This paper considers diversified portfolios in a benchmark framework. A new limit theorem for the approximation of the benchmark, which is the growth optimal portfolio, is obtained. In a diverse market it is shown that there exist approximations for the benchmark that are independent of model specifications. This leads to a robust modeling, calibration and risk management framework. For diversified portfolios with a large number of securities the limit theorem provides significant reductions in the complexity of quantitative applications as statistical inference and Value at Risk calculations.