Measuring Risk Management Performance of Insurers: a DEA Approach Yayuan Ren Illinois State University August, 2007

ARIA Outline  Research purpose  Literature review  DEA model  Discussion of selection of inputs and outputs for RM performance evaluation  Evaluation results  Uses of evaluation results  Summary

ARIA Research Purpose  The research intends to directly evaluate the performance of insurer risk management (RM) using the nonparametric properties of data envelopment analysis (DEA).  The final result of this project is to provide a Risk Management Performance Index (RMPI) for insurers.  This presentation here focuses on discussing the methodology of the proposed project.

ARIA Literature Review  Importance of corporate RM  Evaluate the performance of corporate RM Studies concerning the evaluation of the effectiveness of RM have been scarce (Schmit and Roth, 1990). At present, no widely accepted indicators exist to directly valuate the performance of risk management.

ARIA Literature Review (cont ’ )  About DEA DEA is a tool to evaluate target achievement of decision- making units (DMUs) DEA approach was introduced by Farrell (1957) and advanced by Charnes, Cooper and Rhodes (1978), Banker, Charnes, and Cooper (1984) The major advantages of DEA include: (1) it can handle multiple input and multiple output models; (2) It doesn't require an assumption of a functional form relating inputs to outputs. The special properties of DEA can be applied in measuring risk management performance.

ARIA Literature Review (cont ’ )  Applications of DEA DEA has been largely employed to study efficiency of organizational activities.  Insurer efficiency studies Cummins and Weiss (1993, 1998); Berger, Cummins and Weiss (1997); Cummins, Weiss, and Zi (1998), etc. A recent study using a set of different inputs/outputs : Brockett, Cooper, Golden, Rousseau and Wang (2005)

ARIA Table 1.1: Inputs and Outputs Selections of Cummins, Weiss, and Zi (1998) No.InputsOutputs 1Labor expenseLoss payment 2Business services 3Equity capital 4Debt capital Table 1.2: Inputs and Outputs Selections of Brockett, Cooper, Golden, Rousseau and Wang (2005) No.InputsOutputs 1Surplus previous yearRates of return on investments 2Change in capital and surplus Liquid assets to liability (claims- payment ability) 3Underwriting and investment expenses Solvency scores 4Policyholders supplied debt capital

ARIA Literature Review (cont ’ )  Applications of DEA (cont ’ ) Recent uses of DEA extend from “ efficiency ” to “ effectiveness ” evaluations.  Discussed in article “ DEA: Past Accomplishments and Future Prospects ” by Cooper et al (2005)  Examples Golany and Thore (1997)- evaluate social performances of countries ReTakamura and Tone (2003)- evaluate the functionality of Japanese cities Staat and Hammerschmidt (2005)- evaluate product performance Eling (2006)-evaluate performance of hedge funds

ARIA DEA Models  Charnes, Cooper and Rhodes (CCR) Model (1978)  Banker, Charnes, and Cooper (BCC) Model (1984).  One limitation of the standard CCR or BCC model is that they only estimate "relative" performance of a DMU but not "absolute" performance  To address this problem, Brockett et al (2005) introduce to the insurance literature a new form of the DEA model — Risk Adjusted Measure (RAM) model, which is able to provide ordinal level performance scoring (ranking).  As a result, RAM DEA model is employed to calculate the performance scores of insurer RM

ARIA Discussion of Selection of Inputs and Outputs  The selection of variables to represent inputs and outputs (goals) is crucial to the validity of the analysis.  A thumb rule of selection, as discussed by Charnes and Cooper, is that Ceteris paribus, if it is desirable to increase the quantity of the variable, it is an output; and if it is undesirable to have an increase in its value, it is an input.

ARIA Inputs Inputs resources that a DMU employs in order to conduct its operations. The inputs of RM should be risks born by an insurer. As insurers function as financial intermediaries and managers of a risk pool, the major sources of risk for insurers come from investment and underwriting. -- Input 1: investment risk Input 2: underwriting risk Leverage represents an important financial risk for an insurer. Increase in capital level is a direct substitute for RM. Therefore, leverage is set as the third inputs. -- Input 3: leverage

ARIA Outputs  Outputs are “ final goods or goals ” of RM.  Purpose of corporate RM: minimize the negative impact (cost) of uncertainty (risk) regarding possible losses, serving for the firm ’ s objective of value maximization.  Gains of corporate RM Reduction in bankruptcy and distress costs Reduction in costs of raising funds Reduction in expected payments to stakeholders Reductions in tax payments Notes: the first three gains are analyzed in Smith and Stulz (1985) and the fourth gain is analyzed in Froot, Scharfstein and Stein (1993)

ARIA Outputs (cont ’ )  Two outputs of RM Output 1: solvency Ceteris paribus, the lower the likelihood of financial distress or bankruptcy, the better the performance of RM. Output 2: value added from bearing risk RM increases firm value through the gains discussed earlier.

ARIA Figure 1:Use DEA model to evaluate RM performance Value added from bearing risk

ARIA Table 2: Input and output variables and measurements VariableMeasurement InputsInvestment riskvariance of investment return Underwriting riskvariance of loss ratio Leveragetotal liabilities/total assets OutputsSolvency1-estimated insolvency propensity* Value added from bearing risk return on assets Note: The insolvency probability can be estimated using the neural network model described in Brockett et al (1994)

ARIA Evaluation Results  Results of performance evaluation The RAM DEA model generates performance scoring for each firm and therefore constructs a Risk Management Performance Index (RMPI) for insurers.  Evaluation Windows Short-term windows of 1 or 3 years Long-term windows of 5 years or longer

ARIA Uses of the Evaluations  The RM evaluations can be further examined to study stock versus mutual form of organizational structure, and the relationships of other firm characteristics and insurer RM performance.  The RMPI can be easily incorporated as an explanatory variable in regressions to examine a number of RM hypotheses and issues.  Decision makers of insurance companies and regulators may use RMPI as an indicator to evaluate and improve the effectiveness of their strategies.

ARIA Summary  This study extends the use of DEA from efficiency to effectiveness evaluation in insurance literature.  This study develops a Risk Management Performance Index (RMPI) to evaluate the effectiveness of insurer risk management.  Insurers are risk takers that function as financial intermediaries and managers of a risk pool. The evaluation of insurer RM in this study is based upon this point of view.  Next step is to collect data and report on evaluation outcomes.

ARIA The End Thank you!