Econometry of Financial Markets
with R-project

Daniel Herlemont

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Table des matières

1 Objectives and motivations

The objectives are twofold: The projects will be developed under the powerful statistical and graphical software R-Project, that is the open source version of S-plus.

Different aspects of financial prices will be addressed: All applications will be developed with actual market data.

2 Présentations
Other presentations
3 Practical works

3.1 Exploring Financial Data

Exploring europeans sotck indices, hedge fund data,

3.2 Stylized Facts

3.2.1 Are returns normality distributed ?
3.3 Volatility: Models, Simulations, Estimations and Predictions
Volatility plays a major role in finance, either for risk management or pricing of options. Different practical works are devoted to this main topic:
3.3.1 Efficient Estimations
We study the efficiency of volatility estimators based on highs and lows (Parkinson, Roger Satchell, Garman Klass).
3.3.2 Exponential Weighted Moving Average (Risk Metrics) and GARCH
Objective is to study and compare Volatility estimation using different weighting scheme.
3.4 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].

3.4.1 Tails of distribution and Extreme Value Theory
3.4.2 Measure and Backtesting of the VaR and Active Management
3.4.3 VaR Backtesting, conditionnal coverage
Testing the time dependencies of exceptions.

3.4.4 Estimating the Value at Risk of options

In presence of options, the different methods will examined
4 Factor Models

4.0.5 Estimation of Fundamental Factor Models
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.

4.1 Strategies

4.2 Stratégies d'investissement

4.2.1 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 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 ?"

4.2.2 Kelly criterium and Rebalancing strategies

4.2.3 Buy and Hold versus Rebalacing

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

4.2.4 Trend following and mean reversting strategies

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.

5 Resources

5.1 R
Some ressources on R: books: Other packages
6 References
ARTZNER, P. & DELBAEN, F. & EBER, J.-M. & HEATH, D. ''Coherent Measures of Risk'' , 1998. ...

ALEXANDER, C. ''Market Models: a Guide to Financial Data Analysis''. Wiley, 2003.

ALEXANDER, C. ''Market Risk Analysis: Practical Financial Econometrics''. Wiley, 2008.

BOUCHAUD, J. P & POTTERS, M. ''Theory of Financial Risks'' . Cambridge University Press, 2000.

CHAMBERS, J. M. ''Programming with Data'' . Springer, New York, 1998. ISBN 0-387-98503-4.

CHRISTOFFERSEN, P. ''Elements of Financial Risk Management'' . Academic Press, July 2003.

CONT, R. ''Empirical properties of asset returns - stylized facts and statistical issues'' . QUANTITATIVE FINANCE, 2000. ...

DALGAARD, P. ''Introductory Statistics with R'' . Springer, 2002. ISBN 0-387-95475-9.

GOURIEROUX, C. & SCAILLET, O. & SZAFARZ, A. ''Econométrie de la finance'' . Economica, 1997.

HERLEMONT, D. ''Value at Risk Studies'' , 2004. ...

LO. & CAMPBELL. & MACKINLAY. ''The Econometrics of Financial Markets'' . Princeton University Press, 1997.

LO, A. W & MACKINLAY, A. C. ''A Non-Random Walk Down Wall Street'' . Princeton University Press, Princeton, NJ, 1999.

LINSMEIER, T & PEARSON, N. D. ''Risk Measurement: An Introduction to Value at Risk'' , March 2000. ...

VENABLES, W. N & RIPLEY, B. D. ''Modern Applied Statistics with S. Fourth Edition'' . Springer, 2002. ISBN 0-387-95457-0.

WEST, G. ''Note on Coherent Risk Measures'' . ...

ZIVOT, E. & WANG, J. & ROBBINS, C. R. ''Modeling Financial Time Series With S-Plus'' . Springer Verlag, 2004.