This paper proposes methods to estimate and compare asset pricing models in settings
with a large number of test assets. Models are specified through a linear stochastic discount
factor (SDF). We propose two regularization schemes to extend the Hansen-Jagannathan
distance to high-dimensional environments. In addition to stabilizing the inversion of the
covariance matrix, the proposed regularizations admit an economic interpretation as relaxing
the exact pricing restrictions, thereby accommodating market frictions.
We derive the asymptotic properties of the SDF parameter estimator under a double
asymptotic framework in which both the cross-sectional and time dimensions grow. These
results allow for inference on whether individual factors are priced. We further develop tests
for comparing competing asset pricing models under misspeci cation, providing a formal
procedure to identify the least misspecified model. The analysis covers both nested and
non-nested specifications.
An empirical application compares 4 models using a dataset of 647 test portfolios.
We develop fast methods for conditional forecasting and structural scenario analysis with high-dimensional Bayesian vector autoregressions (VARs). Our general framework features a factor structure on the reduced-form errors, which enables fast and order-invariant equation-by-equation estimation; suitably identified factors admit a structural interpretation. The scenarios are defined through separate distributional restrictions on observables, structural shocks and idiosyncratic components. The computational cost of our proposed algorithm is cubic only in the number of restrictions, while the dimension of the forecasted system enters linearly. In our application with $33$ macroeconomic and financial variables and ten set-identified structural shocks for the US, we compute counterfactual predictions for oil price scenarios in the context of the 2026 closure of the Strait of Hormuz. The same oil price path is consistent with outcomes ranging from a mostly benign episode to pronounced stagflation, depending on which structural and idiosyncratic shocks are allowed to deliver it.
Niko Hauzenberger, Michael Pfarrhofer· 0 citations
This paper presents a comprehensive review of two foundational portfolio models in modern finance: the Markowitz mean-variance model and the Sharpe single-index model. The study systematically examines their theoretical frameworks, computational requirements, empirical performance, and practical applicability. The Markowitz model, as a model-free optimisation framework, aims to achieve theoretically optimal risk-return trade-offs by fully considering pairwise covariances among assets. However, its high sensitivity to estimation errors and intensive data requirements often limit its empirical usefulness, particularly for large portfolios. In contrast, the index model simplifies covariance estimation by attributing asset return variations to a common market factor, thereby reducing parameter dimensionality and enhancing computational efficiency. Multi-factor extensions further improve explanatory power while maintaining practical feasibility. By reviewing existing literature and empirical evidence, this paper highlights the strengths, limitations, and appropriate application scenarios of both models. The findings provide guidance for investors, portfolio managers, and researchers in selecting or integrating portfolio models to balance theoretical rigor with empirical robustness and operational efficiency.
Portfolio replication, or the construction of a tradable basket of assets to match the risk-return profile of a target benchmark, is fundamentally an ill-posed inverse problem. When restricted to a subset of available assets, classical variance-minimizing models often yield unstable, over-leveraged portfolios highly vulnerable to market shocks. We propose a unified, two-stage methodology rooted in information theory to achieve robust portfolio replication. First, we model the constituent asset returns against target factors, estimating parameters within data-driven empirical bounds via an entropy minimization principle. Second, using the same entropic approach, we determine the optimal weight replication. In both cases we use an entropy function of the Fermi-Dirac type defined directly on sets of constraints of the inverse problem. We validate this Entropic Factor Model (EFM) against standard Ordinary Least Squares (OLS) across five numerical experiments, including standard equity tracking, multi-asset synthesis, and severe stress-test scenarios. Empirical results demonstrate that the EFM consistently outperforms OLS in terms of annualized turnover and net-of-fees returns. Crucially, during the COVID-19 market crash and under severe idiosyncratic data corruption, the entropic framework acts as a probabilistic ``circuit breaker", defensively reducing capital allocation to compromised assets and providing a highly robust, risk-averse solution for generalized portfolio replication.
This paper introduces a novel methodology for analyzing anomalies in conditional asset pricing models with time-varying risk exposures and premia. Our approach extends the conventional two-pass methodology to include both ordinary and weighted least-squares estimation in a conditional setting. We establish closed-form standard errors to statistically dissect anomalies, including a version robust to global misspecification. We introduce a novel R
2
criterion to quantify the joint contribution of large anomaly sets in explaining cross-sectional stock return variations. Our analysis highlights the significant impact of anomalies during economic and financial crises, linking them closely with market conditions.
This paper was accepted by Kay Giesecke, finance.
Funding: This project has received funding from the postdoctoral fellowships programme Beatriu de Pinos, funded by the Secretary of Universities and Research (Government of Catalonia) and by the Horizon 2020 programme of research and innovation of the European Union under the [Marie Sktodowska-Curie Grant Agreement 801370].
Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2024.06968 .
Valentina Raponi, P. Zaffaroni· Management Sciences· 0 citations
In this article, we introduce the new community-contributed commands xtdhazard and cfbinout. The former implements the own-differences instrumental-variables estimator proposed by Farbmacher and Tauchmann (2023, Econometric Reviews 42: 635-654) for dealing with time-invariant unobserved heterogeneity in the discrete-time hazard model. cfbinout is called by xtdhazard if a nonlinear discrete-time hazard model is specified. cfbinout can also be used as a standalone command that generalizes ivprobit, twostep by allowing discrete endogenous regressors and link functions that are different from the normal link, specifically logit and complementary log-log. In terms of the underlying econometric theory, cfbinout is guided by Wooldridge (2015, Journal of Human Resources 50: 420-445). We illustrate the use of xtdhazard in an empirical example.
H. Tauchmann, Elena Yurkevich· The Stata Journal· 0 citations
We introduce the nonlinear arbitrage correction (NAC), the residual that renders a linear benchmark model arbitrage-free while preserving the law of one price. The price of NAC captures the marginal Sharpe ratio increase consistent with no-arbitrage and upper-bounds the constrained Hansen–Jagannathan distance. Using four decades of international equity, currency, and factor returns, NAC is strongly countercyclical, peaking during crises when linear models turn negative. The implied Sharpe ratio increase reaches 0.3, underscoring its economic relevance. While linear models perform well on average, they fail in distressed states, underpricing nonlinear payoffs. Incorporating NAC restores positivity and stabilizes pricing across regimes. (JEL G11, G12, G15)
Mirela Sandulescu, P. Schneider· The Review of financial stud...· 0 citations
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