Mohammad Esmaeil Fadaeinejad - Associate Prof., Department of Financial Management and Insurance, Shahid Beheshti University, Tehran, Iran.
Mohamad Taghi Vaziri - Assistant Prof, Department of Financial Management and Insurance, Shahid Beheshti University, Tehran, Iran.
Hossein Asadi - Associate Prof., Department of Financial Management and Insurance, Shahid Beheshti University, Tehran, Iran.
Mohammad Javad Faryadras - Ph.D. Candidate, Department of Financial Management and Insurance, Shahid Beheshti University, Tehran, Iran.

Given the lack of a specific approach to the explanation of values of optimal portfolio weights in the portfolio optimization, the present study aimed to examine large-scale portfolio optimization according to both stock weighting and utilization of SCAD function to minimize the portfolio risk based on the "weight-modified conditional value at risk (CVaR)" and its comparison with the "conditional value at risk (CVaR)" method in the Tehran Stock Exchange. Therefore, the price information of companies listed in the Tehran Stock Exchange and Over-the-counter (OTC) from ۲۰۱۲ to the end of September ۲۰۲۰ was collected, screened, and analyzed daily, and then the risk and return of the portfolios were examined by forming optimal portfolios. The results indicated that the efficiency limit of the stock portfolio and also the ranks of different companies were different according to the types of the optimization method. Based on the behavior of the TEDPIX, the investors' degrees of risk-taking, and the risk management, diversification, and computational complexity of each method, the weight-modified CVaR had a better performance due to better diversification and risk management. Furthermore, the SCAD function added computational complexity to this method.

portfolio optimization, conditional value at risk (CVAR), Smoothly-clipped absolute deviation (SCAD) penalty function