3.1. CHAPTER OVERVIEW

In this chapter, we go through the second part of the stepwise distribution modeling (SDM) approach. The objective is to model the linear dependence, or correlation, between returns on different assets, such as IBM and Microsoft stocks, or on different classes of assets, such as stock indices and Foreign Exchange (FX) rates. Once this is done, we will be able to calculate risk measures on portfolios of securities such as stocks, bonds, and foreign exchange rates.

We start by calculating risk measures such as value at risk for very simple portfolios and discussing how the models of correlation will allow for a quick recalculation of risk measures when the portfolio weights change.

We then present a general model of portfolio risk for large portfolios and consider ways to reduce the problem of dimensionality in such portfolios. Just as the main topic of the previous chapter was modeling the dynamic aspects of variance, the main topic of this chapter is modeling the dynamic aspects of correlation. We consider dynamic correlation models of varying degrees of sophistication, both in terms of their specification and of the information required to calculate them.

3.2. VALUE AT RISK FOR SIMPLE PORTFOLIOS

Value at risk, or VaR, is a simple risk measure that answers the following question: What dollar loss is such that it will only be exceeded p 100% of the time in the next K trading days? The $VaR loss is implicitly defined from the probability of getting...