Benchmarking and Rebalancing
with Daniel Gabay (CNRS-EHESS & ESILV), Conférence AFG sur le Benchmarking, 29 June 2007
We compare in this note 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 show, both in simulation and through the analysis of closed form formulae in a Black-Scholes
framework, that rebalancing the portfolio captures an excess growth which increases
with time and volatility. This main result is also confirmed by some empirical tests.
Can Financial Strategies Based on Information Theory Beat The Market?
with Daniel Gabay (CNRS-EHESS & ESILV), M.Grasselli
Europlace, 22 June 2006
Long/Short portfolio formulas
This article provides some simple formulas to build long/short portfolio in different models (Markowitz, one factor model). We retrieve some well known formulas like Treynor-Black. We compare the Sharpe ratios for different strategies: growth optimal (without constraints), dollar neutral and market neutral strategies. We quantify the cost of being neutral in terms of Sharpe ratios. The role of correlations are highlighted
Notes on compensation structure for Hedge Fund Managers
how to optimize the wealth of hedge fund managers ? How incentive fees (and more generally incentive fees) may explain some market anomalies such as over valued assets, excessive volatility, abnormal correlations, excessive risk taking, etc ...
Notes on Risk Adjusted Performance Measures
Technical note to highlight some drawbacks of the Sharpe ratio and review alternative risk adjusted performance measures, such as the Stutzer index, Hodges measure, Omega, ... specially, the Bonnet Nagot article toward an axiomatic approach for measuring (and optimizing) performance.
Risk Management Study
an application to a typical Hedge Fund trading Future Contracts, exploring statistical properties (tails, extreme value theory, ...), selecting the best volatility model, estimating and backtesting Value at Risk, as well as conditional Value at Risk (CVaR) or Expected Shortfall ...
Volatility Pumping : optimal growth portfolios revisited
with Daniel Gabay,
Quantitative Methods in Finance
Conference, 2004, Sydney (Australia)
This paper aims at a synthesis of various recent contributions on optimal growth portfolios arising from different scientific communities: information theory, artificial intelligence & learning algorithms, econophysics and of course mathematical finance and market practice.
Their common ground lies in the recognition of the important role played by portfolios invested in constant proportions between the various financial assets and of the resulting efficient performance obtained by the rebalancing necessary to maintain these fixed proportions while the market prices of assets fluctuate. While asset volatility is considered as the enemy in the static Markowitz world of one period portfolio optimization, it turns out to be a precious ally to boost performance once investors ajust dynamically their positions as markets evolve. This feature has been first acknowledged by Kelly (1956) and Breiman (1961) who characterized the optimal long term growth rate solution as a Constant Rebalanced Porfolio (CRP). In addition to a review of the remarkable (and some less favorable) properties of such CRP, we recall that they also provide the solutions in the continuous time setting of Merton's model (1971) for more general utility criteria (HARA), which allows to relate the portfolio risk measure to the investor's risk aversion.
Kelly's CRP strategies form the core of Cover's proposal for Universal Portfolios (1984 - 1996) to adress the issue of estimating the proportions of the optimal CRP using only on-line learning from market data. Cover coined the expression " volatility pumping " to explain his construction of a portfolio which approximates the best CRP in hindsight and outperforms the best asset performance without knowing it in advance! He actually proved the convergence of his algorithm for quite general asset returns distributions ; but a good approximation may require a very long sequence of prices observations.
We review several recent works which improve Cover's algorithms by introducing sophisticated non parametric methods (Cross & Barron, 2003 ; Gyorfi & Lugosi, 2003) or by taking into account transaction costs (eg Iyengar, 2004). We also present several tests run with our implementation of Universal Portfolios which attempts to capture complex time dependencies between assets ; it is backtested on the universe of the 30 stocks of the Dow Jones Index and the Index itself over the period 1994 -2004 : the results are often spectacular and always overperform the best CRP portfolio in hindsight. They exhibit a robust structure of the portfolio solutions, long in the stocks and short in the index. Moreover the portfolios can be adjusted to satisfy some risk management constraints (volatility, VaR, drawdowns…) without significantly altering the Sharpe's ratio which remains close to 3.
Marchés Futures Intraday: Faits Stylisés et Modélisations avec présentation de la plateforme de trading automatique RAPT.
EURO WORKING GROUP on FINANCIAL MODELING
34 th EWG Meeting (Spring 2004) May 12-14, 2004 Paris
Gestion de Portefeuille et
Croissance Optimale, propriétés et méthodes universelles et non paramétriques, applications
aux actions du Dow Jones et CAC40, indices US et Européens.
Cet article examine des stratégies de gestion
de portefeuille à long terme dites de "croissance optimale", également connues sous le nom de critère de Kelly ...
Nous présentons une nouvelle méthode d'estimation, YAUP, pour Yet Another Universal Portfolio
La stratégie présente un ratio de Sharpe de l'ordre de 3, le maximum de la perte historique est du même ordre de grandeur que la volatilité. Avec une aversion relative de 30, nous obtenons une croissance annuelle de 1.77 avec 20% de volatilité, une Value At Risk journalière de -1.7% au seuil de 5% et 14% de perte maximale historique (max drawdown) ...
Pairs trading, convergence trading, co-integration, ....
Notes on Herding in Financial Markets
Probability Distributions related to stochastic processes
distribution of the minimum, the maximum, first hitting time,
exit time from barriers, ...
some about prediction
Probabilities and statistics
: notes on probabilities and statistics
General purpose questionnary for
Asset Management Company
and Risk Management Assessment
L'apport de la recherche à l'innovation financière
Alain Dubois, Chairman of Managing Board, LYXOR Asset Management.
Jean Michel Lasry, head of Quantitative Research and Risk Advisory, CAI.
Philippe Taffin, head of Actuarial and Financial Engineering, AXA IM.
Modérateur: Pascal Junghans, La Tribune.
propos receuillis lors du
Forum Emploi Europlace Institute of Finance, Paris Dauphine, 16 & 17 Mars 2004.
L'Avenir de l'Asset Management
Conférence X-Banque du
2 Octobre 2003,
- Vivien Levy-Garboua,
(BNP Paribas, Membre du Comité Exécutif,
Responsable de la Gestion d'Actifs, des Assurances et de la Banque Privée Internationale)
- Alain Dromer
CEO HSBC Asset Management Limited à Londres