Optimizing Portfolio Based on Prospect Theory and Wavelet Transform

Abstract

The balance between risk and return is one of the issues raised in the investment area. Forming a stock portfolio is considered the simplest and most effective way to reduce investment risk and increase return on investment. In the present study, the index tracking model and the prospect theory optimization model were investigated using index tracking. The data were analyzed using wavelet transform . The results were examined after removing the high frequency of the data and two algorithms including genetic and gray wolf algorisms were used in this regard. A significant assumption is that the behavioral characteristics of the prospect theory model provide better negative protection than traditional methods for the portfolio selection problem. In this study, the computational results of the prospect theory model for the real data of the financial market of the Dow Jones index and its 30 stocks were examined. To improve and confirm the result, wavelet transform was used to analyze the high-frequency and low-frequency data. The prospect theory model with the reference point which is the index is compared with the index tracking model. A major limitation was implemented for base index tracking and prospect theory models. The primary results of this work are: The advantage of stock portfolio diversification is evident in the prospect theory model. The tendency to obtain higher returns than the index in the prospect theory model with the reference point of the index leads to better performance of this model in the bull market. However, it performed worse than the index tracking model in a bear market. Finally, to confirm the implementation of the model, this model was compared with Markowitz's initial model.  The prospect theory model obtained a higher return.