logarithms of total assets, total writings, and total liabilities, respectively.
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Endogenous variables
For capital, we take the ratio of adjusted capital to total assets.
5 Since most life insurers are not publicly traded, the market value of equity is not generally available. As noted above, we use two measures of asset risk. Computational procedures and other comparative information about regulatory asset risk and opportunity asset risk are provided in convenient summary form in Table 2. Note particularly that regulatory asset risk uses static weights over time, but the weights for opportunity asset risk are dynamic over time.
5 The adjusted capital formula is the sum of Capital and Surplus, Asset Valuation Reserve (AVR), Voluntary
Investment Reserve, Dividends Apportioned for Payment, Dividends not yet Apportioned, and the Life Subsidiaries
AVR, Voluntary Investment Reserves and Dividend Liability less Property/Casualty Subsidiaries Non-Tabular
Discount. (Source: page LR022 of the 1996 Life NAIC Risk Based Capital Report Including Overview and
Instructions for Companies.)
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Table 2
Side-By-Side Comparison of the Asset Risk Measures
Computational process
Similarities:
Differences
Regulated Asset Risk
(RegARisk – RAR)

Calculate raw regulatory asset risk measure based on C-1 component of risk-based capital: Total low quality bonds*(.30+.20+.09)/3 + total high quality bonds*(.04+.01+.003)/3 + total stocks*(.30+0.023)/2 + total mortgages*.03 (an average between
.001 and 0.06) + total real estate*(.1+.15+.1)/3 + (total short term investments and cash)*.003.

Since this penalty driven portfolio measure depends on the size of the insurer, it is normalized by dividing by firm assets.

Regulatory asset risk measure =
(C-1 measure of risk-based capital / total assets)
Broad asset mix of insurers
Based on weighted average of asset portfolio
Portfolio changes annually
Default based penalties – Assets with lower credit rating have higher
“penalty weights.”
Weights are static throughout the years
Risk measure is the weighted average of estimated (possible) losses of the portfolio
Exogenous/Predetermined Variables
Opportunity Asset Risk
(OppARisk -OAR)

Prevailing monthly exogenous market returns (from
T-bills, S&P 500 stocks, bonds of various credit and duration classes, real estate, mortgages, etc.) are applied to the firm’s specific asset portfolio values in 14 asset classes to yield estimated portfolio earnings for each month based on the proxy returns.

The standard deviation of the twelve monthly earnings is calculated for each year for each insurer – this is the raw opportunity asset risk .

Since this standard deviation depends on the size of the insurer, it is normalized by dividing by firm assets.
 Opportunity Asset Risk measure = (insurer’s standard deviation of monthly proxy returns / total assets)
Broad asset mix of insurers
Based on weighted average of asset portfolio
Portfolio changes annually
Gain and loss variability – depends on exogenous returns in the market
Weights are dynamic from year to year
Risk measure is the variability in the weighted average of the portfolio proxy of earnings/losses.
Business-strategy variables
Following Baranoff and Sager (2003), we first discuss the business strategy variables. In brief, the business strategy hypothesis views major firm decisions like the choice of capital structure and extent of asset risk as devolving from a logically prior choice of the type of
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Working Paper – Draft business to be in. We therefore treat the business strategy/product focus as a predetermined
6 variable for the capital structure and asset risk analysis. If we are to view business products as drivers for the business-strategy hypothesis, then we need quantifiable variables to represent them in our models. In this study, we measure the life insurer’s involvement with life products by the proportions of total insurer premiums written in annuities, life and health.
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This assures inclusion of both the riskiest (health) and least risky (annuities) lines as discussed in both
Baranoff and Sager (2002 and 2003) and explained briefly in the Hypothesis section below.
Other Exogenous Variables
In capital structure studies of financial institutions, the following exogenous variables are usually assumed to influence the capital/risk interrelationships (see summary in Baranoff and
Sager, 2002 and 2003): An indicator for the governance structure (NTYPE – mutual or stock), an indicator for group affiliation (NGROUP – yes or no), insurer size (LogATotal), regulatory forbearance (RBCratio), market concentration (log of premiums), return on capital (RetOnCap), and the log of liabilities (LogLiab). An indicator for the governance structure (NTYPE – mutual or stock) is suggested by agency-theory-based studies as noted in a wide body of prior research.
Under agency theory, risk taking is inversely related to the degree of separation of ownership
6 The distinction between an exogenous and a predetermined variable is that the value of an exogenous variable is, in fact, determined externally to the system under study, whereas the value of a predetermined variable is treated as though it is determined externally for the purpose of the study. (However, their mathematical treatment is the same.)
For example, an indicator variable for a year would be clearly exogenous. The firm’s business strategy just as clearly is not exogenous in this sense, since it is the firm that decides its own strategy. However, the businessstrategy hypothesis views the capital and asset risk decisions under study in this article as consequences – indeed logical consequences – of the choice of what business to be in, even though in a temporal sense, all of these decisions may be made almost simultaneously. Therefore, in this article, we pick up the analysis of the firm after and conditioned upon its business-strategy decision. We thus treat the business-strategy as predetermined, but not exogenous. Although our results are not inconsistent with the business-strategy hypothesis, we do not provide formal tests of business-strategy endogeneity.
7 Because our measures of product involvement are proportions, not all business lines can be entered explicitly into the model equations, as an exact multicollinearity would then ensue, since the sum of proportions across all lines is
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Working Paper – Draft from management. This implies that managers of mutual insurance companies take less risk than do those of stock companies. Additionally, we added an indicator for whether the insurer is a member of a group of affiliated companies (NGROUP). Insurers who are part of a larger group may have superior access to investment opportunities and may have different mechanisms for monitoring/controlling managerial performance. Insurer size is an important determinant of insurer behavior according to the insurance literature on economy of scale and scope. Size is proxied by the logarithm of total assets (LogATotal), the logarithm of total liabilities (logLiab) and the logarithm of total premiums (logWTotal). Inclusion of both assets and liabilities in log form also provides an assessment of asset-liability matching. The log of premiums also reflects market concentration, as it is essentially the Herfindahl index of market concentration.
8
The
RBC ratio is a statistic deriving from NAIC-sponsored studies that reflects the regulatory forbearance imposed on an insurer.
1.0. However, life insurance, together with some reinsurance, constitutes the main part of the omitted lines. Life insurance occupies a middle position in the spectrum of product risks.
8 The Herfindahl index for a company is (W/

