A Quantitative Framework to Assess the Risk-reward Profile of Non-equity Products

Faced with myriad choices, retail investors choose between different financial products based on their liquidity attitude, risk appetite, budget constraints and performance objectives. But how, given the vast range of products and the innumerable ways of describing them, can an investor know the fundamental information to make an enlightened investment decision? In this new book, Marcello Minenna provides a framework for assessing the risk-return profile of non-equity products. The framework is: practical - it combines commonly used techniques; scalable - it can be applied across a range of products; and transferable - it enables the investor, structurer or regulator to look across and compare performances. The methodology developed is comprised of three indicators or pillars which will reveal the material risks of the products: Pillar 1: Price unbundling and probabilistic scenarios. This pillar is about understanding what will impact the value of the non-equity financial product over its lifetime. Pillar 2: Degree of risk. This displays the degree of risk that characterises the product throughout the entire investment time horizon (summarising the temporal evolution of the risk) and the variability of the product's returns over the entire period. Pillar 3: Recommended investment time horizon. This acts as an indicator which expresses a recommendation regarding the holding period of the product, for instance how long would an investor expect to hold a product before, say, breaking even. Individual chapters explain each pillar, offering a detailed illustration of the analytical tools underlying each of these indicators. A final chapter applies the three pillars to six non-equity products that feature various solutions of financial engineering (one risk-target, one benchmark, three return-target products and one structured liability). These practical examples show in a concrete way the strict connections and the complementarity of the pillars in revealing the material risks and essential characteristics of any non-equity product. This information can be easily gathered in a short document of great utility: For issuers and structurers, it represents a practical and useful way to describe a product; For investors, it is a snapshot of the investment's characteristics to help them decide whether to invest; For regulators, it presents a transparent and consistent way for investments to be described. Marcello Minenna's practical guide represents the standardisation of one methodology for assessing the risk-return of financial products. His quantitative approach is a new touchstone for retail investors, issuers, structurers, distributors and regulators, and is essential reading for those working in the measurement and management of risk.

Table of Contents:
About the Author Foreword Preface Acknowledgements List of Figures List of Tables 1 Introduction 2 The First Pillar: Price Unbundling and Probabilistic Scenarios 2.1 The risk-neutral density of a non-equity product 2.2 Price unbundling via the financial investment table 2.3 First pillar and non-elementary products 2.3.1 Increasing the detail of the financial investment table 2.3.2 The table of probabilistic scenarios 2.3.3 Methodology to build the table of probabilistic scenarios 2.3.4 Probabilistic scenarios for "non-equity exchange structures" 2.4 First pillar and elementary products 2.5 Closing remarks 3 The Second Pillar: Degree of Risk 3.1 Methodology to calibrate an optimal grid 3.2 The model for the automatic asset manager 3.3 The model to simulate the volatility 3.4 The predictive model for the volatility 3.4.1 The diffusion limit of the M-Garch(1,1) 3.4.2 Distributive properties and volatility prediction intervals 3.4.3 Estimation of the parameters 3.5 Management failures and the optimal grid 3.5.1 Definition of management failures and introduction to the calibration problem 3.5.2 Relation between relative widths and management failures 3.5.3 The optimal grid on the reduced space of volatilities 3.5.4 The optimal grid on the full space of volatilities 3.6 Risk Classification 3.7 Detecting migrations 3.8 Closing remarks 4 The Third Pillar: Recommended Investment Time Horizon 4.1 The minimum time horizon for risk-target and benchmark products 4.1.1 The strong characterisation of the cost-recovery event 4.1.2 The weak characterisation of the cost-recovery event 4.1.3 The closed formula for the cumulative probability of the first-passage times 4.1.3.1 The case of the standard Brownian motion 4.1.3.2 The case of the arithmetic Brownian motion 4.1.3.3 The case of the geometric Brownian motion 4.1.3.4 The case of the geometric Brownian motion specific to the product 4.1.4 Asymptotic analysis 4.1.5 Sensitivity analysis 4.1.5.1 First-order partial derivatives 4.1.5.2 Limit representations of the first-order partial derivative with respect to the volatility 4.1.5.3 Second-order partial derivatives 4.1.6 Existence and uniqueness of the minimum time horizon for local correct ordering 4.1.7 The function of the minimum times 4.1.8 Existence and uniqueness of the minimum time horizon for a global correct ordering 4.1.9 Switching to a discrete volatility setting 4.1.10 Extensions to more general dynamics for the process 4.1.11 Technical remarks 4.2 The recommended time horizon for return-target products 4.2.1 Illiquid products 4.2.2 Liquidity and liquidability 4.3 Closing remarks 5 Some Applications of the Risk-Based Approach 5.1 A risk-target product 5.2 A benchmark product 5.3 Return-target products: the case of a plain-vanilla bond with significant credit risk 5.4 Return-target products: the case of a VPPI product 5.5 Return-target products: the case of an index-linked certificate 5.6 Non-equity exchange structures: the case of a collar replacing a fixed-rate liability 6 Conclusions

