This research first gives a review of risk measures and risk capital allocation, along with the important property of coherency, and the relationships between different coherent risk measures.Secondly, relative accuracy measures are used as model-based criteria to study whether or not bias adjustment by various bootstrap techniques could improve estimates of the expected shortfall (ES) as a risk measure.Thirdly, different tests for backtesting Value-at-Risk (VaR) and ES are investigated as data-based criteria of evaluating risk models.Fourthly, multivariate framework is developed for estimating (conditional) ES and ES risk contributions (ESC), as a principle of capital allocation. Finally, an empirical study of estimating ES and ESC with backtesting is carried out for historical data from Russell Indices.