W) 2 , where W is the company’s sales in the market and

W is the sum of all companies’ sales in the market. So log(W/ 
W) 2 = 2 log(W) – 2 log(

W). In an ordinary regression, the
–2log( 
W) is a constant that is absorbed into the intercept, and the other 2 is absorbed into the coefficient of log(W).
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Table 2
Comparison of the underlying theory for the interrelationship between the two asset risk measures and the capital ratio
Cap

RAR
H1: Positive interrelationship.
Cap

OAR
H1: Positive interrelationship.
Theoretical support:
Solvency/preservation subject to agency theory and transaction cost economics theory and bankruptcy cost and regulatory cost hypotheses (finite risk hypothesis)
H2: Negative interrelationship.
Theoretical support:
“Go for broke” subject to the risk-subsidy hypothesis (excessive risk).
Theoretical support: a.
For Cap => OAR:
Value maximization subject to agency theory and transaction cost economics theory, bankruptcy cost and regulatory cost hypotheses (finite risk hypothesis) and augmented by relaxation of perfect markets (Berger,
1995): higher Cap => higher returns => higher OAR b.
For OAR = > Cap:
Value maximization subject to agency theory and transaction cost economics theory, bankruptcy cost and regulatory cost hypotheses (finite risk hypothesis) and augmented by retained earnings (Berger, 1995): higher
OAR => higher returns => higher Cap
H2: Negative interrelationship.
Theoretical support: a.
For Cap => OAR:
Value maximization subject to the risk-subsidy hypothesis (excessive risk) and augmented by tax shield and perfect markets (Berger, 1995): higher Cap
=> lower returns => lower OAR b.
For OAR => Cap:
Value maximization subject to the risk-subsidy hypothesis (excessive risk): higher OAR => lower Cap
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OAR (Loss and Gain)
+
(finite risk, retain earnings)
-perfect markets,
Tax shield, excessive risk)
-(excessive risk)
+
(relaxation of perfect markets, finite risk)
CAR (Value Max)
RAR (loss only)
+
(finite risk)
-
(excessive risk)
Capital to asset ratio
CAR (minimal)
The Business Strategy Hypothesis Impact on Capital Structure and Asset Risk
Before discussing the theoretical foundation for the interrelationship between capital structure and the asset risks, we explain some of the underlying theories regarding the businessstrategy hypothesis, which views the choice of business line, or product, as a driver of other major firm decisions. As explained in detail in Baranoff and Sager (2003), the business-strategy hypothesis draws support from transaction-cost economics (TCE), agency theory (the monitoring hypothesis), bankruptcy cost avoidance, and regulatory cost hypotheses. In TCE, the level of transaction costs and the risk embedded in the products largely determine the capital structure
(Williamson, 1988, with further explanation in Baranoff and Sager, 2002 and 2003). Products that involve large potential contractual disputes, uncertainties and major development costs, as in
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Working Paper – Draft health insurance contracts, are considered riskier and would not lend themselves to financing by debt. Therefore, for higher risk products, the method of financing tends to favor capital rather than debt. In TCE, there is no explicit implication to the relationship between the complexity of the product and the risk of the assets held by a firm. Such a linkage can be inferred, as noted in
Baranoff and Sager (2003), by augmenting TCE with elements of agency theory. When contracts (for trading the products) create conflicts among the stakeholders, owners develop monitoring techniques to control management from taking excessive risk. Thus, it can be inferred that risky products will be associated with higher capital and constrained risk taking on the assets side of the insurance business. If both higher capital and lower asset risk are observed, then it may seem that the business strategy hypothesis will have induced a negative interrelationship between capital and asset risk – an outcome ordinarily associated with theories of excessive risk rather than the finite risk theories that underlie the business strategy hypothesis.
But these are ceteris paribus expectations, and it is well to recall that in a multivariate environment the sign of the correlation between product and capital and between product and asset risk need not determine the sign of the correlation between capital and asset risk – the outcome depends on the strengths of the multivariate relationships.
To apply the business strategy hypothesis to this study of the interrelationship between capital and asset risk, we must identify and quantify those features of products sold by the life insurance industry that are relatively riskier and those that are less risky. The broad spectrum of the life industry products can be divided into three main categories, the life health and annuity products. Health insurance is viewed as the riskiest line since it is subject to relational contracts because of the ever changing states of the world, advances in medical technology, and aging populations. Annuities are considered least risky from an insurance contractual point of view.
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The annuity contract is not relational in TCE terms and does not pose major underwriting risks on insurers. The life product falls between annuities and health in terms of product risk (further explanation is provided in Baranoff and Sager, 2002 and 2003).
Interrelationship between Regulatory Asset Risk and Capital Structure
Baranoff and Sager (2002 and 2003) introduced the regulatory asset risk and its interrelationship with the capital structure and product risk (or the business strategy.) Thus, we first provide an overview of the expected interrelationship between the regulatory asset risk and capital structure based on prior research. See Summary in Table 2. Part of the expected interrelationship stems from the foundation of the business hypothesis regarding the more risky and less risky products. Overall, the prevailing finite risk and excessive risk hypotheses underlie the expected signs in the interrelationship of the regulated asset risk and the capital ratio.
For the capital/ regulatory asset risk interrelation as for the business strategy hypothesis, the literature entertains the distinct and conflicting theories that are summarized as (or culminate in) the hypotheses of finite risk and excessive risk taking. As described above, under TCE theory, agency theory, and the bankruptcy and regulatory costs hypotheses, adoption of a less risky strategy in capital is associated with more asset risk taking and vice versa. The competing hypothesis of excessive risk taking is entrenched in the risk-subsidy hypothesis, which suggests that a risky strategy leads directly to greater risk taking in the capital (leverage risk) and regulatory asset risk – a negative interrelation between the capital and regulatory asset risk. The excessive risk taking stems from having the security of guarantee funds or deposit insurance.
Formally, these hypotheses are depicted in the left-hand column of Table 2 above.
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Interrelationship between Opportunity Asset Risk and Capital Structure
The theories collectively known as finite risk (TCE, agency theory with monitoring, regulatory and bankruptcy costs) also predict a positive interrelationship between capital and opportunity asset risk, just as between capital and regulatory asset risk, and through the same theoretical mechanisms. Similarly, excessive risk theories predict a negative interrelationship.
But one can buttress both arguments in the case of opportunity asset risk by appealing to theories that link capital and asset risk through returns .
9
Such an exercise provides additional insights into the capital – opportunity asset risk interrelationship, so we now devote some space to sketching the ideas. Our discussion borrows from and extends Berger (1995), who studied the relationship between capital and returns.
The contribution of returns to the OAR  Cap interrelationship.
Obtaining high investment returns is one aspect of the drive to maximize firm value. But portfolio theory posits that high expected returns correlate positively with high volatility of returns.
10 Opportunity asset risk reflects the potential volatility of returns for each insurer’s asset portfolio, with respect to benchmark market yields. Thus opportunity asset risk represents the possibility of gains and losses from the assets, whereas regulatory asset risk focuses exclusively on the potential for loss. Therefore, opportunity asset risk responds to the objective of value maximization and not just to the minimum capital requirement to ensure solvency, which is the objective of the regulatory asset risk.
9 This is especially important as the opportunity asset risk is computed using the variability in returns. Returns are the core foundation of this asset risk measure.
10 See basic portfolio theory in basic Financial Management text books.
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In the framework of value maximization, an important question is, what is the interrelationship between the capital structure and the risk of returns as represented by their volatility? Berger (1995) points out that if a firm gains high returns and it retains those returns, then capital increases if the gains are retained. To this observation, we add that higher returns are correlated with higher volatility in the form of higher opportunity asset risk. Thus the linkage is that higher volatility of returns (higher opportunity asset risk) leads to higher returns, which leads to higher capital if the earnings are retained. That is, higher OAR=> higher returns
=> higher capital ratio.
Returns can also play a role in explaining the converse relationship: the effect of capital on opportunity asset risk. According to Berger (1995) the conventional wisdom is that a higher capital ratio leads to lower return on capital since there is less financial risk-taking on account of lower leverage (higher Cap => lower expected returns). Berger (1995) attributes this negative relationship to perfect markets and the favorable tax shield accorded debt. We add that lower returns are associated with lower volatility of returns and hence lower opportunity asset risk.
Connecting the links, we have higher Cap => lower expected returns => lower OAR. This implies a negative relationship between capital ratio and opportunity asset risk. Berger (1995) proposes that a positive effect of capital on returns may result from relaxing the perfect markets assumption. To this relaxation, we add the association of higher returns with higher volatility of returns to complete the linkage higher Cap => higher returns => higher OAR. As a caveat, however, we should again recall that transitivity of the sign of correlation does not necessarily hold in a multivariate environment.
Table 2 and Figure 2 are provided as visual aids to illustrate the underlying theories leading the positive and negative interaction of this opportunity asset risk with capital structure.
18

