Portfolio Decision Using Time Series Prediction and Multi-objective Optimization

Randomness, volatility, and nonlinearity displayed by the stock market lead to the uncertainty of the stock market index and stock prices. The purpose of the study is to find a straightforward method for portfolio decision applicable to strong-form and weak-form efficient markets. Thus, a methodology for porfololio decision base on the Nonlinear Autoregressive Exogenous Model (NARX) and multi-objective optimization (MO) was proposed. First, two of eight quarters from 2018 to 2019 were chosen to buy S&P 500 stocks on the basis of the predicted stock market trend using the NARX with a single exogenous variable. The variable was selected from 67 macroeconomic factors by Shannon entropy or relevance. Then, the stocks were selected for a portfolio on the basis of the predicted stock returns from the NARX with a mean relative error as the criteria. Next, a reverse conditional probability indicator was imported as a risk indicator for the objective function of MO, and the stock weights of the portfolio were allocated by MO following the principle of maximizing predicted portfolio return and minimizing portfolio risk. The final findings demonstrate that the portfolio return is 8%–14% below the S&P 500 return and is increased to approximately 5% above the S&P 500 return after the stock weights were allocated by MO. The final investment return for eight quarters is 60% above the S&P 500 return if the proposed investment strategy was adopted. Therefore, the proposed method in the study combining the NARX and MO with certain criteria can guide investors to make a rational portoloio decision and give a reference for scholars to establish effective method for the prediction of stock prices and assets allocation.