In this paper we present a framework for backtesting all currently popular risk measurement methods for quantifying market risk (including value-at-risk and expected shortfall) using the functional delta method. Estimation risk can be taken explicitly into account. Based on a simulation study we provide evidence that tests for expected shortfall with acceptable low levels have a better performance than tests for value-at-risk in realistic financial sample sizes. We propose a way to determine multiplication factors, and find that the resulting regulatory capital scheme using expected shortfall compares favorably to the current Basel Accord backtesting scheme.