Working Paper – Draft
The SSEM model featured in this article is a two-stage procedure, analogous to the twostage least squares (2SLS) procedure in econometrics. The major difference is that the SSEM model form is not linear. We begin with a set of structural equations that define the expected relationships among the endogenous and exogenous variables:
C

R
 f
C
( R )
 f
R
( C )
 f
C 0
( lagC )
 f
R 0
( lagR )
 f
C 1
( X
1
)
   f
R 1
( X
1
)
   f
Cm
( X m
)
 
C f
Rm
( X m
)
 
R
Eqns (1)
In these equations, C stands for the capital-to-asset ratio and R is the asset risk measure (either opportunity or regulatory). C and R are endogenous. X
1
,  , X m
, lagC and lagR are the exogenous and predetermined variables.

C
and

R
are error terms.
In conventional two-stage least squares, the functional form of the various f 's is linear.
In SSEM, each f is a semiparametric function of its argument. The particular implementation of the semiparametric approach that we use is the stochastic spline. Stochastic splines were introduced by Wahba (1978) for single equation models. For an elementary discussion, see
Baranoff, Sager, and Shively (2000). For an advanced exposition of nonparametric methods for simultaneous equation modeling, see Pagan and Ullah (1999), who focus on kernel estimation, a different methodology from ours. The term semiparametric arises because the model includes both a simply parameterized linear form and a more complex nonlinear form. Each f has the form f ( x )
 
0
 
1
( x
 x
0
)
   x x
0
( x
 s ) W ( ds ) Eqn (2)
19

Working Paper – Draft
If the parameter

is 0, then the functional form reduces to the linear case. ( x
0 is a location constant, usually set near the minimum of the range of x.) But if

is not zero, then the nonlinear part of the model, x 
( x
 x
0 s ) W ( ds ) , comes into play. This latter part of the model is stochastic because W(s) is a Wiener process, which is the stochastic process counterpart of the normal distribution. The larger

is, the more flexibility is accorded the nonlinear portion to adapt to the data. The smaller

is, the closer the model is to the simple linear portion

0
 
1
( x
 x
0
) . In the estimation procedure,

is selected automatically, depending on the extent to which the data conform to a linear structure.

