Attributing returns and optimising United States swaps portfolios using an intertemporally-consistent and arbitrage-free model of the yield curve

Abstract

This paper uses the volatility-adjusted orthonormalised Laguerre polynomial model of the yield curve (the VAO model) from Krippner (2005), an intertemporally-consistent and arbitrage-free version of the popular Nelson and Siegel (1987) model, to develop a multi-dimensional yield-curve-based risk framework for fixed interest portfolios. The VAO model is also used to identify relative value (i.e. potential excess returns) from the universe of securities that define the yield curve. In combination, these risk and return elements provide an intuitive framework for attributing portfolio returns ex-post, and for optimising portfolios ex-ante. The empirical applications are to six years of daily United States interest rate swap data. The first application shows that the main sources of fixed interest portfolio risk (i.e. unanticipated variability in ex-post returns) are first-order (‘duration’) effects from stochastic shifts in the level and shape of the yield curve; second-order (‘convexity’) effects and other contributions are immaterial. The second application shows that fixed interest portfolios optimised ex-ante using the VAO model risk/relative framework significantly outperform a naive evenly-weighted benchmark over time.