7. Covariance and Correlation Models
The objective of this chapter is to model the linear dependence, or correlation, between returns on different assets. Correlation models will enable us to calculate risk measures on portfolios of securities such as stocks, bonds, and foreign exchange rates for many different combinations of portfolio weights. We first present a general model of portfolio risk for large-dimensional portfolios with many assets and then consider ways to reduce the problem of dimensionality. The main challenge of the chapter is modeling the dynamic aspects of correlation. We will consider dynamic correlation models of varying degrees of sophistication, both in terms of their specification and of the information required to calculate ...
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