About the Author :
Marcello Minenna Marcello Minenna addressed by Risk magazine as the "quant enforcer" and the "quant regulator" is the Head of the Quantitative Analysis Unit at CONSOB (the Italian Securities and Exchange Commission) where he develops quantitative models for surveillance and supports the enforcement and regulatory units in their activities. Marcello has been teaching in several Universities and holding courses for practitioners in the field of financial mathematics all around the world. He graduated at Bocconi University and received his PhD and MA in mathematics for finance from State University of Brescia and from Columbia University. He is the author of several publications including the bestselling Risk-book A Guide to Quantitative Finance.

Review :
Testimonials "This book fills the gap that exists between the risk management tools available to industry insiders, and those available to investors. It is a welcome contribution that will be helpful to anyone who needs to assess the risk of non-equity products." Jaksa Cvitanic Professor of Mathematical Finance Caltech "Rigor and clarity characterize this methodology to assess the risk of every non-equity product. Well established stochastic techniques are applied in an original way to convey the key information on the time horizon, the degree of risk, the costs and potential returns of the investment and therefore to match the investor's preferences in terms of liquidity attitude, risk taking, desired returns and acceptable losses." Prof. Svetlozar Rachev Department of Statistics and Applied Probability University of California at Santa Barbara "I warmly welcome the publication of this book which describes a probabilistic framework for risk evaluation. The specific aim is that of providing financial institutions and regulators with tools and techniques for an objective and clear representation of key investor information. This shall help in orientating buyers through the difficult path of non-equity products selection." Prof. Francesco Corielli Department of Finance Bocconi University "This book constitutes an excellent collection of quantitative methods to the measurement and representation of the risks of non-equity products that comes from a simple but also winning intuition: the information needs of retail investors are not really different from those of financial institutions since they both want the upside gain by trying to contain the downside risk." Prof. Helyette Geman School of Business, Economics and Informatics Birkbeck, University of London "This important book establishes a benchmark for a future financial regulation based on quantitative techniques. At the same time it casts a serious challenge to the financial industry on the need of quantitative disclosure, that will be the future of the financial system worldwide. Hope the challenge will be accepted." Prof. Umberto Cherubini Department of Mathematical Economics University of Bologna "This book contains a valid quantitative methodology to shed light on the risks embedded in any non-equity product. By answering the key questions of any investor about the potential performances, the risk rating and the optimal holding time of the product, the three "pillars" of the book are the best candidates to definitely remove the informative lack that worldwide regulators have recognized in the existing rules on risks disclosure. The adoption of these "pillars" would be the ideal completion of the regulatory reform undertaken by the European Authorities regarding the revision of the information contents for Packaged Retail Investment Products. Should the quantitative framework set forth in this work become the reference to update the regulatory framework on transparency, an authentic reversal of the traditional approaches to risks transparency would be realized with effective benefits for investors' comprehension and for allowing them to pick the product that best fits their needs." Prof. Riccardo Cesari Professor of Mathematical Methods for Economic and Financial Sciences University of Bologna "This innovative book sheds a light on the dark path of the financial risks intrinsic to non-equity financial products, which are often underestimated, or even poorly understood, by investors seeking higher returns. Mathematical finance techniques are here applied in an original and unconventional manner for the purpose of effectively disclosing these risks and properly assessing their impact on investments' returns." Fabio Mercurio, Head of Quant Business Managers at Bloomberg LP and adjunct professor at NYU Book Presentations Timely The book is a timely addition to the wold of structured products. The angle is not from the buy side, nor the sell side, but from investors' side in the context of market regulations. It provides insights into how the regularors view the risks, and how these risks should be measured. More importantly, the book illustrates in depth how to calculate and communicate to investors consistent risk profiles. The methododolies are based on quantitatvie analysis, hence project more objective risk pirctures, rather than semi-subjective opinions. Clearly the book is a very good read, not just for investors, but for the sell side as the product providers are now under increasing pressure to do even better in terms of communicating accurate risks to the investors. Review by Dong , 01/02/2012 At last! Finalmente!, at last the Italians would say. This book advocates with unmatched rigor and narrative simplicity the need and the opportunity for applying quantitative methods to the benefit of buy-side industry experts, as well as the broader community of private investors. The author investigates the thin boundary between the advantages and the risks of market innovation. I think the proposed approach is going to influence and permanently shape market regulation in the years to come. The spell for transparency is rigorous but not detrimental to the industry freedom to act: abandoning the prescriptive dogmatism of classical regulation, modern risk-based regulation here outlined will provide a consistent framework for wealth managers to operate freely, but will also enforce ethical and objective standards for aligning industry interests to the investors' benefits. Worth reading! Review by Paolo , 08/11/2011