There is a growing awareness among financial researchers that the traditional models of asset returns cannot capture essential time series properties of the current stock return data. We examine commonly used models, such as the autoregressive integrated moving average (ARIMA) and the autoregressive conditional heteroskedasticity (ARCH) family, and show that these models cannot account for the essential characteristics of the real Istanbul Stock Exchange and Moscow Stock Exchange returns. These models often fail, and when they succeed, they do at the cost of an increasing number of parameters and structural equations. The measures of risk obtained from these models do not reflect the true risk to traders, since they cannot capture all key features of the data. In this paper we offer an alternative framework of analysis based on multifractal models. Compared to the traditional models, the multifractal models we use are very parsimonious and replicate all key features of the data with only three universal parameters. The multifractal models have superior risk evaluation performance. They also produce better forecasts at all scales. The paper also offers a justification of the multifractal models for financial modeling.