Conditional Dynamics and the Multi-Horizon Risk-Return Trade-Off
NBER Working Paper No. 25361
We propose testing asset-pricing models using multi-horizon returns (MHR). A correctly specified stochastic discount factor prices the cross-section of returns at all horizons. We show that MHR are informative about the model's conditional implications. Different from typical conditioning variables, MHR-implied conditioning variables are endogenous to the model. Further, MHR are economically important as they explicitly test the model's ability to take present values of streams of risky cash flows that accrue at different horizons, a core concept in financial economics. 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. We find that strong and, surprisingly, pro-cyclical time-variation in the pricing kernel's factor loadings and implied prices of risk is needed to jointly price returns at multiple horizons in these models.
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Document Object Identifier (DOI): 10.3386/w25361