Constant Proportion Portfolio Insurance Strategies in Hybrid Markets
Frank Ranganai Matenda
Abstract: Financial decisions are made under the state of indeterminacy. Randomness and fuzziness are two basic forms of indeterminacy. Probability theory (Kolmogorov, 1933) models randomness and fuzzy set theory (Zadeh, 1965) deals with fuzziness. However, in some cases, randomness and fuzziness appear simultaneously in a mathematical system. In order to deal with mathematical systems that contain both fuzziness and randomness, chance theory has been developed. Portfolio insurance refers to investment strategies which guarantee that the portfolio value at maturity or at any time before maturity will not go below a stated lower bound (also known as the floor), usually fixed as a fraction of the initial principal investment (Cont and Tankov, 2007). Constant proportion portfolio insurance (CPPI) is a popular example of portfolio insurance techniques. Various research papers have examined CPPI strategies based on probability theory (for example, Neftci, 2008 and Cont and Tankov, 2007) and credibility theory (see, for instance, Matenda, 2016). This study aims to analyse the mechanics of CPPI strategies in hybrid markets. Hybrid markets are markets in which asset prices are driven by hybrid processes. Basically, hybrid processes model both randomness and fuzziness. Assuming diffusion models with continuous trading, CPPI strategies are not exposed to gap risk. However, in reality, CPPI techniques are exposed to gap risk which needs to be analytically quantified. The multiplier value, m, and the CPPI-insured portfolio value, Vt, are positively correlated. A direct relationship between the CPPI-insured portfolio risk of loss and the multiplier value has been substantiated. The research paper constructs a strong foundation for the calculation of the multiplier value in accordance with the risk tolerance of the investors. This peace of research work also unfolds the basis for the analytical quantification of gap risk for CPPI strategies when asset price processes evolve as hybrid processes with jumps. The study is the first peace of research work to analyse CPPI strategies in hybrid markets.
Keywords: Portfolio insurance, indeterminacy, randomness, fuzziness, chance theory, hybrid processes, hybrid markets, gap risk, multiplier value.
Pages: 189 – 207 | Full PDF Paper