A Heuristic Approach to Forecasting and Selection of a Portfolio with Extra High Dimensions

The performance of a financial portfolio depends on the output of two tasks: first, a forecasting process, where quantities of interest for the investors, such as the rate of return and risk for each stock, are predicted into the future, and second, an optimization process, where those individual stocks are formed into the portfolio optimizing the combined risk and reward features. However, in very large dimensions, when the number of stocks is high, those two quantitative problems often become intractable because of a loss in precision. This paper introduces a forecasting and portfolio formation strategy in multiple periods based on the splitting of the multivariate forecasting model into multiple bivariate forecasting models and updating investment weights at each period based on the predicted target quantities for the returns and the covariances. The methodology proposed is suitable for a very large portfolio of assets. The experimental results are based on a sample of one thousand stocks from the Chinese stock market. For such a large sample, the forecast and optimization process is executed speedily. The investment strategies are benchmarked with the equally weighted portfolio. In the long run, they offer a better investment performance in terms of a higher rate of return or lower risk, compared with this portfolio, demonstrating the applicability and economic value of the proposed methodology in practice.