Portfolio Construction Based on the ARMA Model and the Mean-Variance Theory

Abstract

It is an essential process for investors to construct a portfolio in the equity market. However, the uncertain volatility in the market is a drag to construct a certain portfolio. Based on several blue-chip stocks from S&P, this paper aims at constructing an optimal portfolio with risky assets. The autoregressive moving average (ARMA) model and the Mean-Variance model are selected for investigations. Specifically, the paper builds time series models and forecasts the future returns with a rolling window based on the ARMA model. Then, the predicted weekly returns are used to calculate the Efficient Frontier (EF) of every single period using Monte Carlo simulation. Furthermore, the optimal point with the highest Sharpe Ratio locates the upper-left area of the EF is adopted to set up and adjust the portfolio of each period. The back-test results show that the portfolio performed well compared to the S&P500 index. On top of that, the ARMA model selected performed well in predicting the future return of targeted stocks. Moreover, the Mean-Variance Model, abbreviated as MV model afterward, with maximized Sharpe ratio, also generates agreeable results. Specifically, the weight on new advanced industrial stocks and retail stocks are relatively high in the portfolio. This empirical process further proves two important facts in financial markets. (1) It is feasible to forecast future stock by returns in the past; (2) it is advisable to pay more attention to new advanced industrial stocks and retail stocks. Adding these kinds of stocks into the portfolio is more potential to gain high returns with correspondingly low volatility.