Price forecasting and risk portfolio optimization

Nowadays, the stocks trading is very popular. That is why the problem of forecasting assets' prices is of a special scientific interest. ARIMA (Autoregressive Integrated Moving Average) models for forecasting the stock prices are presented in this paper. For every model the expected return of the shares is calculated and the variance of the rate of returns is analyzed based on a given historical data. Quarterly data on stock prices of the four biggest banks in the United States, that are classified by total assets,areexamined for the period 01.01.2014 - 01.04.2019. An optimization problem is formulated, that is based on Harry Markowitz's model. The solution of this problem leads to finding an optimal risk portfolio for one period ahead and gives an estimate value of the expected rate of return. Depending on the coefficient of risk aversion, a comparative analysis of the structure of a complete portfolio of a risky and a risk-free asset is made. A Matlab programming code is developed, giving the results for an optimal risk portfolio with n assets.