A hierarchical Bayesian methodology is used to estimate all parameters of the model.
One of the attractive features of the methodology is that the model in (2) reduces to a linear model if
 
0 . Therefore, the linear model is a special (nested) case of the semiparametric model. If a linear model is appropriate in practice then the estimate of

will be close to zero and for practical purposes we will estimate a linear relationship. Alternatively, we could use a
Bayesian model selection technique to determine whether
 should be set to zero, i.e. whether the nonlinear part of (2) should be removed. For a full discussion of the estimation methodology and other issues for this model, see Baranoff, Sager and Shively (2000).
The first stage of SSEM is to estimate the reduced form of each of Eqns (1). We write
C

R
 f
CC
*
( lagC )
 f
RC
*
( lagC )
 f
CR
*
( lagR )
 f
RR
*
( lagR )
 f
C 1
*
( X
1
)
   f
R 1
*
( X
1
)
   f
Cm
*
( X m
)
 f
Rm
*
( X m
)


C
*
Eqns (3)

R
*
The asterisks denote different functions than those in Eqns (1). In (3), the exogenous and predetermined variables play the role of instruments. We apply the stochastic spline/hierarchical
20

Working Paper – Draft
Bayes estimation methodology separately to each equation in (3). The resulting estimates for C and R are
C
ˆ 
 f
ˆ
CC
*
( lagC )
 f
ˆ
RC
*
( lagC )
 f
ˆ
CR
*
( lagR )
 f
ˆ
RR
*
( lagR )
 f
ˆ
C 1
*
( X
1
)
   f
ˆ
R 1
*
( X
1
)
   f
ˆ
Cm
*
( X m
) f
ˆ
Rm
*
( X m
)
Eqns (4)
C
ˆ and
R are then substituted for C and R in (1) above. The second stage of estimation then commences. With C
ˆ and
replacing C and R , we then estimate the two equations in (1) separately via the stochastic spline/hierarchical Bayes estimation methodology.
It is therefore evident that SSEM is an adaptation of the stochastic spline methodology to the setting of simultaneous equations, in which the adaptation is carried out by means of the twostage estimation principle. One important caveat is that the issue of parameter identifiability remains theoretically difficult in nonparametric simultaneous equation modeling, in general
(Pagan and Ullah, 1999). For a discussion of identifiability in the Bayesian context, see Zellner
(1996). In practical terms, identifiability may not be a problem. There are two reasons for this.
First, if the standard errors of the parameter estimates are relatively small, then those estimates are probably consistent, and consistency implies identifiability (Mittelhammer, Judge and Miller,
2000). Second, if the model cross-validates well, then the parameters are also probably identified. Indeed, if the focus is on prediction, then it can be maintained that cross-validation trumps all other concerns.
The results of the SSEM models are featured using leverage plots. The leverage plot is an effective tool for understanding and displaying the effects of changes in regressor values on the capital or risk measure (the two endogenous variables). A table of coefficients is not applicable
21

Working Paper – Draft to illustrate the results of the SSEM since the interrelationship between the dependent endogenous variables and the regressors changes at different levels of the regressors. These are functional relationship type of models and provide managerial tools for each company. The leverage plots shown here are for a hypothetical insurer that has the median levels of the variables used in the model.
The models fit well in general. For each year, one-third of the insurers were randomly assigned to a holdout sample for cross-validation purposes. The models were fit on the remaining two-thirds of the insurers and the in-sample functional estimates were then applied to estimate capital and asset risk variables of the hold-out companies for each equation in each model. R-squares and other performance measures were calculated for the in-sample and holdout insurers. Table 3 summarizes the R-squares for in-sample and holdout fit.
Table 3. R-squares for Cross-Validation Analysis
MODEL I (RegARisk)
Cap (Equation 1)
In-sample
Holdout
1994 1997
MODEL II (OppARisk)
2000 Cap (Equation 1)
0.968 0.980 0.988 In-sample
0.902 0.826 0.895 Holdout
RegARisk (Equation 2) 1994 1997 2000 OppARisk (Equation 2)
In-sample
Holdout
0.963 0.939 0.942 In-sample
0.871 0.822 0.935 Holdout
1994 1997 2000
0.945 0.977 0.973
0.951 0.841 0.962
1994 1997 2000
0.731 0.559 0.707
0.597 0.485 0.659
There is generally only a modest drop in R-square from the in-sample fit to the holdout sample, indicating that there is probably not much overfitting occurring. We also observe that most of the models have high explanatory power, that the capital equation fits better than the asset risk equation, that Model I (with RegARisk) fits better than Model II (with OppARisk), and that 1997 fits somewhat less well than the other two years.
As explained above, two models were developed using Eqns (1). The first model used the regulatory measure (RegARisk) as the asset risk variable and the second model used the
22

