Capital Adequacy and AllocationCapital Adequacy and Allocation

John M. Mulvey

Princeton University

Michael J. Belfatti & Chris K. Madsen

American Re-Insurance Company

June 8th, 1999

John M. Mulvey

Princeton University

Michael J. Belfatti & Chris K. Madsen

American Re-Insurance Company

June 8th, 1999

Discussion OverviewDiscussion Overview Background Elements of a DFA system Integrated Risk Management Capital Allocation Issues

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

BackgroundBackground 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

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

What is DFA?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

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

Methodology to Model Economic Statistics, Asset

Returns, and Insurance Losses

Methodology to Model Economic Statistics, Asset

Returns, and Insurance Losses

Employ stochastic processes for economic factors: interest rates inflation GDP currencies

Sample with discrete time and discrete scenarios

Employ stochastic processes for economic factors: interest rates inflation GDP currencies

Sample with discrete time and discrete scenarios

Model Calibration (Fitting)Model Calibration (Fitting) Monthly inflation (‘74-’98) Monthly inflation (‘74-’98)

Frequency of Monthly Inflation

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

-1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

Inflation

Fre

qu

ency

Simulated

Actual

Frequency of Monthly Inflation

0.0%

5.0%

10.0%

15.0%

20.0%

25.0%

30.0%

35.0%

-1.0% -0.5% 0.0% 0.5% 1.0% 1.5% 2.0%

Inflation

Fre

qu

ency

Simulated

Actual

SimulationDefining ther/i structure

Modeling the

portfolio

Gross loss

Net loss

Ceded loss

Retained premiums

Ceded premiums

Loss Simulation with DFA

Loss data

PremiumsCustomer requirements

Limits

Prices

Integrated Risk ManagementIntegrated Risk Management

Company OptimizationCompany Optimization

Russell’s System for Yasuda in Japan Towers Perrin-Tillinghast CAP:Link/OPT:Link,

TAS Ortec’s Pension Planning in Netherlands American Re-Insurance - ARMS

Russell’s System for Yasuda in Japan Towers Perrin-Tillinghast CAP:Link/OPT:Link,

TAS Ortec’s Pension Planning in Netherlands American Re-Insurance - ARMS

Strategic Asset & Liability Systems

Strategic Asset & Liability Systems

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

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

Integrated Risk Management at American Re-Insurance

Integrated Risk Management at American Re-Insurance

Model Uncertainties

Simulate Organizationscenarios

Calibrate and sample Optimize

ARMS - A Brief OverviewARMS - A Brief Overview

FinancialMarket

Economic

UnderwritingLiability

InsuranceMarket

AssetModel

Liability &Re-

InsuranceModel

Bu

siness M

od

el

Acco

un

ting

Fra

mew

ork

GE

M (G

lob

al

Econ

om

ic M

od

el)

Model Calibration & OptimizationInput

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.)

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.)

Capital Optimization FrameworkCapital Optimization Framework

Key Decision LeversKey Decision Levers Asset Allocation Amount and type of

business activities Retrocessional

coverage Capital structure

Asset Allocation Amount and type of

business activities Retrocessional

coverage Capital structure

Capital C

SafetyRelative Profit

Change reward to ROC and risk to EPD ratio, for example: Asset Liability Efficient Frontier

Then choose company position on frontier

Change reward to ROC and risk to EPD ratio, for example: Asset Liability Efficient Frontier

Then choose company position on frontier

AL Reward

AL Risk

Asset Only

Asset Liability with Deterministic Rates

Asset Liability with Stochastic Rates

The more flexible the model, the better you can manage risk

Next step: Stochastic Re-Insurance Structure

Optimal ResultOptimal Result

Capital Allocation for Strategic DFA

Capital Allocation for Strategic DFA

Centralized ApproachCentralized 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

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

Decentralized ApproachDecentralized 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)

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)

Linking Strategic and TacticalLinking Strategic and Tactical

Tactical Asset Systems

Tactical Liability Systems

Strategic System

Re-insurance contracts

Prices of Risk (t,s)

Target benchmarks

Risk Adjusted Profit

RequirementsRequirements 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”)

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”)

Goals of AllocationGoals of Allocation Managing safety (stand-alone) Marginal Analysis Performance attribution

Shapley Values (cooperative games)

Modern Portfolio Theory Diversification benefits Concentration penalties

Managing safety (stand-alone) Marginal Analysis Performance attribution

Shapley Values (cooperative games)

Modern Portfolio Theory Diversification benefits Concentration penalties

Managing SafetyManaging 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

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

duuuEPD

)(0

Marginal AnalysisMarginal Analysis Additional capital needed for activity

(“last-in method”)Next incrementFixed size (buying price)

Where to grow and shrink businesses

Additional capital needed for activity (“last-in method”)Next incrementFixed size (buying price)

Where to grow and shrink businesses

Shapley ValuesShapley 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)

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)

Modern Portfolio TheoryModern Portfolio Theory Easy to administrate

Correlation with company ROEStandalone volatility

Volatility based less desirable if business lines are

heterogeneousIgnores shape of distribution

Easy to administrateCorrelation with company ROEStandalone volatility

Volatility based less desirable if business lines are

heterogeneousIgnores shape of distribution

SummarySummary Integrated DFA captures joint impacts of

business levers Decentralized allocation is today’s reality EPD (stand-alone) is conservative (over

capitalizes) EPD adjusted for diversification or

Shapley values is optimal

Integrated DFA captures joint impacts of business levers

Decentralized allocation is today’s reality EPD (stand-alone) is conservative (over

capitalizes) EPD adjusted for diversification or

Shapley values is optimal