B1745
Title: Comparing duration vectors
Authors: Manfred Jaeger-Ambrozewicz - Hochschule für Technik und Wirtschaft (HTW) Berlin (Germany) [presenting]
Abstract: Bond duration measures interest rate risks caused by parallel shifts of the yield curve. Since neither the term spread nor the curvature is constant, duration is a crude one-dimensional measure of risk. Duration vectors generalize duration taking variations of the whole yield curve into account. Instead of a scalar, a vector of dimension $K$ summarizes the exposures to the whole yield curve. Duration vectors are derived from factor representations of the yield curve with $K$ factors $x_j$ and coefficients/loadings $L_j$. Duration is a term weighted sum of cash flow fractions. Duration vectors have for each dimension $j$ additional weights $L_j$. Frequently used methods are special cases: principal components, key rate durations, empirical characteristics (level, spread and curvature), Nelson-Siegel loadings and no-arbitrage model-based loadings. All these models are used in practice. Yet, a systematic comparison is not available. PCA has statistical merits, but the enforced orthogonality complicates interpretability. Empirical characteristics, key rates and Nelson-Siegel-loadings are easy to interpret. Only NA-model-based duration vectors offer an approach consistent with pricing and risk measurement. Tentative quantitative results suggest that differences in risk assessment are rather limited. Hence focusing on interpretability or consistency is not costly.
