Bertrand

Publications

Analysis and Comparison of Leveraged ETFs and CPPI-type Leveraged StrategiesJournal articlePhilippe Bertrand and Jean-Luc Prigent, Finance, Volume 34, Issue 1, pp. 73-116, 2013

Among leveraged funds, leveraged ETFs are designed to achieve multiple exposure (e.g., twice) to some financial index returns, on a daily basis. In this paper, we provide and analyze various properties of the value process of a leveraged ETF. We examine its main statistical properties and point out that there is some probability that the stock index price increases while, at the same time, the leveraged fund decreases. This is an event that is difficult to accept for an investor in such a fund. In the continuous-time framework, we prove an equivalence result stating that a leveraged ETF can also be viewed as a CPPI fund with a floor proportional to the portfolio value itself. Next, from a more practical point of view, we compare Leveraged ETFs and Leveraged CPPI having a specific variable leverage. This type of Leveraged CPPI portfolio is not fully equivalent to a Leveraged ETF because the leverage is reduced in falling markets as well as bounded from above. We derive a quasi explicit expression for the value of such Leveraged CPPI. Then, using Monte Carlo simulations, we compare the Leveraged ETFs and Leveraged CPPI return distributions by means of their moments as well as by relying on Omega and Kappa performance measures.

Omega performance measure and portfolio insuranceJournal articlePhilippe Bertrand and Jean-Luc Prigent, Journal of Banking & Finance, Volume 35, Issue 7, pp. 1811-1823, 2011

We analyze the performance of the two main portfolio insurance methods, the OBPI and CPPI strategies, using downside risk measures. For this purpose, we introduce Kappa performance measures and especially the Omega measure. These measures take account of the entire return distribution. We show that the CPPI method performs better than the OBPI. As a-by-product, we determine the set of threshold values for these risk/reward performance measures.

A Note on Risk Aversion, Prudence and Portfolio InsuranceJournal articlePhilippe Bertrand and Jean-Luc Prigent, The Geneva Risk and Insurance Review, Volume 35, Issue 1, pp. 81-92, 2010

This paper examines some properties of portfolio insurance that are linked to the risk aversion and the prudence of the investor. We provide explicit conditions to measure portfolio sensitivity to downside risk. We also characterize the degree of portfolio insurance by means of the ratio of absolute prudence to absolute risk aversion.

The Statistics of The Information RatioJournal articlePhilippe Bertrand and Costin Protopopescu, International Journal of Business, Volume 15, Issue 1, pp. 71-86, 2010

In a recent paper, Lo (2002) derives the asymptotic distribution of the Sharpe ratio under several sets of assumptions for the return-generating process. In thi

Risk-adjusted performance attribution and portfolio optimisations under tracking-error constraintsJournal articlePhilippe Bertrand, Journal of Asset Management, Volume 10, Issue 2, pp. 75-88, 2009

This paper examines whether the risk-adjusted performance attribution process is consistent with portfolio optimisation under tracking-error constraints. Since Mina (2003), Bertrand (2005, 2008b) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process. This paper analyses and discusses the information ratio decomposition proposed by Menchero (2007) in the light of the analysis of risk-adjusted performance attribution developed by Bertrand (2005). It is also shown that only optimisation under the tracking-error constraint alone is consistent with the risk-adjusted performance attribution process. Indeed, as soon as additional constraints (for example, on total risk) are introduced, the component information ratios of the decisions are no longer the same or equal to the information ratio of the whole portfolio. This means that no equilibrium between expected return and relative risk has been reached.

The Sensitivity of the Asymptotic Variance of Performance Measures with Respect to Skewness and KurtosisJournal articlePhilippe Bertrand and Costin Protopopescu, International Journal of Business, Volume 13, Issue 4, pp. 349-360, 2008

Performance measures such as the Sharpe ratio and the information ratio are estimation subject to estimation error. Lo (2002) derives the explicit expressions for the statistical distribution of the Sharpe ratio. Bertrand and Protopopescu (2007) have extended his work to the bivariate case which corresponds to the Information ratio. In the present paper, we analyze the effects of skewness and kurtosis of portfolio and benchmark returns on the precision of the estimation of the Sharpe ratio and of the information ratio. We show that these effects are in line with what decision theory suggests about preferences of investors about skewness and kurtosis. Moreover, these effects are significant and can disturb the performance evaluation process if they are neglected.

Risk Attribution and Portfolio Optimizations Under Tracking-Error ConstraintsJournal articlePhilippe Bertrand, The Journal of Performance Measurement, Volume 13, Issue 1, 2008

This paper examines wether risk attribution process is consistent with portfolio optimizations under tracking-error constraints. Since Mina (2003), Bertrand (2005) and Menchero and Hu (2006), risk attribution has been widely used in the performance attribution process. This article presents an extension of our previous work on risk attribution to others portfolio optimization contexts. It is shown that only optimization under the tracking-error constraint alone is consistent with the risk attribution process. Indeed, as soon as additional constraints (e.g. on total risk) are introduced, the risk attribution method conflicts with the performance attribution process, preventing us from legitimating all the optimal decisions taken by a portfolio manager.

Mesure de performance Oméga : applications en gestion alternative et garantieBook chapterPhilippe Bertrand and Jean-Luc Prigent, In: Finance d'entreprise et finance de marchés: complémentarités et nouvelles avancées, 2007, Hermes, 2007

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Gestion de portefeuille : analyse quantitative et gestion structurée, 2e éd.BookPhilippe Bertrand and Jean-Luc Prigent, Collection Gestion, 2006, Economica, 2006

Découvrez le livre Gestion de portefeuille : analyse quantitative et gestion structurée, 2e éd. BERTRAND Philippe, PRIGENT Jean-Luc disponible dans la collection Finance de l'éditeur de livres

Performance des partenaires locaux dans les coentreprises internationales en Asie : valorisation boursière et application de la théorie des coûts de transactionJournal articlePhilippe Bertrand and Pierre-Xavier Meschi, Management International, Volume 10, Issue 2, pp. 1-16, 2006

Cet article propose une analyse de la performance des partenaires locaux dans les coentreprises internationales à partir de la théorie des coûts de transaction. Cette analyse a été conduite dans le cadre d'un échantillon de 213 partenaires locaux qui ont annoncé entre janvier 2000 et décembre 2004, la création d'une coentreprise internationale dans l'un des cinq pays asiatiques suivants : République Populaire de Chine, Corée du Sud, Malaisie, Singapour et Taiwan. Dans un premier temps, une méthodologie d'étude d'événements a été utilisée pour mesurer la performance des partenaires locaux en calculant leurs rentabilités anormales. Dans un deuxième temps, des modèles de régression multiple ont été élaborés afin de tester l'impact de différentes variables explicatives (cf. contrôle, secteur d'activité des coentreprises internationales, expérience des partenaires et risque pays) sur les rentabilités anormales des partenaires locaux. Les différents résultats empiriques concourent à envisager une analyse de la performance des partenaires locaux qui soit distincte de celle des partenaires étrangers. Il ressort aussi de ces résultats que la théorie des coûts de transaction est un cadre d'analyse de la performance qui est davantage applicable aux partenaires étrangers qu'aux partenaires locaux dans les coentreprises internationales.Mots Clés : Coentreprise Internationale, Partenaire Local, Asie, Théorie de Coûts de Transaction et Méthodologie d'Etude d'Evénements