Conditional Dynamics and the Multihorizon Risk-Return Trade-Off

Abstract

We propose testing asset pricing models using multihorizon returns (MHRs). MHRs effectively generate a new set of test assets that is endogenous to the model and that identifies a broad set of possible conditional misspecifications. We apply MHR-based testing to prominent linear factor models and show that these models typically do a poor job of pricing longer-horizon returns, with pricing errors that are similar in magnitude to the risk premiums they were designed to explain. We trace the errors to the conditional factor dynamics. Explicitly incorporating factor timing into the models often makes mispricing worse, thereby posing a challenge for future research.

Pricing Currency Risks

“…Since our focus is on excess returns only, we normalize the unconditional mean of this SDF to one. See Chernov, Lochstoer, and Lundeby (2022) for a recent distillation of these results.…”

“…We further follow Chernov, Lochstoer, and Lundeby (2022) and use multihorizon returns (MHR) on the selected assets to generate additional test assets that are endogenous to the model of the SDF. Specifically, using the projected SDF associated with the UMVE in equation (4), we test whether $$$$\begin{eqnarray*} E(M^*_{t,t+h}R_{t,t+h}^i)=1 \end{eqnarray*}$$$$for a range of horizons h .…”

“…The set of test assets includes the same currency strategies as well as the UMVE portfolio. Chernov, Lochstoer, and Lundeby (2022) show that unconditional MHR pricing allows for testing most, if not all, aspects of conditional model misspecification.…”

“…The UMVE is tradeable in real time, has an SR in excess of one, and, conveniently, can be compared directly to existing trading strategies using standard regression-based tests. We verify that it prices both excess returns on nine individual currencies versus the USD and the nine above-mentioned trading strategies via the unconditional and conditional pricing tests of Gibbons, Ross, and Shanken (1989) and Chernov, Lochstoer, and Lundeby (2022), respectively. We also use the above-mentioned additional strategies with a non-USD base or measurement currency and again fail to reject the estimated UMVE.…”

Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models

“…Naturally, our paper also contributes to the active and growing body of work that critically reevaluates existing findings in the empirical asset pricing literature and develops robust inference methods. Ample empirical evidence shows that most linear factor models are misspecified (e.g., Chernov, Lochstoer, andLundeby (2022), andHe, Huang, and). Following Harvey, Liu, and Zhu (2016), a large body of literature has tried to understand which existing factors (or their combinations) drive the cross section of asset returns.…”