Before revision:  Examining 615 stocks that comprise the S\&P500 and Nikkei 225, we find that  89\\%DIF < of all stocks exhibit general leverage effects.
After revision:  Examining 615 stocks that comprise the S\&P500 and Nikkei 225, we find that relaxing the linear assumption to our proposed nonlinear leverage effect function improves predictive performances for 89\\%DIF < of all stocks exhibit general leverage effects.