A dynamic autoregressive expectile for time-invariant portfolio protection strategies

Abstract

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.

Dynamic allocation strategies for absolute and relative loss control

“…Thus, in that case, one can safely assume expected returns are equal to zero in estimating the expected shortfall, which means that the maximal multiplier implies a risk-based asset allocation program not depending on expected return estimates. Studies on the maximum risk-based multiplier such as Bertrand and Prigent (2002), Cont and Tankov (2009), and Hamidi, Maillet, and Prigent (2014), assume that B is a locally riskless asset paying a constant rate of return considered "relatively small" compared to the worst possible loss in the risky asset. However, when the reserve asset B is locally risky (as in the strategies considered here and the more general version of the CPPI discussed in Mantilla-García (2014)), the right tail of the return distribution of B also becomes relevant to estimate the upper bound of the multiplier.…”

“…For (R S (t, t + ) − R B (t, t + )) < 0, the inequality (42) gets inverted, yielding the upper bound of the multiplier (see Hamidi et al, 2014;Mantilla-García, 2014, for a more detailed derivation)…”

“…The upper bound M t is not known at time t, hence it has to be estimated. Bertrand and Prigent (2002), Cont and Tankov (2009), Prigent (2008, 2009a,b); Hamidi et al (2014), and Ben Ameur and Prigent (2013) address the question of estimating the maximum multiplier of the CPPI. These studies assume a risk-free reserve asset with constant rate of return.…”

Estimating portfolio risk for tail risk protection strategies

“…Andersen, Bollerslev, Christoffersen, & Diebold, 2006;Longin & Solnik, 1995), other studies (e.g. Hamidi, Maillet, & Prigent, 2014) propose to model the multiplier as time-varying and conditional. The corresponding strategy is known as dynamic proportion portfolio insurance (DPPI).…”

Dynamic portfolio insurance strategies: risk management under Johnson distributions

“…Hamidi et al (2009a, b) and Ben Ameur and also consider a modified quantile hedging strategy and show how a conditional multiple can be determined. For this purpose, Hamidi et al (2014) introduce quantile regressions, like for example Engle and Manganelli (2004) who study Conditional Auto Regressive Value-at-Risk by Regression Quantile (CAViaR).…”