Capital 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 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

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 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? 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

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) Monthly inflation (‘74-’98)

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

Integrated Risk Management Company 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

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

Model Uncertainties Simulate Organization scenarios Calibrate and sample Optimize

ARMS - A Brief Overview

Capital t = Assets t - Liabilities t 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 t = Assets t - Liabilities t 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 Framework

Key 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 Safety Relative 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 Result

Capital Allocation for Strategic DFA

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

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”) 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 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 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

Marginal Analysis Additional capital needed for activity (“last-in method”)  Next increment  Fixed size (buying price) Where to grow and shrink businesses Additional capital needed for activity (“last-in method”)  Next increment  Fixed size (buying price) Where to grow and shrink businesses

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

Summary 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