This course is an introduction to portfolio theory and is structured around four main parts. The first part introduces the basic tools and concepts: measures of return, portfolios, long and short positions, types of indices, and so on. The second part covers mean-variance analysis, which allows for the introduction of performance measures, the concepts of the efficient frontier, and efficient portfolios, including the tangent portfolio. The third part presents asset pricing models: the Capital Asset Pricing Model (CAPM) and the Arbitrage Pricing Theory (APT). The CAPM is presented in two versions, depending on whether or not there are borrowing constraints. The APT also provides an opportunity to discuss the Fama and French model. Finally, the fourth part is dedicated to the efficiency hypothesis. Once this hypothesis is introduced, many of its predictions are discussed, and a review of the empirical literature evaluating them is provided. Finally, this course is completed by several applications on Python (replication portfolio, portfolio optimization, minimum variance and maximum Sharpe ratio portfolios, estimation of the CAPM and Fama-French models on market data).
Chapter 1. Assets, portfolios, and indices
Chapter 2. Portfolio choice
Chapter 3. Capital Asset Pricing Model
Chapter 4. Arbitrage Pricing Theory
This course builds on the Portfolio Theory course offered in the first semester. It introduces a range of methods for empirically analyzing and testing the assumptions underlying the topics covered in portfolio theory. Topics include tests of the weak-form efficiency hypothesis. Event studies are then used to explore the semi-strong form of market efficiency. Subsequently, methods for statistically testing asset pricing models (CAPM and APT) are discussed. The course then presents statistical modeling techniques designed to overcome empirical challenges arising from the specific characteristics of financial returns, which cannot be adequately addressed by standard linear time series econometrics. These methods include volatility modeling techniques (ARCH, GARCH, and stochastic volatility). Finally, regime-switching models are introduced, including both Markovian and threshold autoregressive types.
Chapter 1. Testing the Efficient Financial Market Hypothesis
Chapter 2. Empirical tests of the CAPM
Chapter 3. Estimating the Fama-French factors
Chapter 4. GARCH and stochastic volatility models
Chapter 5. Non-linear econometrics and regime switching models (Markov and TAR)
This course provides an introduction to risk management and financial risk econometrics. It begins by highlighting the specific characteristics of financial returns that make their probability distributions non-Gaussian. The relevance of variance as a risk measure is then discussed in the context of non-normal distributions. Various alternative risk measures are introduced (target semi-variance, Value at Risk, etc.), and their properties are analyzed. Initially, an axiomatic framework for risk measures is presented, allowing for an evaluation of the advantages and limitations of commonly used measures. From a statistical perspective, a distinction is made between symmetric and asymmetric measures, and their ability to account for fat tails in the distribution is examined. Special attention is given to Value at Risk (VaR) and its extensions (conditional VaR, Tail-VaR, expected shortfall, etc.), both for their desirable properties and for their role in financial regulation. The course then covers various approaches to estimating VaR (historical simulation, Gaussian approach, extreme value theory, Gaussian mixtures, etc.) and concludes with a discussion of methods for backtesting VaR. Finally, this course is completed by several applications on Python (historic, parametric, MonteCarlo VaR and backtesting tests).
Chapter 1. How to measure risk ?
Chapter 2. Axiomatization (VaR, T-VaR, ES)
Chapter 3. Estimating VaR (historical VaR, Gaussian approach, extreme value theory, Gaussian mixtures, MonteCarlo simulations)
Chapter 4. Backtesting
Chapter 5. Regulation framework (Bale)
This course is primarily an introduction to copula theory and its applications in financial risk assessment. It begins by introducing the concept of a copula and its role in inferring the joint distributions of financial returns. Various families of copulas are then presented (Elliptical, Archimedean), with their properties analyzed and discussed. The course also covers estimation methods and their practical implementation. Techniques for constructing high-dimensional copulas are introduced, including C-vine and D-vine approaches. Several financial applications are explored, notably portfolio simulation and the associated Value at Risk (VaR), as well as modeling contagion phenomena in financial markets. Finally, this course is completed by several applications on Python.
