Research

Working Papers

Double Machine Learning Inference for Conditional Latent Factors

(with Patrick Gagliardini) Formerly titled “Extracting Statistical Factors When Betas Are Time-Varying.” Updated version coming soon!

Presented at EFA 2020, MFA 2020, CFE-CMStatistics 2019, EEA & ESAM 2019, SoFiE 2019, University of Geneva, Università della Svizzera italiana (USI Lugano)

This paper deals with identification and asymptotically normal inference in conditional latent factor models for large, unbalanced panels of asset returns. The setting is nonparametric regarding the time-variation of risk exposures. For a general class of parameters of interest relevant for asset pricing with latent factors, we show identification via a semiparametric moment condition involving an unknown vector function containing the conditional moments of portfolio returns given (high-dimensional) predictors. We use a doubly-robust moment restriction for serially dependent data and establish feasible asymptotic normality of the estimators. For a panel of monthly returns of U.S. stocks, the number of conditional factors is large and counter-cyclical, and the spanning of the latent space involves dynamically e.g. leverage, time-series reversal and liquidity on top of Fama-French factors. The implied SDF outperforms competitors in pricing benchmark universes of test assets. Conditioning information plays an important role when estimating moments of conditional risk premia.

Transaction Costs and the Stochastic Discount Factor

(with Daniele Bianchi and Teng Jiao)

We show that transaction costs fundamentally reshape the stochastic discount factor (SDF) by determining which characteristics matter in equilibrium. Using deep neural networks, we incorporate transaction costs directly into robust SDF estimation rather than treating them as post-optimization adjustments or arbitrary investment constraints. Transaction cost-aware SDFs yield substantially higher net Sharpe ratios and superior cross-sectional pricing through endogenous portfolio reallocation: increased diversification, reduced turnover, and lower exposure to costly high-turnover characteristics. These effects persist across sample configurations, market regimes, neural network specifications, and alternative definitions of transaction costs, demonstrating that trading frictions are structural determinants of equilibrium asset prices.

Conditional Latent Factor Models Via Econometrics-Based Neural Networks

(Job Market Paper) Updated version coming soon!

Presented at: ESSEC Business School, Duke University, University of Bristol, UC Berkeley (Haas), SoFiE Webinar for Graduate Students, EWMES 2022, CFE-CMStatistics 2021, SFI Research Days 2021, Shanghai University of Finance and Economics, Shandong University, Università della Svizzera italiana (USI Lugano)

I develop a hybrid methodology that incorporates an econometric identification strategy into artificial neural networks when studying conditional latent factor models. The time-varying betas are assumed to be unknown functions of numerous firm characteristics, and the statistical factors are population cross-sectional OLS estimators for given beta values. Hence, identifying betas and factors boils down to identifying only the function of betas, which is equivalent to solving a constrained optimization problem. For estimation, I construct neural networks customized to solve the constrained optimization problem, which gives a feasible non-parametric estimator for the function of betas. Empirically, I conduct my analysis on a large unbalanced panel of monthly data on US individual stocks with around 30, 000 firms, 516 months, and 94 characteristics. I find that 1) the hybrid method outperforms the benchmark econometric method and the neural networks method in terms of explaining out-of-sample return variation, 2) betas are highly non-linear in firm characteristics, 3) two conditional factors explain over 95% variation of the factor space, and 4) hybrid methods with literature-based characteristics (e.g., book-to-market ratio) outperform ones with COMPUSTAT raw features (e.g., book value and market value), emphasizing the value of academic knowledge from an angle of Man vs. Machine.