Analysis of Complex Portfolio Strategies with Return Approximation Techniques

Abstract

Recently, a significant number of researchers have focused on the portfolio selection problem. One of the main issues related to this problem is the approximation of return series. In this thesis, two types of return approximation techniques and their combination are examined and incorporated into complex portfolio selection strategies. Specifically, parametric regression and nonparametric regression using conditional expectations and kernel estimator are considered. The proposed portfolio strategies are put in the context of three issues associated with portfolio and risk management. In particular, the problem of trend–risk measurement, prediction of return series, and application of moving average family trading rules with a multiple alarm are examined. Thus, new measures, approaches, and strategies have been proposed. Moreover, most empirical parts use the dynamic dataset of stock returns that formed a particular index, which makes this analysis more realistic and desirable. In the first analysis, the perspective on trend (time)–dependent risk measurement inspired by Ruttiens (2013) and double optimization strategies employing the mean–variance portfolio selection model applied on approximated returns are discussed and examined. In the second analysis, the scenario generation process that uses the ARMA–GARCH model is examined, where the residuals obtained follow a stable distribution and a skewed t copula dependency. In addition, double PCA to trend–dependent and Pearson correlation matrices is used in order to reduce the portfolio dimensionality while capturing a sufficient percentage of both types of variability. Again, the classical mean–variance portfolio selection framework is applied as a tool to obtain the portfolio weights. Finally, trading rules considering a moving average family of indicators are analyzed in order to preselect the dataset of risky assets. In addition, the same indicators are used to detect systemic risk on the market through an early warning system. The portfolio selection strategy employed in this analysis includes the semiparametric regression with the copula–PCA approach. To find the optimal portfolio, a maximization performance measure framework is used, where several widely used performance measures are incorporated.

For all strategies, portfolio performance and risk measures are compared using commonly used indicators. Additionally, in some analyses, diversification measures are examined. From the results of the portfolio performance, we can observe the benefits of using the nonparametric regression model.