Working Paper – Draft opportunity asset risk measure (OppARisk) as the asset risk variable. All other variables are exactly the same for the two models. In the graphs shown below, Figure “R” refers to the first model, using RegARisk; Figure “O” refers to the second model, using OppARisk. We attach the numeral “1” or “2”, respectively, to the figure letter to refer to a set of graphs using the first equation (for capital) in Eqns (1) or to the second equation (for the asset risk). Thus there are four sets of graphs: Figures O1, O2, R1, and R2. For example, Figure O1 refers to model II
(with OppARisk) and equation 1 (for capital). Within each of the four sets, there are three series, denoted by attaching further numerals “.1”, “.2”, and “.3”. Each of the three series shows the effects of different regressors – respectively, the other endogenous variable (“.1”), the business strategy variables (“.2”), and other exogenous variables (“.3”). For example, Figure O1.2 refers to model II (with OppARisk), equation 1 (for capital), and the proportions of writings in health, annuity, and life lines. First we discuss the leverage plots for the endogenous variables, second the business strategy variables, and finally other exogenous variables.
Endogenous Variables
Insert Figures R1.1 and O1.1
Capital Equation.
In Figure R1.1, RegARisk appears to exert an effect on capital that is modestly positive and fairly linear for all three years, except at elevated levels of RegARisk, where the effect becomes erratic in 1994 and 1997, and strongly negative in 2000. In Figure
O1.1, the effect of OppARisk on capital is fairly linear and positive in 1997 and 2000, except for a high-end negative effect in 1997, but there is a significant range of negative effect in 1994. On balance these results for capital favor finite risk.
Insert Figures R2.1 and O2.1
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Working Paper – Draft
Asset Risk Equation.
In Figure R2.1, we see that capital impacts positively and linearly on RegARisk in 1994, remains mostly monotonically positive in 1997, but becomes negative for most companies in 2000. The collapse of the stock market may have been a contributor to the switch into an excessive risk taking mode from the finite risk mode of the prior years. In Figure
O2.1, OppARisk responds generally positively to capital and roughly linearly except in 1994.
For the most part, we can say that capital impacted opportunity asset risk positively in line with finite risk notions.
In summary, although a positive interrelationship between capital and each asset risk generally prevailed, the leverage plots show some exotic behavior for firms under high asset risk and significant nonlinearities. There are even nonmonotonic years when finite risk may prevail within one range of predictor values and excessive risk in another range.
Business Strategy variables
Insert Figures R1.2 and O1.2
The results for the impact of the business strategy variables of the health, annuity and life writings are shown in Figures R1.2 and R2.2 for the regulatory asset risk and O1.2 and O2.2 for the opportunity asset risk.
Figures R1.2 and O1.2 are strikingly similar since the dependent variable (capital) is the same and most of the predictors are the same. The only difference is the interchange of
RegARisk and OppARisk as predictors in the model. It is interesting that many of the plots show a change in sign of the slope around 70 percent of writings. This level has been taken as a threshold for defining an insurer as a specialist in a line of business (see Baranoff, Sager and
Witt, 1999). In section 3, we posited health writing as the riskiest line of business and predicted its impact on capital ratio would be positive under the finite risk hypothesis. Such a relationship
24

Working Paper – Draft holds in all the years for insurers writing over 70 percent of their business in health. Similarly, if annuities are regarded as the less risky business, there is mostly a negative relationship with capital ratio, albeit not always linear. 1994 is an exception for firms writing over 70 percent annuity business. Life insurance was identified as between health and annuities in terms of product risk. We see a negative effect on capital for life specialists (over 70 percent of writings) for both asset risks and all years except 2000 for the OppARisk model.
Insert Figures R2.2 and O2.2
Figures R2.2 and O2.2 show the effects of the business strategy variables on each of the asset risk variables. Here, there are striking differences between the two Figures, since the dependent variables are different.
In Figure R2.2, more health writings are associated with lower RegARisk, except for nonspecialist insurers in 2000. The annuities story is mixed – conforming to finite risk in 1994, to excessive risk in 1997, and to both in 2000. In Figure O2.2, we have the most striking nonlinearities of all of the plots. For some ranges of predictor values, finite risk seems to prevail, only to cede control to excessive risk in an adjoining range, with the transitions occurring at well-defined points.
Other control Variables
Insert Figures R1.3 and O1.3
The results for the impact of other control variables such as size, concentration, return on capital, etc. are shown in Figures R1.3 and R2.3 for the regulatory asset risk and O1.3 and O2.3 for the opportunity asset risk.
Figures R1.3 and O1.3 are strikingly similar since the dependent variable (capital) is the same and most of the predictors are the same. The only difference is the interchange of
25

Working Paper – Draft
RegARisk and OppARisk as predictors in the model. In both sets we see an inverse relationship of capital with assets and liability. Capital increases monotonically (and nearly linearly) with assets (in log scale); and capital correspondingly decreases monotonically (and nearly linearly) with liabilities (in log scale). Interesting is the plot of the return on capital (RetOnCap) in these
Figures. Berger (1995) regards an increase in returns as leading to increase in capital ratio if earnings are retained. Although the plots for returns display some exotic behavior at the extremes, we can see a small uptrend in the plots for all years but 1997, the year of the stock market bubble. In 1997, insurers with positive returns decreased capital as returns increased.
Insert Figures R2.3 and O2.3
Figures R2.3 and O2.3 show the effects of the other control variables on each of the asset risk variables. Here, there are striking differences between the two Figures, since the dependent variables are different.
Because of fundamental portfolio theory, we would expect that returns would relate positively with OppARisk. In Figure O2.3 that appears to be true, but quite weak, but with some ranges in which the relationship is negative. That is especially true in 1997 for insurers with positive earnings. In Figure R2.3, assets and liabilities tend to be inversely related, except for
1997, and again with a similar pattern in Figure O2.3. It is interesting that RegARisk increased as size increased in 1997 and 2000 while it decreased with size in 1994 before the bubble. For
OppARisk, the decrease as size increased occurred in 2000.
The leverage plot for a binary control variable consists of two distinct points, rather than a line or a curve. Thus we omit showing leverage plots for NTYPE and NGROUP. However, we comment that for Model I (with RegARisk as the asset risk variable), in the capital equation, membership in a group of insurers leads to higher capital ratio in 1994 and 1997, but the opposite
26

Working Paper – Draft in 2000. Also for Model I , capital ratio is lower for stock companies only in 1997, but is higher for stock companies in 1994, before the stock market bubble, and in 2000, after the burst of the bubble. In the RegARisk equation of Model I, membership in a group of insurers leads to higher regulatory asset risk for all three years. But regulatory asset risk is lowered for stock companies, also for all three years. The amount of the decline is somewhat different among the years.
For Model II (with OppARisk as the asset variable), in the capital equation, capital ratio increases for insurers in groups of companies. For the same model, capital ratio is lower for stock companies in 1994 and 1997, but not in 2000. In the OppARisk equation of Model II,
OppARisk is lower for firms in groups in 1994 and 2000, but higher in 1997. Opportunity asset risk is higher for stock insurers in all three years.
This is the first paper in the capital structure to use the SSEM model to study the capital/risk interrelationship. The model is complex and requires intensive computation.
Linearity is not imposed and the interrelationship is simultaneously calculated.
Leverage plots are used to study the results of the models. The effects of two competing hypotheses about the interrelationship between capital ratios and asset risk are examined.
Theories of finite risk predict constrained risk taking by insurers; theories of excessive risk predict expanded risk taking. In general, the leverage plots for median insurers favor finite risk more often than excessive risk. They show that for the life insurance industry, the world contains much nonlinearity. They also vary by year in a way that may reflect effects of the market boom of the late 1990’s and the bust of 2000. Even within the same year, the sign of a relationship may change between contiguous ranges of predictor values. Our results suggest that
27

