Goal-Directed Portfolio Insurance Strategies

author = "Benjamin Penyang Liao",

title = "Goal-Directed Portfolio Insurance Strategies",

school = "Department of Information Management, National Central University, NSYSU",

year = "2006",

address = "Taiwan",

month = jun,

keywords = "genetic algorithms, genetic programming, forest genetic programming, GDPI, implicit piecewise linear GDPI strategy, piecewise nonlinear GDPI strategy, piecewise linear GDPI strategy, goal-directed strategy, Portfolio insurance strategy",

URL = "

http://ir.lib.ncu.edu.tw:88/thesis/view_etd.asp?URN=87443004",

URL = "

http://thesis.lib.ncu.edu.tw/ETD-db/ETD-search-c/getfile?URN=87443004&filename=87443004.pdf",

size = "120 pages",

abstract = "Traditional portfolio insurance (PI) strategy such as constant proportion portfolio insurance (CPPI) only considers the floor constraint but not the goal aspect. There seems to be two contradictory risk-attitudes according to different studies: low wealth risk aversion and high wealth risk aversion. Although low wealth risk aversion can be explained by the CPPI strategy, high wealth risk aversion can not be explained by CPPI. We argue that these contradictions can be explained from two perspectives: the portfolio insurance perspective and the goal-directed perspective. This study proposes a goal-directed (GD) strategy to express an investor's goal-directed trading behaviour 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 strategy and CPPI strategy. This M position guides investors to apply CPPI strategy or GD strategy depending on whether the 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. Moreover, we extend the piecewise GDCPPI strategy to the piecewise GDTIPP strategy by applying the time invariant portfolio protection (TIPP) idea, which allows variable floor and goal comparing to the constant floor and goal for piecewise GDCPPI strategy. Therefore, piecewise GDCPPI strategy and piecewise GDTIPP strategy are two special cases of piecewise goal-directed portfolio insurance (GDPI) strategies. When building the piecewise nonlinear GDPI strategies, it is difficult to preassign an explicit $M$ value when the structures of nonlinear PI strategies and nonlinear GD strategies are uncertain. To solve this problem, we then apply the minimum function to build the piecewise nonlinear GDPI strategies, which these strategies still apply the $M$ concept but operate it in an implicit way. Also, the piecewise linear GDPI strategies can attain the same effect by applying the minimum function to form implicit piecewise linear GDPI strategies. This study performs some experiments to justify our propositions for piecewise GDPI strategies: there are nonlinear GDPI strategies that can outperform the linear GDPI strategies and there are some data-driven techniques that can find better linear GDPI strategies than the solutions found by Brownian technique. The GA and forest genetic programming (GP) are two data-drive techniques applied in this study. This study applies genetic algorithm (GA) technique to find better piecewise linear GDPI strategy parameters than those under Brownian motion assumption. This study adapts traditional GP to a forest GP in order to generate piecewise nonlinear GDPI strategies. The statistical tests show that the GP strategy outperforms the GA strategy which in turn outperforms the Brownian strategy. These statistical tests therefore justify our propositions.",