Comparative Analysis of ARIMA and Modified Differential Equation Approaches in Stock Price Prediction and Portfolio Formation

Abstract

In portfolio management theory, the principle of separation states that with the same input, all investors will have the same optimal risk portfolio. Whether the portfolio will actually be optimal depends on how accurate the results of the technical analysis conducted by the portfolio manager, or the investor is in order to predict the rate of return on the financial assets included in the portfolio. In this article, Autoregressive Integrated Moving Average (ARIMA) models have been used to predict assets’ prices of four Bulgarian companies. Estimated rates of return have been calculated from the models. An optimal risk portfolio has been organized based on the Markowitz model. The resulting portfolio has been compared with a similar one obtained on the same data, using Modified Ordinary Differential Equations (ODE) to derive the forecast rates of return of the assets.