Working Paper – Draft the interplay of economic and financial forces may be more complex than assumed by the linear models in common use. For example, firm behavior may depend on which range of predictor values the firm occupies. Both asset risks models can be used as benchmarks for managerial decision. When the opportunity asset risk is used as a benchmark, an insurer can recompute its opportunity asset risk using its actual rates of return, rather than rates from market indices.
When regulatory asset risk is used, it can be benchmark for regulatory forbearance or an advisory minimum for managerial decision.
With the passage of the Gramm-Leach-Bliley Act and the greater emphasis on financial risk management by financial institution, the results and the tools of this study can be a starting point for development of an enterprise risk management that may be more responsive to the accuracy needed in capital/risk models.
28

Working Paper – Draft
REFERENCES
Baranoff, Etti G., And Thomas W. Sager “The Interrelationship Among Organizational And
Distribution Forms And Capital And Asset Risk Structures In The Life Insurance Industry”
Journal Of Risk and Insurance, Sept. 2003, v70 i3 p375(26)
Baranoff, Etti G. and Thomas W. Sager “The Relationship between Asset Risk, Product Risk, and Capital in the Life Insurance Industry ,
”
Journal of Banking and Finance, 26 (2000): 1181-
1197
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Spline Model as a Managerial Tool for Potential Insolvency,”
Journal of Risk and Insurance , 67
(2000): 369-396 .
Baranoff, Etti G., Thomas W. Sager and Robert C. Witt “ Industry Segmentation And
Predictor Motifs For Solvency Analysis Of The Life/Health Insurance Industry
”
Journal of Risk and Insurance, March, 1999
Berlin, Mitchell and Loretta J. Mester (editorial article) “Retail credit risk management and measurement: An introduction to the special issue,”
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Pagan, A. and Ullah, A., 1999, Nonparametric Econometrics, Cambridge University Press.
Wahba, Grace, “Improper Priors, Spline Smoothing and the Problem of Guarding Against Model
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Zellner, Arnold, An Introduction to Bayesian Inference in Econometrics, Wiley (1996).
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NAIC
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-0.1
1.5
1
0.5
0
-0.5
0
1994 f(Rregarisk)
0.1
Regarisk
0.2
0.3
0.4
Figure R1.1
Model I (asset risk = Regulatory Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictor = Regulatory Asset Risk
1997 2000 f(Regarisk) f(Regarisk)
-0.1
0.6
0.5
0.4
0.3
0.2
0.1
0
0 0.1
Regarisk
0.2
0.3
0.4
-0.1
0.6
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
-1
-1.2
0 0.1
Regarisk
0.2
0.3
0.4
Figure O1.1
Model II (asset risk = Opportunity Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictor = Opportunity Asset Risk
0.325
0.32
0.315
0.31
0.305
0.3
0.295
0.29
0.285
0.28
0
1994 f(OpARisk)
0.02
0.04
OpARisk
0.06
0.08
1997 f(OpARisk)
0.3
0.25
0.2
0.15
0.1
0.05
0
0 0.01
0.02
0.03
OpARisk
0.04
0.05
-0.02
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0
2000 f(OpARisk)
0.02
0.04
OpARisk
0.06
0.08
31

Working Paper – Draft
1994 f(pHealth)
0.332
0.33
0.328
0.326
0.324
-0.2
0.322
0.32
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
Figure R1.2
Model I (asset risk = Regulatory Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictors = Health, Annuity and Life
1997 f(pHealth)
0.278
0.276
0.274
0.272
0.27
0.268
0.266
0.264
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
2000 f(pHealth)
0.312
0.31
0.308
0.306
0.304
0.302
0.3
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.325
0.32
0.315
0.31
0.305
0.3
0.295
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pAnnuity)
0.27
0.26
0.25
0.24
-0.2
0.23
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pAnnuity)
0.305
0.3
0.295
0.29
-0.2
0.285
0.28
0.275
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.34
0.33
0.32
0.31
0.3
-0.2
0.29
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pLife)
0.275
0.27
0.265
0.26
0.255
0.25
0.245
0.24
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pLife)
0.315
0.31
0.305
0.3
0.295
0.29
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
32

Working Paper – Draft
Figure O1.2
Model II (asset risk = Opportunity Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictors = Health, Annuity and Life
1994 f(pHealth)
0.312
0.31
0.308
0.306
0.304
0.302
0.3
0.298
0.296
0.294
-0.2
0.292
0 0.2
0.4
pHealth
0.6
0.8
1 1.2
f(pAnnuity)
0.295
0.29
0.285
0.28
0.275
-0.2
0.27
0 0.2
0.4
pAnnuity
0.6
0.8
1 1.2
f(pLife)
0.32
0.315
0.31
0.305
0.3
0.295
0.29
0.285
0.28
-0.2
0.275
0.27
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(NType)
-0.2
0.304
0.302
0.3
0.298
0.296
0.294
0.292
0 0.2
0.4
NType
0.6
0.8
1 1.2
1997 f(pHealth)
0.288
0.286
0.284
0.282
0.28
0.278
0.276
0.274
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
2000 f(pHealth)
0.29
0.285
0.28
0.275
0.27
-0.2
0.265
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.28
0.275
0.27
0.265
0.26
0.255
-0.2
0.25
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.282
0.28
0.278
0.276
0.274
0.272
0.27
0.268
0.266
0.264
0.262
0.26
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pAnnuity)
0.27
0.265
0.26
0.255
0.25
-0.2
0.245
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.28
0.278
0.276
0.274
0.272
0.27
0.268
0.266
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(NType)
-0.2
0.29
0.288
0.286
0.284
0.282
0.28
0.278
0.276
0 0.2
0.4
NType
0.6
0.8
1 1.2
0.269
0.2685
0.268
0.2675
0.267
-0.2
0.2665
0.266
0 f(Ntype)
0.2
0.4
NType
0.6
0.8
1 1.2
33

