One approach to handling the risk arising from groups of highly correlated market variables is principal components analysis. This is a standard statistical tool with many applications in risk management. It takes historical data on movements in the market variables and attempts to define a set of components or factors that explain the movements.

The approach is best illustrated with an example. The market variables we will consider are swap rates with maturities 1 year, 2 years 3 years, 4 years, 5 years, 7 years, 10 years, and 30 years. Tables 22.7 and 22.8 show results produced for these market variables using 2,780 daily observations between 2000 and 2011. The first column in Table 22.7 shows the maturities ...

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