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Testing asset pricing factor models: An out-of-sample perspective

资产定价因子模型检验:样本外视角

We develop the Sample Splitting Alpha (SSA) test, a formal out-of-sample (OOS) test for evaluating whether an asset pricing factor model satisfies the zero-alpha restriction in high-dimensional settings. The test uses sample splitting to separate portfolio weight estimation from model evaluation and ridge regularization to stabilize the portfolio problem when the number of test assets is large. We show that each single split SSA statistic is asymptotically Gaussian under…

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High dimensional alpha test for linear factor pricing model with Lq-norm

高维线性因子定价模型的 Lq 范数 alpha 检验

We consider testing zero pricing errors in high-dimensional linear factor pricing models. Existing methods are mainly based on either an $L_2$ statistic, which is effective under dense alternatives, or an $L_\infty$ statistic, which is powerful under very sparse alternatives. To bridge these two regimes, we develop a class of $L_q$-based tests for finite $q$, including the practically useful $L_4$ and $L_6$ cases. We show that larger $q$ leads to greater sensitivity to…

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High-Dimensional Sliced Inverse Kendall’s Tau Estimation for Heavy-Tailed Data

面向重尾数据的高维切片逆 Kendall 秩相关估计

Sufficient dimension reduction is an important branch of statistical learning, which performs an optimal projection of covariates under a supervised learning framework. Most of the existing sufficient dimension reduction algorithms require strict restrictions on the distribution of models, making them sensitive to heavy-tailed predictors and outliers. In this article, we propose a novel method called Sliced Inverse Kendall’s tau Estimation (SIKE) designed for analyzing…

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Finite-State Markov-Chain Approximations: A Hidden Markov Approach

有限状态马尔可夫链近似:一种隐马尔可夫方法

This paper proposes a novel finite-state Markov chain approximation method for Markov processes with continuous support, providing both an optimal grid and a transition probability matrix. The method can be used for multivariate processes and processes with time-varying components. It is based on minimizing the information loss between a Hidden Markov Model and the true data-generating process. We provide sufficient conditions under which this information loss can be made…

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A general randomized test for Alpha

资产定价模型中 Alpha 的一般随机化检验

We propose a methodology to test for the null hypothesis that the alphas of a panel of asset returns are jointly equal to zero in a linear factor pricing model with observable and tradable factors — that is, the null of “zero alpha”. The test is based on equation-by-equation estimation, using a randomized version of the estimated alphas, which only requires rates of convergence. The distinct features of the proposed methodology are that it does not require the estimation of…

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Testing Alphas in Linear Factor Models: A Portfolio Approach

线性因子模型的 Alpha 检验:投资组合方法

This paper develops a test for evaluating linear factor models in high-dimensional settings. The proposed Maximum Random Sparse Portfolio (MRSP) test generates L random sparse portfolios, each obtained through K random draws, and then selects the hardest-to-price portfolio to assess factor model performance. By evaluating multiple randomly generated sparse portfolios, the MRSP test retains a portfolio-based economic interpretation while avoiding reliance on a single…

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Coordinated testing for identification failure and correct model specification

识别失败与模型设定正确性的协调检验

We develop a specification test for GMM and Minimum Distance (MD) inference that is: (i) robust to weak identification; (ii) easy to implement and broadly applicable; and (iii) has meaningful power. Our specification test is based on a conditional inference approach: information about the existence of strongly identified directions in the parameter space is exploited to define a data-dependent critical value, which, in turn, increases the power of the resulting specification…

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Specification LASSO and a Flexible Characteristics-Based Asset Pricing Model

设定 LASSO 与灵活的特征型资产定价模型

This paper studies a partially linear semiparametric additive model that allows for interactions among variables in high-dimensional settings. We propose the Specification LASSO (S-LASSO), a two-step method that integrates LASSO and Adaptive Group LASSO to simultaneously perform variable selection and model specification. Theoretically, we establish that S-LASSO possesses oracle properties in terms of selection consistency and asymptotic normality. Monte Carlo simulations…

