Estimation of large dimensional conditional factor models in finance

Abstract

This chapter provides an econometric methodology for inference in large-dimensional conditional factor models in finance. Changes in the business cycle and asset characteristics induce time variation in factor loadings and risk premia to be accounted for. The growing trend in the use of disaggregated data for individual securities motivates our focus on methodologies for a large number of assets. The beginning of the chapter outlines the concept of approximate factor structure in the presence of conditional information, and develops an arbitrage pricing theory for large-dimensional factor models in this framework. Then we distinguish between two different cases for inference depending on whether factors are observable or not. We focus on diagnosing model specification, estimating conditional risk premia, and testing asset pricing restrictions under increasing cross-sectional and time series dimensions. At the end of the chapter, we review some of the empirical findings and contrast analysis based on individual stocks and standard sets of portfolios. We also discuss the impact on computing time-varying cost of equity for a firm, and summarize differences between results for developed and emerging markets in an international setting.

Skill, Scale, and Value Creation in the Mutual Fund Industry

“…9 Gagliardini, Ossola, and Scaillet (2016) use a similar sampling scheme for testing the arbitrage pricing theory (see also Gagliardini, Ossola, and Scaillet (2020) for a review of the literature). 10 We can illustrate the concept of asymptotic stationarity with an AR(1) model x t = ρx t−1 + ε t initialized at a given value x 0 = 0 (with |ρ| < 1).…”

When Do Investors Go Green? Evidence From a Time-Varying Asset-Pricing Model

“…Based on this identification we build six portfolios formed on size and greenness, and we define the greenness and transparency factor. Next, we estimate the time-varying greenium assuming a conditional factor model for excess returns under no-arbitrage opportunities (see Gagliardini et al, 2020 for a review on the estimation of large dimensional conditional factor models).…”

Inference for Heteroskedastic PCA with Missing Data

“…Mathematically, the task can often be phrased as constructing valid confidence intervals/regions for both U and S based on the incomplete and corrupted observations {y l,j | (l, j) ∈ Ω}. Noteworthily, this model is frequently studied in econometrics and financial modeling under the name of factor models (Bai and Wang, 2016;Fan et al, 2021a;Fan and Yao, 2017;Gagliardini et al, 2019), and is closely related to the noisy matrix completion problem (except that the current goal is not to reconstruct all missing data) (Candès and Plan, 2010;Candès and Recht, 2009;Chi et al, 2019;Keshavan et al, 2010b).…”