Enterprise Risk Management, Insurer Pricing, And Capital Allocation

1
Enterprise Risk Management, Insurer Pricing, And
Capital Allocation
11 July 2007
Acknowledgement The authors acknowledge
financial support from Australian Research
Council Discovery Grants DP0663090 and DP0556775
and support from the UNSW Actuarial Foundation of
the Institute of Actuaries of Australia. Yow
acknowledges the financial support of Ernst and
Young and the award of the Faculty of Business
Honours Year Scholarship
2
Introduction

• Economic capital is central to enterprise risk
  management for insurers and reinsurers
• Value-at-Risk (VaR) is widely used to determine
  economic capital and methods of capital
  allocation are used to price lines of business
• We consider a single-period model of a
  multiple-line property-liability insurer
  incorporating
• Taxes, agency costs of capital, and bankruptcy
  costs
• Policyholder preferences for financial quality
• Price elasticities by line of business
• Capital and pricing strategies are evaluated by
  maximising shareholder value

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Agenda

• Key findings
• Approach
• Numerical results
• Further work

4
Key findings

• When policyholders have imperfectly elastic
  demand, prices are significantly influenced by
  the price elasticity of demand
• Firms typically focus on the risk of a line of
  business
• VaR must be carefully implemented to be
  consistent with maximising shareholder value
• Minimum solvency requirements produce low credit
  spreads, creating additional frictional costs
• Using a firm-wide cost of capital may
  significantly reduce shareholder value
• The cost of capital should differ by line of
  business incorporating by-line price elasticities

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Agenda

• Key findings
• Approach
• Numerical results
• Further work

6
Approach

• Model insurer has a large, mature portfolio with
  approximately 10 market share
• Business portfolio includes 5 lines motor,
  household, fire ISR, liability, and CTP
• Asset mix fixed 15 cash, 65 bonds, and 20
  equities
• Insurance markets are relatively competitive
• Price elasticities are assumed according to
  personal, commercial, or compulsory lines
• Frictional costs no tax impact, 2 agency costs
  of capital and 25 bankruptcy costs
• Default risk is the value of the put option to
  default on liabilities
• Assets and liabilities are assumed to be joint
  log-normally distributed1
• Solved and optimised using MATLAB and a direct
  search method
• Data sources
• APRAs Half Yearly GI Bulletin Tillinghast Risk
  Margin Analysis

1. Sherris and van der Hoek (2006)
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Economic model of an insurer1
1. Approach is similar to Zanjani (2002)
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Four strategies for capitalisation and pricing
are considered
Capital Strategy
Pricing Strategy
Cost of Capital

• Optimal capital and prices that maximise
  shareholder value added
• VaR at 99.5 confidence level
• VaR at 99.5 confidence level
• VaR at 99.5 confidence level

• Not applicable
• Capital allocated proportionally
• By-line returns must meet the cost of capital
• Capital allocated proportionally
• By-line returns must meet the cost of capital
• Capital allocated proportionally
• By-line returns must meet the cost of capital

• Not applicable
• 15
• 20
• 15 commercial lines

Note VaR at the 99.5 confidence level is
consistent with APRAs minimum solvency
requirements
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Agenda

• Key findings
• Approach
• Numerical results
• Further work

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Using a firm-wide cost of capital significantly
reduces shareholder value
Enterprise value added (EVA) for different
strategies ( of liabilities)
EVA ( of liabilities)
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VaR-based strategies incorrectly price lines of
business...
By-line economic profit margins for different
strategies
Profit margin ()
CTP
Profit margins are significantly influenced by
the price elasticity of demand
Liability
Fire ISR
Household
Motor
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...creating a sub-optimal portfolio mix
Business portfolio mix for different strategies
Portfolio mix ( of liabilities)
CTP
Strategies that ignore demand elasticities are
biased toward low-risk lines
Liability
Fire ISR
Household
Motor
13
VaR at the 99.5 confidence level creates
additional frictional costs...
Economic capital vs. frictional costs for
different strategies
Capital ( of liabilities)
Frictional costs (m)
Frictional costs
Economic capital
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...and lowers default risk below optimal levels
across all lines of business
By-line default value for different strategies
Default ratio ()
A Credit Rating
AAA Credit Rating
CTP
Frictional costs create a trade-off between the
benefits of financial quality and the costs of
holding capital
Liability
Fire ISR
Household
Source Ratings based on SP one-year default
rates 19812003
Motor
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Agenda

• Key findings
• Approach
• Numerical results
• Further work

16
Further work

• Cost of capital should vary by line of business
  for pricing purposes
• Results based on assumed price elasticities
• A better understanding of price elasticities by
  line of business and preferences for financial
  quality is required
• Frictional costs of capital need to be better
  understood
• Trade-off between financial quality and
  frictional costs

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Back-up slides
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Price elasticity and volatility assumptions by
line of business
Line of business
Price elasticity
Default elasticity
CVs1
Motor Household Fire ISR Liability CTP
15.6 16.4 26.1 24.8 11.7
0.48 0.50 0.78 0.74 0.37
11.1 13.2 14.1 19.0 23.5
1. CVs based on results of the Tillinghast Risk
Margin Analysis of Australian General Insurance
Industry data 19972001