Working Paper – Draft
34

Working Paper – Draft
Figure R1.3
Model I (asset risk = Regulatory Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictors = other exogenous vars
4
3
2
1
0
-1
0
1994 f(logATotal)
5 10 15 logATotal
20 25 30
1997 f(logATotal)
-1
-2
3
2
1
0
5
4
0 5 10 15 logATotal
20 25 30
2000 f(logATotal)
5
4
3
2
-1
-2
1
0
0 5 10 15 logATotal
20 25 30 f(logWTotal)
0.35
0.34
0.33
0.32
0.31
0.3
0 5 10 15 logWTotal
20 25 f(logWTotal)
0.4
0.2
0
-0.2
-0.4
-0.6
-0.8
0 5 10 15 20 25 30 logWTotal f(logWTotal)
0.4
0.3
0.2
0.1
0
0 5 10 15 logWTotal
20 25 f(logLiab)
2
-2
-3
1
0
-1
0 5 10 15 20 25 30 logLiab
-2 f(RetOnCap)
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0 2
RetOnCap
4 6 f(RBCratio)
0.5
0.4
0.3
0.2
0.1
0
-0.1
0 20000 40000
RBCratio
60000 80000 f(logLiab)
3
2
1
0
-1 0
-2
-3
-4
5 10 15 20 25 30 logLiab f(logLiab)
4
2
0
-2
0
-4
5 10 15 20 25 30 logLiab
-6
1.5
1
0.5
0
-0.5
0
-4 f(RetOnCap)
-2
0.3
0.25
0.2
0.15
0.1
0.05
0
0
RetOnCap
2 f(RBCratio)
4 6
20000 40000
RBCratio
60000 80000
-4 -3 -2 f(RetOnCap)
0.33
0.32
0.31
0.3
0.29
0.28
0.27
0.26
-1 0
RetOnCap
1 2 3 f(RBCratio)
0.6
0.4
0.2
0
-0.2
0
-0.4
-0.6
10000 20000 30000 40000 50000
RBCratio
35

Working Paper – Draft
2.5
2
1.5
1
0.5
0
-0.5
0
-1
5
1994 f(logATotal)
10 15 20 25 30 logATotal f(logWTotal)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 5 10 logWTotal
15 20 25 f(logLiab)
0
-0.5
0
-1
-1.5
-2
2
1.5
1
0.5
5 10 15 20 25 30 logLiab f(RetOnCap)
-2 -1
0.5
0.4
0.3
0.2
0.1
0
0.8
0.7
0.6
0 1 2
RetOnCap
3 4 5 6 f(RBCratio)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 10000 20000 30000 40000
RBCratio
50000 60000 70000
Figure R1.3
Model II (asset risk = Opportunity Asset Risk)
Equation 1 (dependent var = Capital Ratio)
Predictors = other exogenous vars
1997 f(logATotal)
5
4
3
2
1
0
-1
0
-2
5 10 15 20 25 30 logATotal f(logWTotal)
0.4
0.2
0
-0.2
0
-0.4
-0.6
5 10 15 20 25 30 logWTotal f(logLiab)
3
2
1
0
-1
-2
-3
0
-4
-5
5 10 15 20 25 30 logLiab
-6 -4 f(RetOnCap)
-2
0.3
0.25
0.2
0.15
0.1
0.05
0
0
RetOnCap
2 4 6 f(RBCratio)
1.2
1
0.8
0.6
0.4
0.2
0
-0.2
0
-0.4
20000 40000
RBCratio
60000 80000
2000 f(logATotal)
3
2.5
2
1.5
1
0.5
0
-0.5
0
-1
-1.5
5 10 15 20 25 30 logATotal f(logWTotal)
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 5 10 15 logWTotal
20 25 f(logLiab)
-2
-3
3
2
1
0
-1
0 5 10 15 20 25 30 logLiab
-4 -3 -2 f(RetOnCap)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
-1 0
RetOnCap
1 2 3 f(RBCratio)
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
0 10000 20000 30000
RBCratio
40000 50000
36

Working Paper – Draft
Figure R2.1
Model I (asset risk = Regulatory Asset Risk)
Equation 2 (dependent var = Regulatory Asset Risk)
Predictor = Capital
-0.5
0.04
0.035
0.03
0.025
0.02
0.015
0.01
0.005
0
0
1994 f(Cap)
0.5
Cap
1
1997 f(Cap) f(Cap)
-0.5
0.025
0.02
0.015
0.01
0.005
0
0 -0.5
0.025
0.02
0.015
0.01
0.005
0
0
1.5
0.5
Cap
1 1.5
Figure O2.1
Model II (asset risk = Opportunity Asset Risk)
Equation 2 (dependent var = Opportunity Asset Risk)
Predictor = Capital
0.5
Cap
2000
1 1.5
1994 f(Cap)
-0.5
0.025
0.024
0.023
0.022
0.021
0.02
0 0.5
Cap
1 1.5
2
1997 f(Cap)
0.025
0.02
0.015
0.01
0.005
0
0 0.2
0.4
0.6
Cap
0.8
1 1.2
1.4
-0.5
0.04
0.03
0.02
0.01
0
0 f(Cap)
0.5
Cap
2000
1 1.5
37

Working Paper – Draft
Figure R2.2
Model I (asset risk = Regulatory Asset Risk)
Equation 2 (dependent var = Regulatory Asset Risk)
Predictors = Health, Annuity and Life
1994 f(pHealth)
-0.2
0.014
0.012
0.01
0.008
0.006
0.004
0.002
0
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.0135
0.013
0.0125
0.012
0.0115
-0.2
0.011
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
1997 f(pHealth)
0.015
0.0145
0.014
0.0135
0.013
0.0125
0.012
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.0145
0.014
0.0135
0.013
0.0125
0.012
0.0115
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
2000 f(pHealth)
0.0155
0.015
0.0145
0.014
0.0135
0.013
0.0125
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.014
0.0135
0.013
0.0125
0.012
0.0115
0.011
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.013
0.0125
0.012
0.0115
-0.2
0.011
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pLife)
0.015
0.01
0.005
-0.2
0
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pLife)
0.02
0.015
0.01
0.005
-0.2
0
0 0.2
0.4
pLife
0.6
0.8
1 1.2
38

