Capital Adequacy and Allocation

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Capital Adequacy and Allocation

• John M. Mulvey
• Princeton University
• Michael J. Belfatti Chris K. Madsen
• American Re-Insurance Company
• June 8th, 1999

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Discussion Overview

• Background
• Elements of a DFA system
• Integrated Risk Management
• Capital Allocation Issues

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Background

• Price of risk has all but vanished in many
  financial transactions
• Methodology is needed to evaluate business
  opportunities
• Efficient use of capital is increasingly needed
  to play
• The risk adjusted price for same business may
  differ from company to company - even if they are
  using identical approaches

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What is DFA?

• Dynamic Financial Analysis
• It is a tool - not a crystal ball
• It consistently links together all modeled
  assumptions
• A set of plausible paths for the future

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Methodology to Model Economic Statistics, Asset
Returns, and Insurance Losses
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• Employ stochastic processes for economic factors
• interest rates
• inflation
• GDP
• currencies
• Sample with discrete time and discrete scenarios

scenarios
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Model Calibration (Fitting)

• Monthly inflation (74-98)

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Loss Simulation with DFA
Gross loss Net loss Ceded loss Retained
premiums Ceded premiums
Simulation
Defining the r/i structure
Modeling the portfolio
Loss data Premiums
Customer requirements Limits Prices
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Integrated Risk Management

• Company Optimization

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Strategic Asset Liability Systems

• Russells System for Yasuda in Japan
• Towers Perrin-Tillinghast CAPLink/OPTLink, TAS
• Ortecs Pension Planning in Netherlands
• American Re-Insurance - ARMS

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Integrated Risk Management at American
Re-Insurance

• Manage risk while maximizing expected return on
  capital
• Evaluate mergers - acquisitions
• Optimize retrocessional reinsurance decisions
• Analyze corporate capital structure/ capital
  allocation
• Propose alternative asset allocations
• Business mix analysis

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Model Uncertainties
Simulate Organization
scenarios
Calibrate and sample
Optimize
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ARMS - A Brief Overview
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Capital Optimization Framework

• Capitalt Assetst - Liabilitiest
• Grow capital over planning period
• t 1, 2, , T
• maximize risk-adjusted profit for entire company
• analyze over representative set of scenarios S
• Constraints on GAAP, STAT, plus risk measures
• Defining risk measure is often difficult (EPD,
  utility based, MPT, probability of ruin, etc.)

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Key Decision Levers

• Asset Allocation
• Amount and type of business activities
• Retrocessional coverage
• Capital structure

Relative Profit
Safety
Capital C
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Optimal Result
The more flexible the model, the better you can
manage risk
AL Reward

• Change reward to ROC and risk to EPD ratio, for
  example Asset Liability Efficient Frontier
• Then choose company position on frontier

Next step Stochastic Re-Insurance Structure
Asset Liability with Stochastic Rates
Asset Liability with Deterministic Rates
Asset Only
AL Risk
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Capital Allocation for Strategic DFA
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Centralized Approach

• Single DFA system
• optimize company
• Real-time marginal analysis
• Accept deal if company risk-adjusted
  profitability is acceptable, else reject
• Difficult to implement for large companies

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Decentralized Approach

• Allocate capital to divisions
• Provide profit targets (hurdle rates)
• Maintain safety of entire organization
• Reward superior performance
• Communicate management financial goals to areas
  of underwriting responsibility (Meyers)

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Linking Strategic and Tactical
Strategic System
Prices of Risk (t,s) Target benchmarks
Risk Adjusted Profit
Tactical Asset Systems
Tactical Liability Systems
Re-insurance contracts
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Requirements

• Additive
• Sum of allocations should equal desired firm
  capital
• Sub-Additive
• Super-Additive
• Coalitions should be stable (cooperative games)
  for performance attribution
• No one is worse off for having joined
  (individual rationality)
• No sub-group would be better off on their own
  (collective rationality)

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Goals of Allocation

• Managing safety (stand-alone)
• Marginal Analysis
• Performance attribution
• Shapley Values (cooperative games)
• Modern Portfolio Theory
• Diversification benefits
• Concentration penalties

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Managing Safety

• Compute expected policy holder deficit for each
  division
• Stand-alone (first-in) EPD is over-capitalized
  but safe (superior to VaR)
• Sub-additive
• For additivity, revise capital based on
  diversification benefits

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Marginal Analysis

• Additional capital needed for activity (last-in
  method)
• Next increment
• Fixed size (buying price)
• Where to grow and shrink businesses

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Shapley Values

• Calculate capital if division is first added,
  second added, third and so on
• Average amounts of capital under all ordering
  scenarios -- capital needed for division
• No re-scaling, but computationally intensive (5
  divisions over 100 runs)

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Modern Portfolio Theory

• Easy to administrate
• Correlation with company ROE
• Standalone volatility
• Volatility based
• less desirable if business lines are
  heterogeneous
• Ignores shape of distribution

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Summary

• Integrated DFA captures joint impacts of business
  levers
• Decentralized allocation is todays reality
• EPD (stand-alone) is conservative (over
  capitalizes)
• EPD adjusted for diversification or Shapley
  values is optimal