Verification of Loss Cut Effect in Scenario-tree-type Multi-period Probability Planning Model

Abstract

In this study, we add a new loss-cutting constraint formula to the scenario-tree-type multi-period stochastic programming model, which is used in conventional portfolio theory when a portfolio is held for multiple periods, and examine the effect of loss-cutting. Specifically, we compare the return, risk, and Sharpe ratio before and after the addition of the loss-cutting constraint equation, and examine how the loss-cutting constraint equation affects the objective function value. Assuming that stock prices follow a geometric Brownian motion, we create a scenario tree using the simulated results. In this study, we assume that the portfolio holding period is three periods and that the scenario has four branches in each period. Next, we set the probability of occurrence of each node at the end of the plan. We assume that the occurrence probability of each node follows a uniform distribution. Specifically, random numbers that follow a uniform distribution are generated, and in order to treat them as random variables, the sum of the occurrence probabilities of each node is obtained, and the value of each node divided by the obtained sum is used as the occurrence probability. Using the above simulation results, we implement a scenario-tree type multi-period stochastic programming model and obtain the objective function value. Furthermore, we define and implement the loss-cut constraint equation, calculate the objective function value again, and verify how the return, risk, and Sharpe ratio change before and after adding the loss-cut constraint equation. The experimental results show that the return increases or decreases and the risk increases or decreases depending on the price of loss-cutting. The results also show that the Sharpe ratio improves depending on the price of loss-cutting, and thus the effectiveness of the proposed method is verified.