Estimate Value-at-Risk (VaR) and then use backtesting to measure the accuracy of the VaR calculation.

Perform estimation and backtesting of Expected Shortfall models.

Fit tail data to the Generalized Pareto distribution by maximum likelihood estimation.

Compute the expected shortfall (ES) for a portfolio of equity positions using three different methods. ES is a market risk metric that supplements a calculated value-at-risk (VaR) value. For an example of ES computation on a single market index, see Expected Shortfall Estimation and Backtesting. The 95% VaR represents the threshold loss amount that is only violated about 5% of the time, while ES is an estimate of the average amount of money the portfolio loses on the 5% of days when the VaR is violated.

Estimate the value-at-risk (VaR) for a portfolio of equity positions using two parametric methods, normal VaR and exponentially weighted moving average (EWMA) VaR. Parametric VaR methods, also known as variance-covariance methods when the returns are normally distributed, assume a closed form for the return distribution of the portfolio. Using a parametric model simplifies the problem of VaR calculation to that of estimating the parameters of the distribution. Parametric methods are often contrasted with nonparametric approaches, such as Monte Carlo VaR or historical VaR, that do not assume an analytic formula for the return distribution of the portfolio. For a similar example of VaR calculation on a single index, see Value-at-Risk Estimation and Backtesting.