Nonlinear Goal-Directed CPPI Strategy

Abstract

An investor will in general designate a goal in the investment process. The traditional constant proportion portfolio insurance (CPPI) strategy considers only the floor constraint but not the goal aspect. This paper proposes a goal-directed (GD) strategy to express an investor’s goal-directed trading behavior and combines it with the portfolio insurance perspective to form a piecewise linear goal-directed CPPI (GDCPPI) strategy. This piecewise linear GDCPPI strategy shows that there is a wealth position M at the intersection of the linear GD strategy and linear CPPI strategy. This M position guides investors to apply the CPPI strategy or GD strategy depending on whether the current wealth is less or greater thanM, respectively. In addition, we extend the piecewise linear GDCPPI strategy to a piecewise nonlinear GDCPPI strategy with a minimum function. These piecewise GDCPPI strategies when applying the minimum function can fully maintain the features of the CPPI strategy and the GD strategy without considering the explicitM. This minimum function in fact can obtain the concept of the explicit M, but it operates the M implicitly. Furthermore, we argue that the piecewise nonlinear GDCPPI strategy owns a larger solution space and it can then outperform the piecewise linear GDCPPI strategy in terms of the return rate performance measure. This paper performs some experiments using the Brownian, GA and forest GP techniques to prove with statistical significance that the piecewise nonlinear GDCPPI strategy can outperform the piecewise linear GDCPPI strategy and that there are some data-driven techniques that can find better piecewise linear GDCPPI strategies than strategies based on the Brownian technique.