بازده و مخاطرات سبد سرمایه گذاری در سقوط بازار سهام

• The returns and risks of investment portfolio in stock market crashes were investigated.• Both the maximum dispersion of investment portfolio and an optimal stop-loss position maximally enhance the stability of returns.• A worst dispersion is associated with the maximum risks.• The increasing stop-loss position enhances the risks.The returns and risks of investment portfolio in stock market crashes are investigated by considering a theoretical model, based on a modified Heston model with a cubic nonlinearity, proposed by Spagnolo and Valenti. Through numerically simulating probability density function of returns and the mean escape time of the model, the results indicate that: (i) the maximum stability of returns is associated with the maximum dispersion of investment portfolio and an optimal stop-loss position; (ii) the maximum risks are related with a worst dispersion of investment portfolio and the risks of investment portfolio are enhanced by increasing stop-loss position. In addition, the good agreements between the theoretical result and real market data are found in the behaviors of the probability density function and the mean escape time.