Measuring Risk Management Performance of Insurers: a DEA Approach

1. Measuring Risk Management Performance of Insurers: a DEA Approach Yayuan Ren Illinois State University ARIA 2007

2. 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 2007 yren2@ilstu.edu

3. 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 project. ARIA 2007 yren2@ilstu.edu

4. Literature Review • Importance of corporate RM • Evaluate the performance of corporate RM • Studies concerning the evaluation of the effectiveness of RM have been scarce. • At present, no widely accepted indicators exist to directly valuate the performance of risk management. ARIA 2007 yren2@ilstu.edu

5. 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 2007 yren2@ilstu.edu

6. 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 2007 yren2@ilstu.edu

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8. 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 2007 yren2@ilstu.edu

9. 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—Range 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 2007 yren2@ilstu.edu

10. 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 • Other things being equal, 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 2007 yren2@ilstu.edu

11. 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 2007 yren2@ilstu.edu

12. 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 2007 yren2@ilstu.edu

13. Outputs (cont’) • Two outputs of RM • Output 1: solvency Other things being equal,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 2007 yren2@ilstu.edu

14. Value added from bearing risk Figure 1:Use DEA model to evaluate RM performance Risk Management -- Reinsurance -- Retention/self-insure -- Hedging -- Increase capital -- Diversification, etc ARIA 2007 yren2@ilstu.edu

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16. 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 2007 yren2@ilstu.edu

17. 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 2007 yren2@ilstu.edu

18. Summary • This study extends the use of DEA from efficiency to effectiveness evaluation in insurance literature. • 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. • This study develops a Risk Management Performance Index (RMPI) to evaluate the effectiveness of insurer risk management. • Next step is to collect data and report on evaluation outcomes. ARIA 2007 yren2@ilstu.edu