8.1. CHAPTER OVERVIEW

The first seven chapters covered various methods for constructing risk management models. Along the way we also considered several ways of diagnostic checking. For example, in Chapter 1 we looked at the autocorrelations of returns to see if the assumption of a constant mean was valid. In Chapter 2 we looked at the autocorrelation function of returns squared divided by the time varying variance to assess if we had modeled the variance dynamics properly. We also ran variance regressions to assess the forecasting performance of the suggested GARCH models. In Chapter 4 we studied the so-called QQ plots to see if the distribution we assumed for standardized returns captured the extreme observations in the sample. In Chapter 5 we looked at the reaction of various risk models to an extreme event such as the 1987 stock market crash. Finally, in Chapter 6 we illustrated option pricing model misspecification in terms of implied volatility smiles and smirks.

The objective in this chapter is to consider the ex ante risk measure forecasts from the model and compare it with the ex post realized portfolio return. The risk measure forecast could take the form of a value at risk (VaR), an expected shortfall (ES), the shape of the entire return distribution, or perhaps the shape of the left tail of the distribution only. We want to be able to backtest any of these risk measures of interest. The backtest procedures developed in this chapter can be seen as a final...