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Session C-5: ARIA Prize Paper CAS Spring Meeting May 2006 The Use of DFA to Determine Whether an Optimal Growth Rate Exists for a Property-Liability Insurer. by Stephen P. D’Arcy and Richard W. Gorvett University of Illinois Published in the Journal of Risk and Insurance , December, 2004.

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Session C-5: ARIA Prize PaperCAS Spring Meeting May 2006The Use of DFA to Determine Whether an Optimal Growth Rate Exists for a Property-Liability Insurer

by Stephen P. D’Arcy and Richard W. Gorvett

University of Illinois

Published in the Journal of Risk and Insurance,

December, 2004

overview
Overview
  • Introduction
  • Dynamic Financial Analysis
  • Aging Phenomenon
  • Market Value of P-L Insurance Company
  • Optimal Growth Rate
  • Analysis of Results
dynamic financial analysis
Dynamic Financial Analysis
  • An approach to modeling insurance companies
  • Solvency testing
  • Ratings
  • DFA models also allow managers to test various operational strategies
objective of paper
Objective of Paper
  • Utilize a DFA model to determine the optimal growth rate based on
  • - mean-variance efficiency
  • - stochastic dominance
  • - constraints of leverage
  • Based on the latest version of a public access DFA model (DynaMo3) http://www.pinnacleactuaries.com/
aging phenomenon
Aging Phenomenon
  • New business has a very high loss ratio, often in excess of the initial premium
  • The loss ratio then declines with each renewal cycle to the profitable point
  • Longer-term business has an even lower loss ratio, making it very profitable
  • A P-L insurer’s growth rate has a significant effect on profitability
market value of p l insurance company
Market Value of P-L Insurance Company
  • Determining the market value of a hypothetical property-liability insurer is not a simple task.
  • Only a few P-L insurers are stand-alone companies that are publicly traded, allowing the market value of the firm to be observed
approaches to determine company value
Approaches to Determine Company Value
  • Fama-French model (three factor model)
  • r - Rf =  beta x ( Km - Rf ) + bs x SMB + bv x HML + alpha
  • SMB - small [cap] minus big
  • HML - high [book/price] minus low
  • CAPM
  • Multiple Regression (our method)
multiple regression approach
Multiple Regression Approach
  • The market value of an insurer is measured by
  • - Policyholders’ Surplus
  • - Net Written Premium
  • (the size of the book of business)
  • - Combined Ratio and Operating Ratio
  • (profitability)
optimal growth rate
Optimal Growth Rate

Target Metric

Net income over the projection period plus the terminal value of the company at the end of the five-year period

sensitivity test
Sensitivity Test
  • Assume several different growth rates within the range of reasonable values
  • Mean-Variance analysis
  • First-degree stochastic dominance
  • Second -degree stochastic dominance
operating constraints
Operating Constraints
  • The optimal growth rate cannot be determined based on
    • mean-variance analysis
    • first- or second-degree stochastic dominance
  • Impact of adding constraints
constraining premium to surplus ratios
Constraining Premium-to-Surplus Ratios
  • The proportion of outcomes that lead to unacceptable premium-to-surplus levels can be added as a constraint in the maximization process.
comparative statics
Comparative Statics
  • Initial state of the insurance market
  • Acuity of the aging phenomenon
  • Renewal rate
  • Starting interest rates
dfa model characteristics
DFA Model Characteristics
  • Implied rate change variable depends on

- current market condition (mature hard, immature soft, mature soft and immature hard)

  • - targeted growth rate
  • - rate change impacts profitability
  • Potential impact on persistency (renewal rate)
  • - rate changes could impact persistency
  • - effect could vary by age of business
  • Managing growth rates
  • - DFA program uses constant growth rate
  • - managers likely to vary growth target based on market conditions
  • - need to modify DFA program
caveats
Caveats
  • Models are simplified versions of reality
  • This DFA model deals with quantifiable risk only
  • Excludes the following risks
  • - A line of business being socialized
  • - Management fraud
  • - Catastrophic risks other than historical patterns
conclusions
Conclusions
  • Increasing the growth rate reduced statutory policyholders’ surplus and current net income, but increased both the future market value of the insurer and the volatility of results
  • The optimal growth rate for the modeled insurer varied from zero to 7.5 percent
  • Growth rates of 10 percent or higher generated unacceptable premium to surplus ratios too frequently
  • Low initial interest rates increased the incentive for growth
  • High initial interest rates lowered the optimal growth rate
  • Varying the other key parameters did not affect the optimal growth rate significantly
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