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Testing for common latent factors across two short panels

检验两个短面板中的共同潜在因子

This paper develops inference tools for the number of common latent factors across two large cross-sectional panels observed over a short time span (large n, small T). Our approach builds on a general test for determining the dimension of the intersection of two matrix column spaces, where each matrix is estimated with noise. The proposed test statistics are based on canonical correlations, and their asymptotic distributions are derived via perturbation methods. An empirical…

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Heterogeneous predictability on mutual fund alphas: A sparse clustering GMM approach

共同基金 alpha 的异质可预测性:稀疏聚类 GMM 方法

Mutual fund managers' skills, measured by risk-adjusted alphas, are predictable using fund characteristics identified by machine learning (e.g., Kaniel et al., 2023, JFE; DeMiguel et al., 2023, JFE). However, alpha's predictive power varies across funds and periods, with most funds exhibiting negligible alphas. To model this heterogeneous predictability, this paper introduces Sparse Clustering GMM, a nonparametric approach for uncovering latent fund groups. SCGMM clusters…

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Bayesian evaluation of mutual fund performance with non-random missing data: Application to the Chinese market

非随机缺失数据下的共同基金绩效贝叶斯评估:中国市场应用

This paper studies mutual fund performance evaluation, where non-random missing data is an important issue. Ignoring sample selection issues can lead to biased parameter estimates and invalid performance evaluation. Therefore, we propose a novel Beta selection model to characterize this non-random missingness mechanism. We can significantly reduce the bias in alpha estimates, by introducing our Beta selection mechanism into the Noise-Reduced Alpha (NRA) model of Harvey and…

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Structural breaks, model uncertainty and factor selection

结构突变、模型不确定性与因子选择

This paper addresses the non-standard problem of detecting multiple structural breaks when the data-generating model in each regime is uncertain, with an application to factor selection in empirical asset pricing. Detection is based on the marginal likelihood of break points, obtained by a novel integration over all possible pairings of models across regimes, from all possible models within regimes. The optimal break points maximize this marginal likelihood. Applying this…

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Model uncertainty in the cross-section of stock returns

股票收益横截面中的模型不确定性

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…

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STABILITY OF LINEAR MODELS UNDER TEMPORAL AGGREGATION

时间聚合下线性模型的稳定性

Linear factor models dominate the field of empirical asset pricing and are largely considered a successful framework even though testing for model adequacy is uncommon in empirical research. This article develops a probabilistic argument under the assumption that return data are generated by a multivariate Lévy process and shows that linear factor models are asymptotically adequate as the return frequency declines. Rate-of-convergence results are provided assuming finite or…

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Jump Contagion among Stock Market Indices: Evidence from Option Markets

股票指数间的跳跃传染:来自期权市场的证据

We analyze the contagious propagation of jumps among international stock market indices, using a rich panel of high-frequency stock and options data ( 692,892 option contracts) over the period 2006–2015. We propose a bivariate option pricing model designed to allow for time and space amplification of jumps in option markets. We develop a semi-parametric estimation procedure, which employs a continuum of moment conditions in GMM with implied states and non-parametric…

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Estimating Multiple Structural Breaks in Large Panels With Unobserved Heterogeneity

含未观测异质性的大型面板多重结构突变估计

This article proposes a novel algorithm to identify potentially multiple breaks in linear panel data models, while the slope coefficients can have individual heterogeneity and the cross-sectional dimension is allowed to diverge jointly with the time span. The algorithm adopts a shrinkage penalty to detect breaks, and delivers a consistent estimator for the number of breaks and fraction-consistent estimators for break dates. In the presence of latent grouped heterogeneity, we…

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Estimating a conditional density ratio model for asset returns and option demand

