This study considers a new stochastic volatility model, in which the sign and magnitude of stock returns play roles in explaining a substantially detailed relationship between stock returns and volatility. The proposed model allows for threshold and leverage effects, and accommodates three regimes (i.e., large negative return; mid-range, including moderate negative and positive returns; and large positive return) to better capture the time-varying aspect of the leverage effect. Applications of the proposed model on the return series of the S&P 500 Index and Microsoft Corporation suggest that the relationship between stock returns and volatility depends on the magnitude of the returns and their signs. The comparison of the deviance information criterion for various stochastic volatility models reveals a good fit of the proposed model for the data.