Books by Ricardo Rebonato are always an inspiring and wonderfully rewarding read. When asked to review ‘Portfolio Management under Stress’ by Rebonato and Denev for Quantitative Finance, I happily agreed and keenly waited for the books arrival. After receiving it, I could not stop reading and after I finished, I concluded this one is as good as his previous books. Let me tell you why.
Rebonato/Denev start with what most good buy-side risk managers do. Instead of routinely estimating covariance matrices (with more or less sophisticated methods), they try to truly understand the data generating process that created a given historical data-set. To achieve this, they suggest splitting the historical return distribution into a normal (non-crisis) part and a non-normal (crisis) part. This alone is relatively uncontroversial and could also be achieved with standard black box like models (for example, a multivariate mixture of normals). However, they go further. Consistent with historical experience (and backward regulatory stress scenarios) they conjecture that each new crisis will unfold differently. This brings us at the heart of the book: the use of forward looking Bayesian nets to derive marginal and joint crisis return distributions. Bayesian nets allow the user to model conditional distributions consistent with both manager views and historical data. Ricardo and Denev understand that beyond the technical elegance of their approach, senior management does not need black box tools (no matter how good they are), but rather decision support systems that fit senior management’s decision process, i.e. that translate their investment views into a coherent risk framework. Bayesian nets are ideal for this purpose. The book is written in a nice modular fashion, where each part is highly self-contained. While the authors never let their methodology out of sight, they cover a whole array of quantitative and statistical asset management methodology (from entropy pooling and resampling to the use of state price deflators in making implied return forecasts) in passing. Without doubt, this book also makes a great reference for quants in general.
Part 1 carefully explains the importance of taking stress events into account. The treatment goes beyond the usual superficial treatment of tail risk hedging. Rebonato/Denev offer a unified framework for addressing tail risk by directly modelling tail events. Essentially, they view portfolio optimization as a scenario optimization exercise, where scenarios are created using Bayesian nets and the various techniques suggested in the book. Part 2 relates the books philosophy to the notion of predictability and causation. This is much needed, in order to give Bayesian nets the desired casual interpretation. Here as well as in other parts of the book, reference to the academic tribe of Econophysicists are somewhat overdone. In particular, when it comes to resurrecting the ideas of power laws in financial data. As far as the reviewer is concerned, this discussion ended a while ago due to the lack of empirical evidence by the so-called Thalesians. Part 3 reviews the creation and consistent use of subjective views, i.e. the framework Rebonato and Denev aim to extend (replace) in the coming chapters. The authors start with the stability problem of Markowitz solutions as the main obstacle to its practical usefulness. They then cover the Bayesian solution to estimation error maximization as represented by the Black/Littterman model and its sometimes heuristic but practically very useful extensions (like entropy pooling), i.e. the current academic comfort zone for asset allocation quants.
Parts 4 and 5 start to teach old quants new tricks. In particular, they carefully introduce the theoretical foundations of using of Bayesian nets to build conditional probability distributions for tail events. It is also practical, offering guidance on the establishment of root events, event horizon, transmission channels, event correlation and portfolio returns. Despite all this, one problem (shared by all Bayesian methods) remains. What do we do if consistently filling in numerical values for a large number of parameters is too burdensome or expert views are deemed too uncertain? Again, the authors have an answer by using maximum entropy principles. In short, the reader will learn nothing less than the use of Bayesian nets to derive conditional (on a crisis event trigger) marginal distributions for the asset classes in question. As in all his previous books, the mathematics is precise without an overload in notation. Readers familiar with R will find it easy to translate equations into executable code. Part 6 reminds us that once we model the conditional tails of a distribution we need to clean the unconditional data series by removing those tail events in order to come up with meaningful estimates of asset returns in normal times. In other words, the authors engage in multivariate outlier detection. While the weapon of choice for most quants will be the Mahalanobis distance, Rebonato and Denev note the circularity in this approach. To determine outliers, we need mean and dispersion estimates without outliers, but to estimate outliers we need mean and dispersion measures. Instead they suggest the minimum ellipsoid method, i.e. finding the most closely packed points. Once normal times are identified, the authors continue to fit marginal distributions and review tools to fit the necessary copulas to glue marginal distributions together. The methods described will be familiar to most quants. Part 7 is the part where the biggest leap of faith is required from the reader. First, the authors need to come up with a method to splice together the distributions for normal and stress times. Second, all distributions have been build so far without reference to an asset pricing model. Without this, some assets might simply look too good to be true. The authors try to resolve this issue with the use of the CAPM. This is a reasonable approach for risk management related questions, but given its troubled empirical record, it will be much more controversial for asset allocation exercises. Part 8 introduces utility maximization as the most general and flexible framework for portfolio choice using the information so carefully derived in Parts 4–7. After all, scenario optimization via expected utility is the ultimate (non-gameable) risk adjusted performance measure. In this way, Rebonato and Denev give their stress generation engine a decision theoretic framework. In my view, this is a key differentiating factor relative to the whole stress testing literature that usually offers a tunnel view on the conditional probability of stress events without any plausible decision theoretic framework. Utility optimization is a brute force technique that is not always computationally feasible. In Part 9, Rebonato and Denev suggest several numerical tricks that will be of great help in practical work.
This book is strong on both the economics and statistics of dealing with stress events. The authors finish with an extensive case study in Part 10. Here, the authors provide a case study repeating and demonstrating the main points derived in the body of their work. It deals in particular with questions of stability and robustness and has a noteworthy section on the Bayesian approach to deal with uncertainty (rather than risk). I conclude that if I did not already own a reviewers copy, I would buy the book. Most importantly, I will use it.
Chief Scientific Officer, First Private Asset Management
© 2015, Bernd Scherer