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Performance measurement is one of the most studied subjects in financial literature. Since the introduction of the Sharpe ratio in 1966, a large variety of newmeasures has appeared constantly in scientific journals as well as in practitioners’ publications. The most complete and significant studies of performance measures, so far, have been written by Aftalion and Poncet, Le Sourd, Bacon, and Cogneau and Hubner. A review of the most recent literature led us to collect several dozen measures that we classify into four families. We first present the class of relative measures, starting with the Sharpe ratio. Secondly, we analyse absolute measures, beginning with the most famous one - the Jensen alpha. Thirdly, we study general measures based on specific features of the return distribution, where the pioneering contributions are those of Bernardo and Ledoit, and Keating and Shadwick. Finally, the fourth set concerns a few measures that explicitly take into account the investor’s utility functions

Constant proportion portfolio insurance" (CPPI) is nowadays one of the most popular techniques for portfolio insurance strategies. It simply consists of reallocating the risky part of a portfolio with respect to market conditions, via a leverage parameter-called the multiple-guaranteeing a predetermined floor. We propose to introduce a conditional time-varying multiple as an alternative to the standard unconditional CPPI method, directly linked to actual risk management problematics. This ex ante approach for the conditional multiple aims to diversify the risk model associated, for example, with the expected shortfall (ES) or extreme risk measure estimations. First, we recall the portfolio insurance principles, and main properties of the CPPI strategy, including the time-invariant portfolio protection (TIPP) strategy, as introduced by Estep and Kritzman (1988). We emphasize the existence of an upper bound on the multiple, for example to hedge against sudden drops in the market. Then, we provide the main properties of the conditional multiples for well-known financial models including the discrete-time portfolio rebalancing case and Lévy processes to describe the risky asset dynamics. For this purpose, we precisely define and evaluate different gap risks, in both conditional and unconditional frameworks. As a by-product, the introduction of discrete or random time portfolio rebalancing allows us to determine and/or estimate the density of durations between rebalancements. Finally, from a more practical and statistical point of view due to trading restrictions, we present the class of Dynamic AutoRegressive Expectile (DARE) models for estimating the conditional multiple. This latter approach provides useful complementary information about the risk and performance associated with probabilistic approaches to the conditional multiple. D'une stratégie d'assurance de portefeuille dynamique fondée sur un modèle autorégressif de quantile Résumé « L'assurance de portefeuille à proportion constante" (CPPI en anglais) est aujourd'hui l'une des techniques les plus populaires pour les stratégies d'assurance de portefeuille. Elle consiste simplement à réallouer la partie risquée d'un portefeuille en fonction des conditions de marché qui déterminent le paramètre de l'effet de levier-appelé multiple-de façon à garantir un plancher prédéterminé de performance. Nous proposons dans cet article d'introduire un multiple variant dans le temps conditionnellement aux turbulences de marché, comme alternative à la méthode CPPI inconditionnelle classique, en utilisant une approche standard de gestion des risques. Le multiple est ainsi modélisé à partir de la moyenne prévue des pertes potentielles (ES), dans le cadre d'un modèle autorégressif dynamique de quantiles, qui présente, au final, l'avantage de conférer à la méthode d'assurance de portefeuille proposée, une certaine flexibilité adaptative de l'exposition au risque.

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