Introduction: handling multiple risk factors Methodological introduction

Traditional interest rate risk management focuses on duration and duration management.
In other words, it assumes that only parallel yield curve shifts are important.
In practice, of course, non-parallel shifts in the yield curve often occur, and represent
a significant source of risk. What is the most efficient way to manage non-parallel
interest rate risk?
This chapter is mainly devoted to an exposition of principal component analysis, a
statistical technique that attempts to provide a foundation for measuring non-parallel
yield curve risk, by identifying the ‘most important’ kinds of yield curve shift that
occur empirically. The analysis turns out to be remarkably successful. It gives a
clear justification for the use of duration as the primary measure of interest rate
risk, and it also suggests how one may design ‘optimal’ measures of non-parallel risk.
Principal component analysis is a popular tool, not only in theoretical studies but
also in practical risk management applications. We discuss such applications at the
end of the chapter. However, it is first important to understand that principal
component analysis has limitations, and should not be applied blindly. In particular,
it is important to distinguish between results that are economically meaningful and
those that are statistical artefacts without economic significance.
There are two ways to determine whether the results of a statistical analysis are
meaningful. The first is to see whether they are consistent with theoretical results;
the Appendix gives a sketch of this approach. The second is simply to carry out as
much exploratory data analysis as possible, with different data sets and different
historical time periods, to screen out those findings which are really robust. This
chapter contains many examples.
In presenting the results, our exposition will rely mainly on graphs rather than
tables and statistics. This is not because rigorous statistical criteria are unnecessary
– in fact, they are very important. However, in the exploratory phase of any empirical
study it is critical to get a good feel for the results first, since statistics can easily mislead. The initial goal is to gain insight; and visual presentation of the results can
convey the important findings most clearly, in a non-technical form.
It is strongly suggested that, after finishing this chapter, readers should experiment
with the data themselves. Extensive hands-on experience is the only way to avoid
the pitfalls inherent in any empirical analysis.