Risk Management: modeling the distribution of prices (tails of distribution, skewness, kurtosis, time dependencies, ...) with the objective to select the best models to estimate risk measures such as the Value at Risk. Different models will be studied, spanning the historical VaR, normal model with different models for volatility (Risk Metrics, GARCH), the Cornish Fisher VaR, VaR models based on Extreme Value Theory. Finally, the different models are backtested to select the 'best model' and use it to manage a fund under dynamic risk constraints.
Active Portfolio Management. This project consists in studying different
active strategies with rebalancing (using the so called Kelly criteria, stochastic portfolios theory, ...),
convergence strategies (pairs trading, ...), ...
The projects will be developed under the powerful statistical and graphical software
R-Projecthttp://www.r-project.org, that is the open source version of S-plus.
Different aspects of financial prices will be addressed:
hypothesis testing for normality: qq-plots, Kolmogorov Smirnov, Jarque-Bera, ...
independence testing: scatter plots, auto correlograms (ACF), Durbin
Watson test, run tests, ...
fitting with different known distributions: student, exponential,
time series aspects: auto correlations of returns and square returns, scaling effects, law of the maximum and minimum, hitting time, ...
linear regression and factors models
Covariance Matrix Filtering, Principal Component Analysis
Style Analysis
Volatility models and estimations: Risk Metrics, GARCH
Risk Measures: Value at Risk, Expected Shortfall, Maximum Drawdown,
VaR for Portfolio with options, Delta Gamma and Monte Carlo Methods
[pdf]Estimations of the volatility and correlations:
Exponential Moving Average (RiskMetrics), GARCH,
estimtes based on Highs and Lows (Garman Klass, Parkinson, Roger Satchell, ...)
Value at Risk, estimating, backtesting and implemeting for fund mangement
The Value at Risk is certainly one of the most important tool to measure the risk of investments
for prudential standaeds. It becomes more and more used in Asset Management as well.
In this project, the objective is to manage a fund with 10 Millions Euros Under Management
with the constrainst to maintain a constant VaR all the time. The 19 days VaR at shall
99% shall be equal to 4% of the Net Asset Value.
Different VaR models will be examined and tested. One of them will be selected and implemented and positions adjusted to meet the risk objective.
Finallt, the performance of the actively managed fund will be compared to the Buy and Hold strategy in terms of perforamnce, sharpe ratio, etc ..
A first step will consist in studying the different VaR models [13] for the assets, including
Historical VaR, delta normal model with RiskMetrics and GARCH volatility, Cornish Fischer VaR, finally VaR based on Extreme Value Theory.
The study will be closed to the steps described in [10].
The objective of this practical work is to provide an empirical case study
of factor decomposition using historical prices of two stocks (Nokia and Vodafone) and four fundamental
factors.
Using regression analysis to build a multi factor model with these factors gives rise to some econometric problems.
The main problem is related to multi-collinearity. The proposed solution is to use orthogonal regression.
Study of the maximum Drawdown et Taux de mortalité des Traders
This practical work is to study the properties ans statistics of the Maximum Drawdown (MDD)
following the Magdon Ismail work (see http://alumnus.caltech.edu/~amir/mdd-risk.pdf). The relation between the sharpe (performance/volatility) and the calmar (performance/drawdown) ratios
This work will also stress on the importance of controling the MDD by
studying the Nassim Taleb article
"Which Ones Are Preferable, a Cancer Patient's or a Trader's 5-Year Survival Rates ?"
http://www.fooledbyrandomness.com/tradersurvival1.pdf
This project is to compare the performance of a passive Buy & Hold (B&H) benchmark portfolio strategy and of the corresponding Constantly Rebalanced Portfolio (CRP) strategy where the weights of the assets (or asset classes) are maintained constant by continuous trading adjustments in function of prices fluctuations.
We study the behavior of rebalanced portfolio in the case of one asset and multiple assets.
The we study the CRP vs BH strategy for the different EUROSTOXX indices, compare the equal weighted strategy in the different sectors with the Buy & Hold strategy, implement and backtest a Long/Short beta neutral strategy: long in a equal weighted sectors and short on the Eurostoxx 50 (with futures) while trying to maintain a constant expected maximum drawdown
This practical work is to characterize and back-test trend following (or mean reverting) strategies on a single asset while controlling for the maximum drawdown.
*** Practical Regression and Anova in R: http://www.stat.lsa.umich.edu/~faraway/book"This a masters level course covering the following topics:Linear Models: Definition, fitting, inference, interpretation of results, meaning of regression coefficients, identifiablity, lack of fit, multicollinearity, ridge regression, principal components regression, partial least squares, regression splines, Gauss-Markov theorem, variable selection, diagnostics, transformations, influential observations, robust procedures, ANOVA and analysis of covariance, randomised block, factorial designs."
*** Rmetrics:
http://www.itp.phys.ethz.ch/econophysics/R an "Introduction to Financial Computing with R" covering areas from data management, time series and regression analysis, extremal value theory and valuation of financial market instruments.