Principal Component Analysis of the UK Term Structure & Its Application to Immunisation Strategies

Abstract

This study will consist of a fully comprehensive analysis of UK term structure of interest rates using the well known statistical model called the Principal Component Analysis (PCA) and it is considered as the main drive for a successful immunization strategy for the time period concerned. Term structure of interest rates from year 1992 to 2003 has been taken as the sample data set and it s very important for carrying out detailed analysis due to the reason that in the beginning of the time period, the term structure has undergone major variations as a result of macro economic changes. Principal Component Analysis will describe the behaviour of correlated random variables in terms of a small number of uncorrelated “principal components”, that means these complex movements of the term structure will be explained by the first three factors the “level”, “steepness” and “curvature”. The core expectation of this study is to analyze the immunization strategies based on the PC based and Moment based durations and to identify the method with a better approximated return to the portfolio. The results concluded that the PC based duration provides a comparatively better approximated return than the Moment based duration strategy. The study found that 99 percent of the total variation of the term structure can be explained by the first three factors and the first factor is significantly constant throughout the time period except the first few years. In addition to the above, it has been found that the standard deviation and the eigenvalue of the first PC are negatively correlated.