傳統的投資組合保險 (portfolio insurance; PI) 策略，例如 constant proportion portfolio insurance (CPPI) 策略，只有考慮保本限制而並未考慮目標因素。然而研究顯示出兩種相互矛盾的投資者風險態度，分別是低財富風險趨避以及高財富風險趨避。雖然低財富風險趨避可以由CPPI策略來解釋，但是高財富風險趨避無法由CPPI策略來解釋。我們認為這些矛盾現象可以經由投資組合保險觀點與目標導向觀點來解釋。本研究提出了一個目標導向 (goal-directed ; GD) 策略來顯示投資者的目標導向投資行為。本研究更進一步的結合與保本無關的GD策略以及與保目標無關的CPPI策略，以建立一個分段線性目標導向CPPI (GDCPPI) 策略。分段線性GDCPPI策略中存在一個經由GD策略與CPPI策略相交的財富水準M值。此一M值能引導投資者當目前的財富低於該M值時應採用CPPI策略，當目前的財富高於該M值時應採用GD策略。 更進一步的，我們擴充分段線性GDCPPI策略成為分段非線性GDCPPI策略。我們也應用time invariant portfolio protection (TIPP) 的允許動態保本底限與目標上限的觀念來取代CPPI的靜態觀念，而將分段GDCPPI策略擴充成分段GDTIPP策略。因此分段GDCPPI策略與分段GDTIPP策略都是分段GDPI策略的兩個特例。當建立分段非線性GDPI策略時，採用明確的M值是不合理的，因為投資者會遭遇到無法事先決定由非線性PI策略與非線性GD策略來產生M值的困難。因此我們採用最小值函數來順利解決此一問題。亦即分段非線性GDPI策略等於非線性PI策略與非線性GD策略的其中一個最小的值。應用此一最小值函數會讓分段非線性GDPI策略仍然保有M值的觀念，但卻是以隱性的方式來操作。同時分段線性GDPI策略亦可以採用此以最小值函數來獲得相同的效果，並建立一個隱性分段線性GDPI策略。 本研究進行了許多的實驗以辯證我們所提的兩個命題：存在分段非線性GDPI策略優於分段線性GDPI策略，以及存在其他資料驅動 (data-driven) 的技術以便於找到比透過Brownian技術所產生的更好的分段線性GDPI策略。本研究採用了遺傳演算法(GA)來找出更好的分段線性GDPI策略。同時本研究調適了傳統的遺傳程式規劃(GP)成為森林式GP，以建立分段非線性GDPI策略。統計檢定結果顯示，由GP所產生的交易策略優於由GA所產生的交易策略，同時由GA所產生的交易策略優於由Brownian技術所產生的交易策略。因此檢定結果能辯證我們所提出的命題。 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 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 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.
