Daily asset returns exhibit two key statistical properties. Price changes are not autocorrelated, but the absolute values of changes are strongly autocorrelated. Nonlinear processes can generate this type of behavior; linear processes cannot. Additively nonlinear processes are consistent with the view that expected returns are time varying. Although much effort has been applied to modeling expected returns, there has been little evidence to support the view that time-varying expected returns can account for the strong nonlinearity in the observed returns data. Multiplicatively nonlinear models are consistent with the view that expected volatilities are time varying. Evidence from price changes, as well as options' implied volatilities, show that volatility is time varying and mean reverting. In fact, multiplicatively nonlinear models have been able to explain a great deal of the nonlinearity in asset returns. Thus, future volatility can be forecast, even though the direction of price changes is difficult to forecast. This finding has important implications for short-term financial risk management.