Macro Strikes Back: Term Structure of Risk Premia, with Svetlana Bryzgalova and Christian Julliard
Abstract: We develop a novel framework that sharply identifies the shocks common to financial markets and the macroeconomy, their propagation across horizons, and the term structure of macro risk premia. We find that macro factors’ risk premia are strongly time-varying and countercyclical, with sharply increasing unconditional term structures. Macro risk premia are small and negligible in the short run, yet grow to match the magnitude of equity risk premia at the business cycle horizon—in a nutshell, we reconnect macro to finance. As we show, this pattern is driven by the slow propagation of almost interchangeable priced shocks that capture most of the persistence in macroeconomic variables. Crucially, it is not mechanically due to factor persistence: while GDP, consumption, industrial production, hours worked, and employment exhibit upward-sloping term structures, other similarly persistent factors—such as the VIX or intermediary-based variables—display downward-sloping or flat ones.
Data Uncertainty in Financial Information, with Serhiy Kozak
Abstract: We develop a Bayesian tensor model that addresses three fundamental data challenges in empirical asset pricing: missing observations, infrequent measurements, and inherent noise in financial information. The model combines two ingredients: multiple imputations of firm characteristics and tensor representations jointly modeling time-series and cross-sectional dependencies in the high-dimensional panel. Our method outperforms traditional approaches, delivering higher prediction accuracy and valid confidence intervals for firm characteristic data. Imputing missing and infrequently updated data, although having negligible impacts on factor tangency portfolios, reduces the number of statistically significant alphas in characteristic-managed portfolios. Imputation of all characteristics, including the observed ones, can be used as synthetic data to perform pseudo out-of-sample tests for cross-sectional asset pricing models.
Conditional Asset Pricing with Text-Managed Portfolios, with Jian Feng, Shiyang Huang, and Ran Shi
Abstract: We construct managed portfolios that exploit information extracted from firms' earnings call transcripts and examine their asset pricing implications. Returns on these text-managed portfolios correlate with investor sentiment and predict macroeconomic outcomes. Individual stocks' exposures to the text-managed portfolios explain as much return variation as those to the characteristics-sorted portfolios. Adding earnings call information to firm characteristics increases mean-variance efficiency, though it does not improve stock-level return predictability. Consistent with the insights from Kozak and Nagel (2024) on mean-variance spanning, our results suggest that earnings calls provide information about return covariances beyond what is captured by firm characteristics alone.
Frequency-Dependent Risks in the Factor Zoo
Abstract: I dissect the factor zoo through the lens of frequency-dependent risks. Empirically, several low-frequency principal components constitute a proper benchmark stochastic discount factor (SDF) that achieves near-optimal out-of-sample performance. It effectively explains the cross-section of average anomaly returns not only at the monthly but also at business-cycle frequencies. Moreover, I decompose the SDF into two orthogonal pricing components. The first component is composed of high-frequency principal components. It is serially uncorrelated and relates to discount-rate news, intermediary factors, volatility risk, and investor sentiment. The second component is persistent and captures business-cycle risks related to consumption and GDP growth.
Consumption in Asset Returns, with Svetlana Bryzgalova and Christian Julliard, forthcoming at Journal of Finance
Abstract: Using information in returns we identify the stochastic process of consumption. We find that aggregate consumption reacts over multiple quarters to innovations spanned by financial markets. This persistent component accounts for over a quarter of consumption variation. These shocks command a large and significant risk premium, driving a large share of stocks and a small yet significant fraction of bonds' time series variation. Nevertheless, we find no support for stochastic volatility of consumption driving time-varying risk premia. Finally, an otherwise standard recursive utility model based on our estimated process explains equity premium and risk-free rate puzzles with low risk aversion.
Model Uncertainty in the Cross Section of Stock Returns, with Ran Shi, Journal of Econometrics, available online 22 July 2025, 106066.
Abstract: We develop a transparent Bayesian framework to measure uncertainty in asset pricing models. By assigning a modified class of g-priors to the risk prices of asset pricing factors, our method quantifies the trade-off between mean-variance efficiency and parsimony for asset pricing models to achieve high posterior probabilities. Model uncertainty is defined as the entropy of these model probabilities. We prove the model selection consistency property of our procedure, which is missing from the classic g-priors. Acknowledging the possibility of omitting true asset pricing factors in real applications, we also characterize the maximum degree of contamination that the omitted factors can introduce to our model uncertainty measure. Empirically, we find that model uncertainty escalates during major market events and carries a significantly negative risk premium of approximately half the magnitude of the market. Positive shocks to model uncertainty predict persistent outflows from US equity funds and inflows to Treasury funds.
Bayesian Solutions for the Factor Zoo: We Just Ran Two Quadrillion Models, with Svetlana Bryzgalova and Christian Julliard, Journal of Finance (2023), vol. 78(1), 487-557.
Full replication codes (including posterior draws and usage examples, 4.56GB)
BayesianFactorZoo R package on CRAN
Abstract: We propose a novel framework for analyzing linear asset pricing models: simple, robust, and applicable to high dimensional problems. For a (potentially misspecified) standalone model, it provides reliable price of risk estimates for both tradable and non-tradable factors, and detects those weakly identified. For competing factors and (possibly non-nested) models, the method automatically selects the best specification – if a dominant one exists – or provides a Bayesian model averaging (BMA-SDF), if there is no clear winner. We analyze 2.25 quadrillion models generated by a large set of factors, and find that the BMA-SDF outperforms existing models in- and out-of-sample.