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.
- Publish date
- 27 Sep 2011
- 155mm x 235mm
at Scuola Normale Superiore of Pisa on December 12th 2011 during the Workshop “Quantitative Approaches to Risk Assessment and Investment Transparency” with a key-note address of Prof. Héliette Geman.
at LUISS of Rome on March 13th 2012 during the Workshop “Risk disclosure and investment decisions through probability methods”, with a key-note address of Prof. Giorgio Di Giorgio
at the 50th meeting of the Euro Working Group for Financial Modelling on May 4th 2012 guested by the Universities of Rome La Sapienza and TRE, with a key-note address from Prof. Rita L. D’Ecclesia.
For further information please email - [email protected]
Table of contents
About the Author
List of Figures
List of Tables
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 [σ0, σn]
3.5.4 The optimal grid on the full space of volatilities [0, +∞[
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
18.104.22.168 The case of the standard Brownian motion
22.214.171.124 The case of the arithmetic Brownian motion
126.96.36.199 The case of the geometric Brownian motion
188.8.131.52 The case of the geometric Brownian motion specific to the product
4.1.4 Asymptotic analysis
4.1.5 Sensitivity analysis
184.108.40.206 First-order partial derivatives
220.127.116.11 Limit representations of the first-order partial derivative with respect to the volatility
18.104.22.168 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
“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.”
Professor of Mathematical Finance
“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
"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. Hélyette 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."
Head of Quant Business Managers at Bloomberg LP and adjunct professor at NYU
at Scuola Normale Superiore of Pisa on December 12th 2011 during the Workshop “Quantitative Approaches to Risk
Assessment and Investment Transparency” with a key note Transparency key-address of Prof. Hélyette Geman.
at LUISS of Rome on March 13th 2012 during the Workshop “Risk disclosure and investment decisions through probability
methods”, with a key-note address of Prof. Giorgio Di Giorgio
For further information please call +39 0685225980 or email [email protected]