In this paper we advance the idea that optimal risk management under the Basel II Accord will typically require the use of a combination of different models of risk. This idea is illustrated by analyzing the best empirical models of risk for five stock indexes before, during, and after the 2008-09 financial crisis. The data used are the Dow Jones Industrial Average, Financial Times Stock Exchange 100, Nikkei, Hang Seng and Standard and Poor's 500 Composite Index. The primary goal of the exercise is to identify the best models for risk management in each period according to the minimization of average daily capital requirements under the Basel II Accord. It is found that the best risk models can and do vary before, during and after the 2008-09 financial crisis. Moreover, it is found that an aggressive risk management strategy, namely the supremum strategy that combines different models of risk, can result in significant gains in average daily capital requirements, relative to the strategy of using single models, while staying within the limits of the Basel II Accord.