Constant Proportion Portfolio Insurance Strategies under Cumulative Prospect Theory with Reference Point Adaptation

Constant Proportion Portfolio Insurance (CPPI) is a significant and highly popular investment strategy within the structured product market. This has led to recent work which attempts to explain the popularity of CPPI by showing that it is compatible with Cumulative Prospect Theory (CPT). We demonstrate that this cannot explain the popularity of ratcheted CPPI products which lock-in gains during strong growth in the portfolio. In this paper we conjecture that CPPI investors not only follow CPT, but crucially that they also adapt their reference point over time. This important distinction explains investors preference for ratcheted product

Portfolio insurance

Diese Magisterarbeit stellt mehrere Wertsicherungs-Strategien vor und präsentiert die Ergebnisse einer Monte Carlo-Analyse zur Beurteilung der impliziten Kosten und der Zuverlässigkeit von zwei weit verbreiteten Strategien. Im ersten Teil der Arbeit wird die Nachfrage nach solchen Strategien erläutert und deren Entstehung dokumentiert. Im nachfolgenden Kapitel werden verschiedene Risko-Maße vorgestellt, welche später in der Simulation verwendet werden. Die einzelnen Strategien werden entsprechend ihrer Kategorisierung in statische und dynamische Strategie, beschrieben. Die vorgestellten statischen Strategien sind 1) Buy&Hold, 2) Stop-Loss, 3) Protective Put und 4) deren Equivalent mit Einsatz von Call-Optionen. Die vorgestellten dynamischen Strategien sind 1) Synthetic Put, 2) Modified Stop-Loss und 3) Constant Proportion Portfolio Insurance (CPPI). Der Hauptteil dieser Arbeit ist eine detaillierte Analyse der Synthetic Put und CPPI Strategien unter Einsatz der Monte-Carlo-Simulation. Das Ziel ist eine Beurteilung der impliziten Kosten und der Zuverlässigkeit beider Strategien durch das Betrachten der gesamten Wahrscheinlichkeitsverteilung der Renditen der abgesicherten Portfolios. Die Simulation zeigt, dass beide Strategien in der Lage sind eine asymmetrische Wahrscheinlichketsverteilung zu generieren welche eine Schiefe in Richtung positiver Renditen hat. Somit ermöglichen es beide einen Portfolio-Mindestwert zu sichern und gleichzeitg die Partizipation an steigenden Märkten zu erlauben. Allerdings verdeutlicht die Simulation auch die Kosten einer solchen Absicherung, welche sich durch eine Verringerung im Mittelwert und Median der Portfolio-Renditen niederschlägt. Die Synthetic Put Strategie hat sich als zuverlässig erwiesen, wenn die Schätzung der Volatilität genau ist. Es ergibt sich lediglich ein kleiner “Abischerungs-Fehler” wenn der Synthetic Put kurz vor auslaufen am Geld steht, welcher jedoch in der Höhe vernachlässigbar ist. Wird die Volatilität unterschätzt, so schafft es die Strategie nicht den gewünschten Mindestwert zu sichern. Die CPPI Strategie hat sich unter allen getesteten Parametern als zuverlässig erwiesen. Mit steigendem Multiplikator stieg auch der Mittelwert und Median der Portfolio-Renditen an. Jedoch zeigte sich auch eine deutliche Verschiebung der Wahrscheinlichkeitsmasse in Rendite-Bereiche weit unter dem risikolosen Zinssatz.This thesis introduces several portfolio insurance strategies and presents the results of an analysis of the implicit cost and reliability of two widely adopted strategies. The first part is an introduction into portfolio insurance and explains why there is a demand for such strategies and how they emerged. It is followed by a chapter on different risk measures, which will be used in the course of the analysis. Following their classification into static and dynamic strategies the properties of several portfolio insurance strategies are described. The static strategies presented are 1) Buy&Hold, 2) Stop-Loss, 3) Protective Put and 4) its equivalent using call options. The dynamic strategies presented are 1) Synthetic Put, 2) Modified Stop-Loss and 3) Constant Proportion Portfolio Insurance (CPPI). The main part of this thesis is a detailed analysis of the Synthetic Put and the CPPI strategies using Monte Carlo simulation. Specifically, considering the resulting probability distribution of the insured portfolio returns, the implicit cost and reliability will be assessed. The analysis proves that both strategies have the desired property of creating an asymmetric return distribution that is skewed toward positive returns. Thus, they effectively limit a portfolios downside to a prespecified floor, while retaining the ability to participate in favourable market movements. However, the analysis also reveals the implicit cost of this property, which is a lower mean and median return as compared to an uninsured portfolio. The Synthetic Put proved to be reliable in securing a desired floor when the volatility estimate was accurate. When the Synthetic Put was at the money while approaching expiration a minor “protection error” appeared in the simulation, which was negligible in its magnitude. When volatility is underestimated the Synthetic Put fails to offer the desired protection. The CPPI strategy was fully reliable under the tested parameter settings. Even though higher multipliers resulted in higher mean and median returns of the CPPI strategy, the probability distribution appeared to be very skewed with half of the probability mass lying in a range of modest returns below the risk-free rate

GP-based rebalancing triggers for the CPPI

The Constant Proportion Portfolio Insurance (CPPI) technique is a dynamic capital-protection strategy that aims at providing investors with a guaranteed minimum level of wealth at the end of a specified time horizon. A pertinent concern of issuers of CPPI products is when to perform portfolio readjustments. One way of achieving this is through the use of rebalancing triggers; this constitutes the main focus of this paper. We propose a genetic programming (GP) approach to evolve trigger-based rebalancing strategies that rely on some tolerance bounds around the CPPI multiplier, as well as on the time-dependent implied multiplier, to determine the timing sequence of the portfolio readjustments. We carry out experiments using GARCH datasets, and use two different types of fitness functions, namely variants of Tracking Error and Sortino ratio, for multiple scenarios involving different data and/or CPPI settings. We find that the GP-CPPI strategies yield better results than calendar-based rebalancing strategies in general, both in terms of expected returns and shortfall probability, despite the fitness measures having no special functionality that explicitly penalises floor violations. Since the results support the viability and feasibility of the proposed approach, potential extensions and ameliorations of the GP framework are also discussed

Banks Balance sheet and Income Statement

Financial Report Complete (additional readings