Working Paper – Draft
Figure O2.2
Model II (asset risk = Opportunity Asset Risk)
Equation 2 (dependent var = Opportunity Asset Risk)
Predictors = Health, Annuity and Life
1994 f(pHealth)
0.024
0.0235
0.023
0.0225
0.022
0.0215
0.021
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
1997 f(pHealth)
0.0192
0.0191
0.019
0.0189
0.0188
0.0187
0.0186
0.0185
0.0184
0.0183
0.0182
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
2000 f(pHealth)
0.0208
0.0206
0.0204
0.0202
0.02
0.0198
0.0196
-0.2
0 0.2
0.4
0.6
pHealth
0.8
1 1.2
f(pAnnuity)
0.0248
0.0246
0.0244
0.0242
0.024
0.0238
0.0236
0.0234
0.0232
0.023
0.0228
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.025
0.0245
0.024
0.0235
0.023
0.0225
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pAnnuity)
0.0198
0.0197
0.0196
0.0195
0.0194
0.0193
0.0192
0.0191
0.019
0.0189
0.0188
0.0187
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.02
0.0198
0.0196
0.0194
0.0192
0.019
0.0188
0.0186
0.0184
0.0182
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
f(pAnnuity)
0.0214
0.0212
0.021
0.0208
0.0206
0.0204
0.0202
0.02
0.0198
0.0196
-0.2
0 0.2
0.4
0.6
pAnnuity
0.8
1 1.2
f(pLife)
0.021
0.0208
0.0206
0.0204
0.0202
0.02
0.0198
0.0196
-0.2
0 0.2
0.4
pLife
0.6
0.8
1 1.2
39

Working Paper – Draft
Figure R2.3
Model I (asset risk = Regulatory Asset Risk)
Equation 2 (dependent var = Regulatory Asset Risk)
Predictors = other exogenous vars
1994 f(logATotal)
0.025
0.02
0.015
0.01
0.005
0
-0.005
-0.01
0 5 10 15 logATotal
20 25 30
1997 f(logATotal)
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logATotal
20 25 30
2000 f(logATotal)
0.12
0.1
0.08
0.06
0.04
0.02
0
-0.02
0 5 10 15 logATotal
20 25 30 f(logWTotal)
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25 f(logWTotal)
0.03
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25 30 f(logWTotal)
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25 f(logLiab)
0.04
0.03
0.02
0.01
0
-0.01
0
-0.02
-0.03
5 10 15 20 25 30 logLiab f(RetOnCap)
-2
0.06
0.04
0.02
0
-0.02
0
-0.04
-0.06
2
RetOnCap
4 6 f(RBCratio)
0.015
0.01
0.005
0
-0.005
0 10000 20000 30000 40000 50000 60000 70000
RBCratio f(logLiab)
0.02
0.015
0.01
0.005
0
0 5 10 15 logLiab
20 25 30 f(logLiab)
0.06
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08
-0.1
0 5 10 15 20 25 30 logLiab
-6 -4 f(RetOnCap)
0.02
0.015
0.01
0.005
0
-2
-0.005
0
RetOnCap
2 4 6
-4 -3 -2 f(RetOnCap)
0.02
0.01
0
-1
-0.01
0
-0.02
-0.03
RetOnCap
1 2 3 f(RBCratio)
0.02
0.015
0.01
0.005
0
0 20000 40000
RBCratio
60000 80000 f(RBCratio)
0.02
0.015
0.01
0.005
0
-0.005
-0.01
-0.015
0 10000 20000 30000 40000 50000
RBCratio
40

Working Paper – Draft
Figure O2.3
Model II (asset risk = Opportunity Asset Risk)
Equation 2 (dependent var = Opportunity Asset Risk)
Predictors = other exogenous vars
1994 f(logATotal)
0.03
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logATotal
20 25 30
0.025
0.02
0.015
0.01
0.005
0
0
1997 f(logATotal)
5 10 15 logATotal
20 25 30
0.04
0.03
0.02
0.01
0
-0.01
0
-0.02
2000 f(logATotal)
5 10 15 logATotal
20 25 30 f(logWTotal)
0.03
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25 f(logLiab)
0.06
0.05
0.04
0.03
0.02
0.01
0
0 5 10 15 logLiab
20 25 30 f(logWTotal)
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25 30 f(logWTotal)
0.025
0.02
0.015
0.01
0.005
0
0 5 10 15 logWTotal
20 25
0.019
0.0188
0.0186
0.0184
0.0182
0.018
0.0178
0 f(logLiab)
5 10 15 logLiab
20 25 30
0.05
0.04
0.03
0.02
0.01
0
0 f(logLiab)
5 10 15 logLiab
20 25 30 f(RetOnCap)
-2
0.04
0.03
0.02
0.01
0
-0.01
0
-0.02
2
RetOnCap
4 6 f(RBCratio)
0.04
0.03
0.02
0.01
0
0 20000 40000
RBCratio
60000 80000
-6 -4 f(RetOnCap)
-2
0.025
0.02
0.015
0.01
0.005
0
0
RetOnCap
2 4 6 f(RBCratio)
0.04
0.03
0.02
0.01
0
0 10000 20000 30000 40000 50000 60000 70000
RBCratio
-4 -3 -2 f(RetOnCap)
0.03
0.025
0.02
0.015
0.01
0.005
0
-1 0
RetOnCap
1 2 3 f(RBCratio)
0.04
0.03
0.02
0.01
0
0 10000 20000 30000
RBCratio
40000 50000
41