Efficient Frontier

In portfolio theory, it is well-known that the distributions of stock returns often have non-Gaussian characteristics. Therefore, we need non-symmetric distributions for modeling and accurate analysis of actuarial data. For this purpose and optimal portfolio selection, we use the Tail Mean-Variance (TMV) model, which focuses on the rare risks but high losses and usually happens in the tail of return distribution. The proposed TMV model is based on two risk measures the Tail Condition Expectation (TCE) and Tail Variance (TV) under Generalized Skew-Elliptical (GSE) distribution. We first apply a convex optimization approach and obtain an explicit and easy solution for the TMV optimization problem, and then derive the TMV efficient frontier. Finally, we provide a practical example of implementing a TMV optimal portfolio selection in the Tehran Stock Exchange and show TCE-TV efficient frontier.

Forming a portfolio of different stocks instead of buying a particular type of stock can reduce the potential loss of investing in the stock market. Although forming a portfolio based solely on past data is the main theme of various researches in this field, considering a portfolio of different stocks regardless of their future return can reduce the profits of investment. The aim of this paper is to introduce a new two-phase approach to forming an optimal portfolio using the predicted stock trend pat-tern. In the first phase, we use the Hurst exponent as a filter to identify stable stocks and then, we use a meta-heuristic algorithm such as the support vector regression algorithm to predict stable stock price trends. In the next phase, according to the predicted price trend of each stock having a positive return, we start arranging the portfolio based on the type of stock and the percentage of allocated capacity of the total portfolio to that stock. To this end, we use the multi-objective particle swarm optimization algorithm to determine the optimal portfolios as well as the optimal weights corresponding to each stock. The sample, which was selected using the systematic removal method, consists of active firms listed on the Tehran Stock Ex-change from 2018 to 2020. Experimental results, obtained from a portfolio based on the prediction of stock price trends, indicate that our suggested approach outperforms the retrospective approaches in approximating the actual efficient frontier of the problem, in terms of both diversity and convergence.

Portfolio optimization has always been the main concern of investors. What differentiates different optimization models from each other is the risk measure. The main contribution of this paper is to provide a portfolio optimization model that considers systemic risk so that it can help investors make optimal investment decisions as a general model. For this purpose, two models are presented. In the first model, systemic and systematic risk were considered simultaneously, and in the second model, only systemic risk was considered. In the two mentioned models, delta conditional value at risk (∆CoVaR) and the Markowitz model are used respectively to measure systemic risk and a benchmark model. Also, the criteria used to compare the performance of the reviewed models include the ratio of reward-to-risk, along with the Sortino ratio and the Omega ratio. The problem of optimization and examination of the results was carried out on a selected sample, 38 companies listed in the Tehran Stock Exchange (TSE) from 2013 to 2023. The results of empirical analysis of out-of-sample data (during a period of 1198 days) show that based on all three mentioned criteria, the first proposed model shows the best performance among the three models. In addition, the performance of the second model is ranked second. In short, it can be said that considering systemic risk in portfolio optimization leads to better performance than the Markowitz model.