Robust Portfolio Optimization under Interval-valued Conditional Value-at-Risk (CVaR) Criterion in the Tehran Stock Exchange

Ever since Harry Markowitz's groundbreaking paper on the mean-variance model was published in 1952, numerous efforts have been dedicated to exploring the applications and advancements of classical models. Following the development of financial markets, active portfolio optimization has become one of the most important topics in finance. This study aimed to examine active portfolio management, a critical and delicate choice for investors, particularly concerning overall portfolio risk. The determination of an optimal stock portfolio that offers both a substantial return rate and controlled risk is consistently a subject of keen interest for analysts, investors, and even portfolio managers.
 

Many methods have been developed to measure investment risk, and the price of risky assets changes rapidly and randomly due to the complexity of the financial market. A random interval is a suitable tool for describing uncertainty with randomness and imprecision. Given the uncertainty in financial markets, this study used stochastic intervals to describe the returns of risky assets and the tail sequence risk, called the interval-valued conditional value at risk (ICVaR). The interval value in this model is an extension of the classic portfolio model, which can comprehensively reflect the complexity of the financial market and the risk-taking behavior of investors.
 

Following the findings from the real data of 10 out of 30 large corporates listed on the Tehran Stock Exchange, the ICVaR model is interpretable and compatible with the practical scenario and can be used to choose the optimal portfolio at different levels of risk and depending on the risk-taking degree of the investor. The present study used the portfolio optimization approach under a new criterion of ICVaR through the closing price, the highest price, and the lowest price on each trading day. In this model, the return range of the risky asset is taken as a random variable with an interval value. Besides, CVaR with an interval value is used to describe the risk instead of the variance at a certain level of return.
 

Uncertainties induced by asset transactions affect the predictions of investment plans. To address such challenging uncertainties in this study, a stable stochastic optimization approach was presented based on the range of optimal solutions produced by the proposed model to determine different operational options. Finally, the model developed in this study showed that investors’ subjective risk preference or aversion can be described by observing the principle of portfolio diversification, which reflects an innovation different from the classic portfolio model. Furthermore, the worst possible case was optimized in all scenarios in the model by robust optimization. The findings indicated that a narrower range corresponds to a higher level of risk aversion among investors.