Portfolio insurance: Gap risk under conditional multiples

• Published in: European journal of operational research Vol. 236; no. 1; pp. 238 - 253
• Main Authors: Ben Ameur, H., Prigent, J.L.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-07-2014; Elsevier Sequoia S.A; Elsevier
• Subjects: Arches; Constants; CPPI with conditional multiples; Expected utility; Finance; Humanities and Social Sciences; Insurance; Investment analysis; Investment policy; Mathematics; Operational research; Optimization; Portfolio insurance; Portfolio management; Quantiles; Quantitative Finance; Rates of return; Risk management; Statistics; Strategy; Studies; Volatility; Investment analysis; CPPI with conditional multiples; Portfolio insurance; Risk management; Finance
• ISSN: 0377-2217; 1872-6860
• DOI: 10.1016/j.ejor.2013.11.027

•We extend one of the two main portfolio insurance methods, namely the CPPI method.•We allow the multiple to vary over time while controlling the risk of such portfolio management.•A quantile approach is introduced together with expected shortfall criteria.•We provide explicit upper bounds on the multiple as function of past asset returns and volatilities.•We show how this new asset allocation method performs for various financial market conditions.
The research on financial portfolio optimization has been originally developed by Markowitz (1952). It has been further extended in many directions, among them the portfolio insurance theory introduced by Leland and Rubinstein (1976) for the “Option Based Portfolio Insurance” (OBPI) and Perold (1986) for the “Constant Proportion Portfolio Insurance” method (CPPI). The recent financial crisis has dramatically emphasized the interest of such portfolio strategies. This paper examines the CPPI method when the multiple is allowed to vary over time. To control the risk of such portfolio management, a quantile approach is introduced together with expected shortfall criteria. In this framework, we provide explicit upper bounds on the multiple as function of past asset returns and volatilities. These values can be statistically estimated from financial data, using for example ARCH type models. We show how the multiple can be chosen in order to satisfy the guarantee condition, at a given level of probability and for various financial market conditions.