Arbitrage-Free Models of Stocks and Bonds

33 Pages Posted: 11 Jan 2014

Date Written: December 1, 2013


A small but ambitious literature uses affine arbitrage-free models to estimate jointly U.S. Treasury term premiums and the term structure of equity risk premiums. Within this approach, this paper identifies the parameter restrictions that are consistent with a simple dividend discount model, extends the cross-section to Germany and France, averages across multiple observable-factor and market prices of risk specifications, and considers alternative samples for parameter estimation. The results produce intuitive trajectories for both sets of premiums given standard samples starting from July 1993. However, the decomposition of nominal U.S. Treasury yields, but not long-run equity risk premiums, is sensitive to data beyond 2008, which raises some questions about the net effects of unconventional monetary policy measures. Nonetheless, the rotation from sharp inversion during the financial crisis to an upward-sloping term structure of equity risk premiums more recently, with modest readings at the front end, is not inconsistent with some net moderation in required compensation for equity risk in the United States.

Keywords: equity risk premium, Treasury term premium, affine arbitrage-free models

JEL Classification: G10, G12, G13, G15

Suggested Citation

Durham, J. Benson, Arbitrage-Free Models of Stocks and Bonds (December 1, 2013). FRB of New York Staff Report No. 656. Available at SSRN: or

J. Benson Durham (Contact Author)

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