Extreme Events: Robust Portfolio Construction in the Presence of Fat Tails


With slight exaggeration, a case can be made that modern finance has been built, in practice, if not in theory, on implicit tolerance and widespread ignorance of extreme events.
Jean Pierre Landau, Deputy Governor, Banque du France

Markets are fat-tailed; extreme outcomes occur more often than many might hope, or indeed the statistics or normal distributions might indicate. In this book, the author provides readers with the latest tools and techniques on how best to adapt portfolio construction techniques to cope with extreme events. Beginning with an overview of portfolio construction and market drivers, the book will analyze fat tails, what they are, their behavior, how they can differ and what their underlying causes are. The book will then move on to look at portfolio construction techniques which take into account fat tailed behavior, and how to stress test your portfolio against extreme events. Finally, the book will analyze really extreme events in the context of portfolio choice and problems. The book will offer readers:

  • Ways of understanding and analyzing sources of extreme events
  • Tools for analyzing the key drivers of risk and return, their potential magnitude and how they might interact
  • Methodologies for achieving efficient portfolio construction and risk budgeting
  • Approaches for catering for the time-varying nature of the world in which we live
  • Back-stop approaches for coping with really extreme events
  • Illustrations and real life examples of extreme events across asset classes

This will be an indispensible guide for portfolio and risk managers who will need to better protect their portfolios against extreme events which, within the financial markets, occur more frequently than we might expect.





1 Introduction.

1.1 Extreme events.

1.2 The portfolio construction problem.

1.3 Coping with really extreme events.

1.4 Risk budgeting.

1.5 Elements designed to maximise benefit to readers.

1.6 Book structure.

2 Fat Tails – In Single (i.e., Univariate) Return Series.

2.1 Introduction.

2.2 A fat tail relative to what?

2.3 Empirical examples of fat-tailed behaviour in return series.

2.4 Characterising fat-tailed distributions by their moments.

2.5 What causes fat tails?

2.6 Lack of diversification.

2.7 A time-varying world.

2.8 Stable distributions.

2.9 Extreme value theory (EVT).

2.10 Parsimony.

2.11 Combining different possible source mechanisms.

2.12 The practitioner perspective.

2.13 Implementation challenges.

3 Fat Tails – In Joint (i.e., Multivariate) Return Series.

3.1 Introduction.

3.2 Visualisation of fat tails in multiple return series.

3.3 Copulas and marginals – Sklar’s theorem.

3.4 Example analytical copulas.

3.5 Empirical estimation of fat tails in joint return series.

3.6 Causal dependency models.

3.7 The practitioner perspective.

3.8 Implementation challenges.

4 Identifying Factors That Significantly Influence Markets.

4.1 Introduction.

4.2 Portfolio risk models.

4.3 Signal extraction and principal components analysis.

4.4 Independent components analysis.

4.5 Blending together principal components analysis and independent components analysis.

4.6 The potential importance of selection effects.

4.7 Market dynamics.

4.8 Distributional mixtures.

4.9 The practitioner perspective.

4.10 Implementation challenges.

5 Traditional Portfolio Construction Techniques.

5.1 Introduction.

5.2 Quantitative versus qualitative approaches?

5.3 Risk-return optimisation.

5.4 More general features of mean-variance optimisation.

5.5 Manager selection.

5.6 Dynamic optimisation.

5.7 Portfolio construction in the presence of transaction costs.

5.8 Risk budgeting.

5.9 Backtesting portfolio construction techniques.

5.10 Reverse optimisation and implied view analysis.

5.11 Portfolio optimisation with options.

5.12 The practitioner perspective.

5.13 Implementation challenges.

6 Robust Mean-Variance Portfolio Construction.

6.1 Introduction.

6.2 Sensitivity to the input assumptions.

6.3 Certainty equivalence, credibility weighting and Bayesian statistics.

6.4 Traditional robust portfolio construction approaches.

6.5 Shrinkage.

6.6 Bayesian approaches applied to position sizes.

6.7 The ‘universality’ of Bayesian approaches.

6.8 Market consistent portfolio construction.

6.9 Resampled mean-variance portfolio optimisation.

6.10 The practitioner perspective.

6.11 Implementation challenges.

7 Regime Switching and Time-Varying Risk and Return Parameters.

7.1 Introduction.

7.2 Regime switching.

7.3 Investor utilities.

7.4 Optimal portfolio allocations for regime switching models.

7.5 Links with derivative pricing theory.

7.6 Transaction costs.

7.7 Incorporating more complex autoregressive behaviour.

7.8 Incorporating more intrinsically fat-tailed behaviour.

7.9 More heuristic ways of handling fat tails.

7.10 The practitioner perspective.

7.11 Implementation challenges.

8 Stress Testing.

8.1 Introduction.

8.2 Limitations of current stress testing methodologies.

8.3 Traditional stress testing approaches.

8.4 Reverse stress testing.

8.5 Taking due account of stress tests in portfolio construction.

8.6 Designing stress tests statistically.

8.7 The practitioner perspective.

8.8 Implementation challenges.

9 Really Extreme Events.

9.1 Introduction.

9.2 Thinking outside the box.

9.3 Portfolio purpose.

9.4 Uncertainty as a fact of life.

9.5 Market implied data.

9.6 The importance of good governance and operational management.

9.7 The practitioner perspective.

9.8 Implementation challenges.

10 The Final Word.

10.1 Conclusions.

10.2 Portfolio construction principles in the presence of fat tails.

Appendix: Exercises.

A.1 Introduction.

A.2 Fat tails – In single (i.e., univariate) return series.

A.3 Fat tails – In joint (i.e., multivariate) return series.

A.4 Identifying factors that significantly influence markets.

A.5 Traditional portfolio construction techniques.

A.6 Robust mean-variance portfolio construction.

A.7 Regime switching and time-varying risk and return parameters.

A.8 Stress testing.

A.9 Really extreme events.