资产收益与期权需求的条件密度比模型估计

Option-implied risk-neutral densities are widely used for constructing forward-looking risk measures. Meanwhile, risk aversion introduces a multiplicative pricing kernel between the risk-neutral and true conditional densities of the underlying asset’s return. This paper proposes a simple local estimator of the pricing kernel based on inverse density weighting. We characterize the asymptotic bias and variance of the estimator and its multiplicatively corrected density…

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Estimation of Out-of-Sample Sharpe Ratio for High Dimensional Portfolio Optimization

高维投资组合优化中的样本外夏普比率估计

Portfolio optimization aims at constructing a realistic portfolio with significant out-of-sample performance, which is typically measured by the out-of-sample Sharpe ratio. However, due to in-sample optimism, it is inappropriate to use the in-sample estimated covariance to evaluate the out-of-sample Sharpe, especially in the high dimensional settings. In this paper, we propose a novel method to estimate the out-of-sample Sharpe ratio using only in-sample data, based on…

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Estimating State Price Densities Implied by American Options

估计美式期权隐含的状态价格密度

We propose a new method to estimate state price densities implicit in American-style options. The method involves estimating the parameters of a Gauss-Hermite series expansion and solving a sequence of recursive equations for the early exercise premium. The resulting estimator can capture sudden shifts in density that may occur during financial crises or in response to significant policy events. It also provides an estimate of the early exercise premium that is of…

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Robust mutual fund selection with false discovery rate control

控制错误发现率的稳健共同基金筛选

In this article, we address the challenge of identifying well-performing mutual funds among a large pool of candidates, utilizing the linear factor pricing model. Assuming observable factors with a weak correlation structure for the idiosyncratic error, we propose a spatial-sign based multiple testing procedure (SS-BH). When latent factors are present, we first extract them using the elliptical principle component method (He et al. 2022) and then propose a factor-adjusted…

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Risk premia from the cross-section of individual assets

从个体资产横截面估计风险溢价

We propose the continuous updating estimator (CUE) for estimating ex-post risk premia from large cross-sections of individual asset returns over limited time periods. We analyze its properties while also allowing for an unknown number of unobserved factors. The CUE then provides an estimator of its, so-called, pseudo-true value, i . e . , the risk premia on the observed factors without assuming that they comprise all priced factors. We develop size-correct procedures for…

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Misspecification-robust bootstrap t -test for irrelevant factor in linear stochastic discount factor models

线性随机贴现因子模型中无关因子的误设稳健自助 t 检验

This paper examines the applicability of the bootstrap approach to test for irrelevant risk factors that are potentially useless in misspecified linear stochastic discount factor (SDF) models. In the literature, the misspecification-robust inference with useless factors is known to give rise to nonstandard limiting distributions bounded stochastically to compute critical values. We show how and to what extent the wild bootstrap yields a more accurate approximation of the…

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Generalized Autoregressive Conditional Betas: Longitudinal Feedback in Multifactor Asset Pricing

广义自回归条件贝塔:多因子资产定价中的纵向反馈

We propose a new class of observation-driven models, Generalized Autoregressive Conditional Betas, which describe the joint dynamics of time-varying slopes in a system of conditionally heteroskedastic simultaneous multiple regressions. The model accommodates large dimensions, parametric longitudinal restrictions, exogenous variables, and the coexistence of constant and time-varying slopes. It also introduces new mechanisms for the transmission of shocks, namely, beta…

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A Nonparametric Bayesian Estimator of Copula Density with Applications to Financial Market

Copula 密度的非参数贝叶斯估计及金融市场应用

We propose a nonparametric Bayesian estimator of copula density based on the Logistic Gaussian Process density estimation method. A Gaussian process prior with flexible mean and covariance functions is placed on the underlying latent function. To avoid the typical boundary issues in copula density estimation, a transformation approach is adopted, allowing the latent process to be defined on an unrestricted support and then back-transformed to obtain the posterior copula…

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