5.1. CHAPTER OVERVIEW

The main objectives of this chapter are twofold. First, we want to introduce methods for forecasting the distribution of portfolio returns, which are very popular in practice but which we argue have some key flaws, namely the so-called historical simulation methods. Second, we want to consider ways in which the daily risk models we have constructed in previous chapters can be used for risk forecasting at multiple horizons. While most risk models are estimated on daily data and therefore automatically forecast 1 day ahead, risk managers are typically interested in the risk across longer horizons as well.

The chapter is organized as follows:

1. We introduce the historical simulation (HS) method and discuss its pros and particularly its cons.

2. We consider an extension of HS, often referred to as weighted historical simulation (WHS).

3. We show how Monte Carlo simulation (MCS) can be used to generate multiday forecasts from the conditional daily risk models constructed in Chapters 2 through 4.

4. We argue the advantages of combining the conditional variance and correlation models from Chapters 2 and 3 with a modified version of HS, which we refer to as filtered historical simulation (FHS). FHS can be used to generate daily as well as multiday forecasts from daily models. The FHS method has been found to perform well, and it can be seen as a model-free alternative to the model-based conditional distribution methods suggested in Chapter 4.

5.2. HISTORICAL SIMULATION (HS)

Before defining exactly what we mean...