Chapter 1. Introduction (bi-variate laws)
Chapter 2. Copulas and stochastic dependence
Chapter 3. Copulas families and applications
Chapter 4. Vines
Chapter 5. Implementing a trading strategy with fitted copulas and 'entry and exit' signals (Python application)
This course focuses on the behavior of banks under imperfect competition, emphasizing market inefficiencies, strategic behavior, and information asymmetries. Topics include the design of deposit and loan contracts, mechanisms to prevent bank runs, ex ante and ex post imperfections, credit rationing.
Basics on Python: NumPy, pandas, SciPy, Plotly, seaborn, statsmodels, scikit-learn, arch and Object Oriented Programming (library free coding).
Basic notions on Data Management on pandas (data pre-processing, joins, vectorizing).
Implementation of:
-MonteCarlo simulations applied to Asset Pricing forecast (assuming the log-returns follow a GBM vs ARMA vs GARCH) and Intrinsic Valuation with DCF Analysis (Discounted Cash Flow) for M&A,
-Portfolio Management models (mean-variance optimization and efficient frontier).
-Asset Pricing models (Bond valuation, CAPM, Fama-French, Black-Scholes-Merton).
-Time Series econometric models for finance (linear regression and statistical tests, ARMA vs GARCH for asset returns).
-Technical Analysis (Momentum & reversion trading signals, Sentiment Analysis on Trump's tweets with VADER and with ML).
-Trading strategies and backtesting procedures
The main goal of this lecture is to automate reportings in corporate finance (M&A, PE, TS) and in asset management.
Notions of data management, database operations and data science (DBMS, relational, hierarchical, object oriented, NoSQL, integrity constraints, DDL, DML, DCL, database conception, database normalization, transaction, ACID properties, permissions, cryptography, General Data Protection Regulation)
Link between Excel and Access with VBA and SQL
Link between Excel and Outlook (mail) with VBA and HTML
Link between Excel and Python with VBA and Python scripts
Different types of reporting (overnight, portfolio management, reconciliation, client, manager, fund...)
SQL:
Chapter 1. Introduction (relational database, ERD, simple queries, projection)
Chapter 2. Arithmetic computation, string operations and dates
Chapter 3. Count, statistical application, aggregates and restrictions
Chapter 4. Merge (natural, inner, outter, multiple joins)
Chapter 5. Subqueries, Exists
Chapter 6. Misc (union, order and limit, intersection, difference)
Python: Python scripts on MacOS (Applescript) and Windows called by VBA macros. Use python course knowledge for better reporting and alternative to SQL for small datasets (pandas).
Computer Science Applied to Finance - Lecture
Bachelor 3rd year, Economics and Financial Engineering
2021 - 2025
Basic notions of coding (typing, loop, function, user interface) and implementation in VBA of various technical analysis and finance models:
Monte Carlo simulations
Runs
High water mark and max DrawDown
Life cycle and retirement
Portfolio screening
Expected recovery
Replicating portfolio
Entry and exit signal indicator
Chapter 1. Some simple criteria
Chapter 2. Expected utility theory
Chapter 3. Notions derived from the utility expectation criterion
Chapter 4. Risk aversion measures
Chapter 5. Risk measurement
Chapter 6. Investment decisions in a risky universe
Microeconomics - Lecture and Tutorial
Bachelor 1st year, Organisational Science
2020-2021
Microeconomics of the consumer and the producer. Introduction of mathematical tools such as constrained optimisation and Lagrangian. Introduction of economic concepts such as the utility function, the marginal utility, the budget constraint, the Pareto rule, or the welfare theorems.
Chapter 1. Introduction microeconomics of the producer
Chapter 2. Production cost
Chapter 3. Returns to scale
Chapter 4. Short term firm equilibrium
Chapter 5. Producer's equilibrium
Chapter 6. Equilibria and optimality