Risk Management in Turbulent Times

The subprime crisis has shown that the sophisticated risk management models used by banks and insurance companies had serious flaws. Some people even suggest that these models are completely useless. Others claim that the crisis was just an unpredictable accident that was largely amplified by the lack of expertise and even naivety of many investors. This book takes the middle view. It shows that these models have been designed for "tranquil times", when financial markets behave smoothly and efficiently. However, we are living in more and more "turbulent times": large risks materialize much more often than predicted by "normal" models, financial models periodically go through bubbles and crashes. Moreover, financial risks result from the decisions of economic actors who can have incentives to take excessive risks, especially when their remunerations are ill designed. The book provides a clear account of the fundamental hypotheses underlying the most popular models of risk management and show that these hypotheses are flawed. However it shows that simple models can still be useful, provided they are well understood and used with caution.

Gilles Bénéplanc is the Head of Europe, Middle East, and Africa region for the Mercer consulting firm.

Jean-Charles Rochet is Professor of Mathematics and Economics at the University of Toulouse.

Introduction	p. 1
Risk management: what must be changed
Lessons From Recent Financial Crises	p. 7
The Basic Goals of Risk Management	p. 7
When Risk Management Fails	p. 7
What Should Be Done?	p. 8
Living in Turbulent Times	p. 11
New and Larger Risks	p. 11
Increased Management Accountability	p. 13
Need for a Global Approach	p. 14
The Need for a Proper Methodology	p. 16
The Necessary Ingredients	p. 16
Risk Mapping	p. 17
Loss Control	p. 22
Risk Allocation	p. 23
What is behind risk modeling
The Basic Tools of Risk Modeling	p. 29
Assessing Probabilities: The Frequentist and Subjective Approaches	p. 29
Bayesian Updating	p. 30
Estimating Loss Distributions	p. 32
Combining Event Trees and Monte Carlo Methods	p. 37
The Dangers of the Stationarity Assumption	p. 39
Statistical Risk Measures	p. 41
The Expectation or Mean	p. 41
The Variance	p. 45
Linear Correlation	p. 49
Copulas	p. 52
The Value at Risk	p. 55
Mutualization and Diversification	p. 60
The Dangers of Using Simple Risk Measures	p. 67
Appendix: Extreme Value Theory	p. 75
Leverage and Ruin Theory	p. 78
Leverage and Return on Equity	p. 78
Economic Capital for a Bank	p. 80
Economic Capital for an Insurance Company	p. 81
The Limits of Ruin Theory	p. 85
The perfect markets hypothesis and its dangers
Risk Neutral Valuation	p. 91
The Expected Present Value Criterion	p. 91
The Magic of Perfect Markets	p. 92
Complete Markets and Absence of Arbitrage Opportunities	p. 94
A Binomial Example	p. 96
The Mirages of the Perfect Markets World	p. 98
The Case of Incomplete Markets	p. 104
Solving the St. Petersburg Paradox	p. 104
Certainty Equivalent	p. 106
Markets for Exchanging Risks	p. 108
The Limits of the Equilibrium Approach	p. 114
Risk Management in a Normal World	p. 118
The Mean-Variance Criterion	p. 118
Portfolio Choice	p. 119
The Diversification Principle	p. 121
Efficient Portfolios and the Sharpe Ratio	p. 122
The Capital Asset Pricing Model (CAPM)	p. 124
Futures Contracts and Hedging	p. 125
Capital Allocation and RAROC	p. 128
The Dangers of Viewing the World as "Normal"	p. 130
Portfolio Choice with Several Risky Assets	p. 136
Deriving the CAPM Formula	p. 137
Risk management and shareholder value
Why Market Imperfections Matter for Shareholder Value	p. 143
Standards Methods for Assessing Shareholder Value	p. 143
Why the Shareholder Value Function Is Likely to Be Non-Linear: A Simple Example	p. 146
Incentive Problems Generate Financial Frictions	p. 147
The Shareholder Value Function	p. 150
A Target Level of Cash	p. 150
A Model for Optimizing Liquidity Management	p. 151
Liquidity and Shareholder Value	p. 153
Stochastic Differential Calculus	p. 154
Derivation of the Shareholder Value Function	p. 156
Risk Management and the Shareholder Value Function	p. 158
Decision 1: How Much Risk to Take	p. 158
Decision 2: Which Risks to Insure	p. 159
Decision 3: How Much Liquidity to Keep in Reserves	p. 162
Decision 4: How Much Hedging to Perform	p. 164
What to do in practice
The Different Steps of the Implementation	p. 169
Estimating the Shareholder Value Function	p. 169
A Unifying Metric for Risk Mapping: The Risk Value Mapping	p. 170
The New Instruments of Risk Management	p. 171
Learning from an Example	p. 178
Presentation of Med Corp	p. 179
Risk Analysis	p. 180
Shareholder Value and Risk Management for Med Corp	p. 182
A Risk Transfer Policy for Med Corp	p. 185
Conclusion: Some Simple Messages	p. 194
Message # 1: Quantitative Models Are Needed But They Must Be Used With Precaution	p. 194
Message # 2: Risk Management Creates Value for Shareholders	p. 194
Message # 3: Things To Do in Practice	p. 195
Message # 4: Key Ingredients for a Successful Risk Management Approach	p. 196
Notes	p. 197
Index	p. 203
Table of Contents provided by Ingram. All Rights Reserved.

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Risk Management in Turbulent Times

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Author Biography

Table of Contents

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