### Durée

30h Th

### Nombre de crédits

Master en sciences économiques, orientation générale, à finalité | 5 crédits | |||

Master en ingénieur de gestion, à finalité | 5 crédits | |||

Master en sciences mathématiques, à finalité | 5 crédits |

### Enseignant

### Langue(s) de l'unité d'enseignement

Langue anglaise

### Organisation et évaluation

Enseignement au premier quadrimestre, examen en janvier

### Horaire

### Unités d'enseignement prérequises et corequises

Les unités prérequises ou corequises sont présentées au sein de chaque programme

### Contenus de l'unité d'enseignement

"Financial Risk Modeling" introduces students to a set of techniques for modeling **market **risks in financial portfolios. As initially emphasized by Markowitz, the two relevant characteristics of an asset portfolio are its expected return and the dispersion of possible returns around the expected return, i.e. the standard deviation of returns. Presuming risk aversion, rational investors will choose to hold efficient portfolios, i.e. those that maximize the expected return for a given degree of risk or, alternatively, minimize risk for a given level of expected return.

The course is both about *risk management* and *risk measurement and modeling*. It not only extends the framework of Markovitz but also presents a few real-life, practical issues in financial risk management. It also demonstrates how stochastic processes can help complement the risk measurement and modeling.

The course focuses on the link between mathematical ingredients and business needs, rather than on theory or applications only.

The course starts by reviewing market risk measurement and diversification and points out several issues (structured into different modules) to be dealt with during the course. The course is then structured as follows.

**Modules 1 and 2** focus on building the equity blocks of an asset allocation problem.

Module 1 reviews Modern Portfolio Theory by emphasizing the limits of a Markowitz analysis and the need for advanced techniques when estimating the input parameters. Module 2 challenges the hypothesis of the value-weighted portfolio as a proxy for the efficient portfolios. It introduces students to fundamental indexing and smart beta strategies.

**Module 3** shows how real-life constraints affect the work of the practitioner confronted to financial risk measurement issues. We discuss the constraints, uses, and limitations of the efficient frontier notion of the Modern Portfolio Theory framework as they occur in applications.

Assets and liabilities are becoming more and more involved in "Financial" Risk Modeling. They are tackled by ALM (Asset and Liability Management) practitioners with techniques derived from approaches that were initially purely financial.

** Modules 4 and 5** introduce the practical use of stochastic processes to complement the risk measurement toolbox, and we demonstrate their use in real-life situations. In these two modules, we observe that the quantitative studies involving stochastic processes that are carried out nowadays in financial institutions relate to (at least) one of the two paradigms made up by the "real-world" and the "risk-neutral" measures. We thus focus on two practical sample cases that enable us to discuss relevant features of stochastic processes in a financial setting. The first case links with the first part of the course by showing how stochastic processes can support an optimization quest for the risk/return combination. The second case lets us present the notion of risk-neutral probability (or equivalent martingale measure) and relate it to the two fundamental theorems of asset pricing that involve its existence and uniqueness when there is no arbitrage opportunity. Those notions are then illustrated on various option pricings.

The final module (**Module 6**) covers higher-moment risk measures (i.e. beyond the mean-variance). It covers extreme risk theory and the impact of these alternative risks for diversification of a multi-asset portfolio.

### Acquis d'apprentissage (objectifs d'apprentissage) de l'unité d'enseignement

Consistently with the Key Learning Outcomes, students will acquire the following capacities at the end of the course:

(1) They will strengthen their knowledge and understanding of financial risk management and rely on their knowledge to perform a rigorous analysis of a management situation. They will **design optimal and creative solutions** (through modeling methods).

(2) They will gain knowledge and understanding of financial engineering and be able to mobilize them in order **to implement solutions** to concrete management problems or cases.

(3) They will **communicate about financial risk management problems** in English and develop team work abilities.

(4) They will **adapt their managerial practice** and research autonomously and methodically the information needed to solve a complex and transversal management problem.

**Specific skills and competencies are trained during this course.**

*Students will be able to*:

- measure robust variance-covariance matrices for asset allocation and risk measurement;

- measure the potential for diversification of a portfolio taking into account its volatility, downside and extreme risks;

- measure the VaR of a stock portfolio using GARCH model;

- define alternative efficient portfolio specification (using heuristic and statistic methods) and test their outperformance over the common commercial (value-weighted) indexes.

- understand and explain how stochastic processes contribute to the modeling of typical financial risk management problems;

- exemplify this contribution on concrete cases;

- describe in business terms the mathematical setups needed for asset pricing, asset value prospective simulation, and VaR estimation of a random financial variable in the future;

- perform simulations and valuations associated to stochastic processes by implementing elementary models in a high-level programming language.

### Savoirs et compétences prérequis

Students attending this course are expected to have a good background in investment and portfolio management and have a good understanding of asset pricing models. For the second part of the course, students should be familiar with basic probability, statistics, and linear algebra concepts and methods.

### Activités d'apprentissage prévues et méthodes d'enseignement

The course is lecture-style with active discussions about practical examples. The course organizes "computer labs" for applying the studied concepts on practical case-studies. The course has been developed to effectively combine each theoretical session with real-business case-studies. For each part of the course, students will work on a group project. They are invited to work in groups of 2 or 3 students.

### Mode d'enseignement (présentiel ; enseignement à distance)

The course is structured into face-to-face lectures, computer labs and group-meetings.

### Lectures recommandées ou obligatoires et notes de cours

The recommended textbook is:
Market Risk Analysis: Practical Financial Econometrics by Carol Alexander ISBN-10: 0470998016 | ISBN-13: 978-0470998014 | Edition: Volume II

Interested students can find further reference material in

- Martin Haugh's works (http://www.columbia.edu/~mh2078)
- Brandimarte, Paolo, Handbook in Monte Carlo Simulation, Wiley and Sons, 2014 (ISBN-10: 0470531118 ISBN-13: 978-0470531112)
- Glassermann, Paul, Monte Carlo Methods in Financial Engineering, Springer, 2003 (ISBN-10: 0387004513, ISBN-13: 978-0387004518)

### Modalités d'évaluation et critères

The final grade will be determined by :

1. Group project: 25%

2. Active class participation (attending class and actively discussing/applying material in class):

- individual grade: 15%

- group grade (case studies): 10%

3. Individual Oral exam: 50%

### Stage(s)

none

### Remarques organisationnelles

Attendance to lectures and computer labs are mandatory and will be controlled and graded: 25% of the final grade. The same rule applies in the second session. This means that in case of no-class-participation, students receive 0/25 in the first as well as the second session exams.

Absences from exams are allowed only for justified medical reasons. Unexcused absences from exams will lead to a zero score in the calculation of the final grade.

### Contacts

**Modeling market risk and optimal risk diversification**

Prof. Marie Lambert - email: marie.lambert@ulg.ac.be

Nicolas Moreno - tutor - n.moreno@ulg.ac.be
N1 (office 109).

Please schedule an appointment by email!

** **

** Stochastic processes, optimization under practitioner's constraints**
Affiliate Prof. Fabien Boniver - email: f.boniver@ulg.ac.be

Please schedule an appointment by email!

### Notes en ligne

online notes

The core materials for the course consist of the required textbook readings. Lecture notes will be available on the course web page (on lol@). Other items such as problem sets will also be available on the course web page. Some additional readings on materials related to the course over the term may be provided throughout the course via the course web page.