Piecewise nonlinear goal-directed CPPI strategy

Traditional portfolio insurance (PI) strategy, such as constant proportion portfolio insurance (CPPI), only considers 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 this floor-less GD strategy with the goal-less CPPI strategy to form a piecewise linear goal-directed CPPI (GDCPPI) strategy. The piecewise linear GDCPPI strategy shows that there is a wealth position M at the intersection of the GD and CPPI strategies. This M position guides investors to apply the CPPI strategy or the GD strategy depending on whether current wealth is less than or greater than M, respectively. In addition, we extend the piecewise linear GDCPPI strategy to a piecewise nonlinear GDCPPI strategy. This paper applies genetic algorithm (GA) technique to find better piecewise linear GDCPPI strategy parameters than those under the Brownian motion assumption. This paper also applies forest genetic programming (GP) technique to generate the piecewise nonlinear GDCPPI strategy. The statistical tests show that the GP strategy outperforms the GA strategy which in turn outperforms the Brownian strategy.