Constant Proportion Portfolio Insurance Strategies in Fuzzy Financial Markets
Frank Ranganai Matenda
Abstract: Portfolio insurance techniques have been in existence for a long period of time. Cont and Tankov (2007) propose that portfolio insurance refers to investment strategies that limit the downside risk of a portfolio whilst maintaining its upside potential at the same time. Constant proportion portfolio insurance (CPPI) is a fundamental and prominent example of portfolio insurance strategies. Several authors have analysed CPPI based on probability theory (for example, Neftci, 2008 and Cont and Tankov, 2007) and uncertainty theory (such as, Matenda, Chikodza and Gumbo, 2015). Probability theory and uncertainty theory recognise randomness and uncertainty, respectively, as the only legitimate forms of indeterminacy. However, there are other forms of material indeterminacy in financial markets, such as fuzziness, which cannot be modelled by probability theory and uncertainty theory. In order to deal with fuzziness, credibility theory was founded. The main aim of this research work is to analyse the mechanics of CPPI strategies in fuzzy financial markets. Assuming continuous time diffusion models, CPPI techniques always work. However, in practice, CPPI strategies are exposed to gap risk which originates from sudden significant downward asset price jumps. In this research paper a direct relationship between the participation rate, and the CPPI-insured portfolio value, has been established. The risk of loss in a CPPI strategy increases with the participation rate. Gap risk for CPPI strategies is not insignificant. Therefore, it has to be quantified. This research paper develops a strong foundation for the analytical computation of gap risk for CPPI strategies when asset price processes evolve as fuzzy differential equations with jumps. This study is the first peace of work to apply credibility theory to CPPI.
Pages: 94 – 109 | Full PDF Paper