Conditional Value at Risk

The problem of optimal portfolio selection has attracted a great attention in the finance and optimization field. The future stock price should be predicted in an acceptable precision, and a suitable model and criterion for risk and the expected return of the stock portfolio should be proposed in order to solve the optimization problem. In this paper, two new criterions for the risk of stock price prediction has been presented, of which the first one is based on the interval predictions which vary with time and proportional to the uncertainty of stock price data, while the second one is a constant risk term that is proportional to the prediction error variances of the neural networks. A novel cost function has been presented to simultaneously consider the expected returns and risks. Genetic algorithm has been used to solve this optimization problem. Finally, 18 shares of the Tehran Stock Exchange have been considered to evaluate the performance of the proposed risk criterions. Two proposed risk criteria, by the conditional value at risk (CVaR) associated with the same stock. The problem of stock portfolio optimization has been solved for all three situations, and the PI-based risk criteria yielded a better return

The purpose of this study is to develop portfolio optimization and assets allocation using our proposed models. The study is based on a non-parametric efficiency analysis tool, namely Data Envelopment Analysis (DEA). Conventional DEA models assume non-negative data for inputs and outputs. However, many of these data take the negative value, therefore we propose the MeanSharp-βRisk (MShβR) model and the Multi-Objective MeanSharp-βRisk (MOMShβR) model base on Range Directional Measure (RDM) that can take positive and negative values. We utilize different risk measures in these models consist of variance, semivariance, Value at Risk (VaR) and Conditional Value at Risk (CVaR) to find the best one as input. After using our proposed models, the efficient stock companies will be selected for making the portfolio. Then, by using Multi-Objective Decision Making (MODM) model we specified the capital allocation to the stock companies that selected for the portfolio. Finally, a numerical example of the Iranian stock companies is presented to demonstrate the usefulness and effectiveness of our models, and compare different risk measures together in our models and allocate assets.

Mutual funds are one of the most paramount investment mechanisms in financial markets. By playing a financial intermediary role, they give nonprofessionals access to professionally managed portfolios of securities and provide numerous benefits for both the capital market and investors simultaneously. This study evaluated and investigated the systemic risk of mutual funds in the Iran capital market by adopting a Conditional Value at Risk (CoVaR) approach and employing quantile regression. In the finance literature, systemic risk is the probability of a downfall in the financial system when a segment or an individual component gets in distress. This risk can trigger instability or shock in financial markets and the real part of the economy. The results revealed that stock (equity) mutual funds were systemically more important than other funds, including fixed-income and balanced mutual funds, due to the high volatility in their return, which makes them riskier. To compare systemic risk and market risk among mutual funds, funds classified into five different groups based on their systemic risk. According to this categorization, analysis of variance illuminated that the market risk of mutual funds had a direct relationship with their systemic risk, such that a higher systemic risk of a fund stood for higher market risk.