Return-Predicting Factors for US Treasuries: On the Similarity of ‘Tents’ and ‘Bats’

15 Pages Posted: 30 May 2014

See all articles by Riccardo Rebonato

Riccardo Rebonato

University of Oxford - Mathematical Institute

Date Written: May 29, 2014


Different authors find optically very different patterns (‘tents’ and ‘bats’) when excess returns from US Treasuries are regressed against forward rates. A separate source of disagreement is whether the recent tent-shaped factor found by Cochrane and Piazzesi is fundamentally different from the slope (in yields) explanatory factor for the time-dependent term premia that has been identified since the early 1990s.

We show that ‘tent’ and ‘bat’ patterns produce predictions of excess returns which are economically indistinguishable, both locally and globally. We also argue that, if the slope (in yield space) is indeed the most important explanatory factor for excess returns, then a simple transformation of the loadings of the forwards rates on the slope factor naturally recovers an approximate tent shape in forward-rate space. However, a transformation from a slope factor in yields to loadings for forward rates does not easily produce a bat pattern. This may provide indirect corroboration to Cochrane and Piazzesi’s (2004) claim that the bat factor is a result of near colinearity for smoothed data, and that the ‘tent’ solution is intrinsically different from the ‘bat’ solution. We do not comment in this paper on the economic and statistic significance of this difference.

Keywords: term premia, excess returns, return-predicting factor

JEL Classification: C10, C40, E40, E43

Suggested Citation

Rebonato, Riccardo, Return-Predicting Factors for US Treasuries: On the Similarity of ‘Tents’ and ‘Bats’ (May 29, 2014). Available at SSRN: or

Riccardo Rebonato (Contact Author)

University of Oxford - Mathematical Institute ( email )

United Kingdom

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