A Robust Analysis of the Risk-Structure of Equilibrium Term Structures of Bond Yields

30 Pages Posted: 18 Mar 2012

See all articles by Anh Le

Anh Le

Penn State University Smeal College of Business

Kenneth J. Singleton

Stanford University - Graduate School of Business

Date Written: March 6, 2012

Abstract

Many prominent equilibrium term structure models (ETSMs) in which the state of the economy zt follows an affine process imply that the variation in expected excess returns on bond portfolio positions is fully spanned by the set of conditional variances ςt2 of zt. We show that these two assumptions alone – spanning of excess returns by the variances ςt2 of affine processes zt – are sufficient to econometrically identify the quantities of risk that span risk premiums from the term structure of bond yields. Using this result we derive maximum likelihood estimates of ςt2 and evaluate the goodness-of-fit of the family of affine ETSMs that imply this tight link between premiums and quantities of risk. These assessments are fully robust to the values of the parameters governing preferences and the evolution of the state zt, and to whether or not the economy is arbitrage free. Our findings suggest that, to be consistent with U.S. macroeconomic and Treasury yield data, affine ETSMs should have the features that: the fundamental sources of risks, including consumption growth, inflation, and yield volatilities are driven by distinct economic shocks; consumption growth risk alone is unlikely to fully account for the predictability of excess returns on bonds; and inflation risk, and not long-run risks or variation in risk premiums arising from habit-based preferences, is likely to be the dominant risk underlying risk premiums in U.S. Treasury markets.

Suggested Citation

Le, Anh and Singleton, Kenneth J., A Robust Analysis of the Risk-Structure of Equilibrium Term Structures of Bond Yields (March 6, 2012). AFA 2013 San Diego Meetings Paper. Available at SSRN: https://ssrn.com/abstract=2024222 or http://dx.doi.org/10.2139/ssrn.2024222

Anh Le (Contact Author)

Penn State University Smeal College of Business ( email )

Business Building
University Park, PA 16801
United States

Kenneth J. Singleton

Stanford University - Graduate School of Business ( email )

Knight Management Center
655 Knight Way
Stanford, CA 94305-7298
United States
650-723-5753 (Phone)

HOME PAGE: http://www.stanford.edu/~kenneths

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