Shape Factors and Cross-Sectional Risk

Galluccio and Roncoroni (2006) empirically demonstrate that cross-sectional data provide relevant information when assessing dynamic risk in fixed income markets. We put forward a theoretical framework supporting that finding based on the notion of "shape factors". We devise an econometric procedure to identify shape factors, propose a dynamic model for the yield curve, develop a corresponding arbitrage pricing theory, derive interest rate pricing formulae, and study the analytical properties exhibited by a finite factor restriction of rate dynamics that is cross-sectionally consistent with a family of exponentially weighed polynomials. We also conduct an empirical analysis of cross-sectional risk affecting US swap, Euro bond, and oil markets. Results support the conclusion whereby shape factors outperform the classical yield (resp. price) factors (i.e., level, slope, and convexity) in explaining the underlying fixed income (resp. commodity) market risk. The methodology can in principle be used for understanding the intertemporal dynamics of any cross-sectional data.