Empirical Factor Models Research Articles

Intangible Capital in Factor Models

The transition from a traditional manufacturing-based economy to a knowledge- and service-based economy over recent decades resulted in a considerable rise in intangible capital, most of which is not reported on companies’ balance sheets. As a result, balance sheet-based valuation ratios, investment measures, and other firm characteristics that do not incorporate off-balance sheet (OBS) intangible capital suffer from significant measurement error problems. We incorporate a new measure of OBS intangible capital into firm characteristics, such as book to market, investment, and profitability, to address these measurement errors. These OBS intangible adjustments improve the performance of the Fama–French three- and five-factor models and the q-factor model, especially during recent decades. We further find that the value factor is no longer redundant in these empirical factor models. This paper was accepted by Lukas Schmid, finance. Funding: The authors are grateful for financial support from the 2019 EDHEC Scientific Beta “Advanced ESG & Factor Investing” Research Chair. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.01261 .

How Robust are Empirical Factor Models to the Choice of Breakpoints?

We comprehensively investigate the robustness of well-known factor models to altered factor formation breakpoints. Deviating from the standard 30th and 70th percentile selection, we use an extensive set of anomaly test portfolios to uncover two main findings: First, there is a trade-off between specification and diversification. More centered breakpoints tend to result in less (idiosyncratic) risk. More extreme sorts lead to greater exposure to the underlying anomalies and thus to higher average returns. Second, the models are robust to varying degrees. Hou et al.’s model [2015, Digesting Anomalies: An Investment Approach, Review of Financial Studies 28, 650–705] is much more sensitive to changes in breakpoints than the Fama–French models.

Assessing the Use of Gold as a Zero-Beta Asset in Empirical Asset Pricing: Application to the US Equity Market

This paper examines the use of the return on gold instead of treasury bills in empirical asset pricing models for the US equity market. It builds upon previous research on the safe-haven, hedging, and zero-beta characteristics of gold in developed markets and the close relationship between interest rates, stock, and gold returns. In particular, we extend this research by showing that using gold as a zero-beta asset helps to improve the time-series performance of asset pricing models when pricing US equities and industries between 1981 and 2015. The performance of gold zero-beta models is also compared with traditional empirical factor models using the 1-month Treasury bill rate as the risk-free rate. Our results indicate that using gold as a zero-beta asset leads to higher R-squared values, lower Sharpe ratios of alphas, and fewer significant pricing errors in the time-series analysis. Similarly, the pricing of small stock and industry portfolios is improved. In cross-section, we also find improved results, with fewer cross-sectional pricing errors and more economically meaningful pricing of risk factors. We also find that a zero-beta gold factor constructed to be orthogonal to the Carhart four factors is significant in cross-section and helps to improve factor model performance on momentum portfolios. Furthermore, the Fama–French three- and five-factor asset pricing models and the Carhart model are all improved by these means, particularly on test assets which have been poorly priced by the traditional versions. Our results have salient implications for policymakers, governments, central bank rate-setting decisions, and investors.

Factorial Structure of the Parent-Reported Version of the Inventory of Callous-Unemotional Traits Among Belgian Children: A Theory-Based Model.

The factorial structure of the Inventory of Callous-Unemotional traits (ICU) is still under debate in the current literature and the published models are predominantly based on the empirical results of the statistical analyses rather than on a strong theoretical background. Aimed at overcoming these limits, the current study examined a factorial structure initiated by a theoretical framework for the parent-version of the ICU, based on a community sample of Belgian children aged 3–9 (N = 437; M age = 5.59; 54.7% boys). Further, the current study investigated measurement invariance across age and gender, and the external validity of this structure. Confirmatory factor analysis (CFA) indicated that empirical factor models from the current literature demonstrated a relatively poor fit to the data. Alternative models were built based on theory, specifically criteria from the DSM-V specifier “with limited prosocial emotions.” CFA supported an 18-item second order model with three first order factors (Lack of conscience, Unconcern about performance, Lack of emotional expression), a second order latent factor (General dimension of CU traits) and a methodological factor encompassing negatively worded items. Results supported measurement invariance across child gender, and to a lesser extent across age. As expected, the general dimension correlated with measures of aggressive behavior, attention problems, internalizing behavior and empathy. The Lack of emotional expression subfactor showed a different pattern of associations in comparison to the two other subfactors. The implications of these findings are discussed, specifically in relation to the DSM-V LPE specifier.

Intangible Capital in Factor Models

Fully expensing intangible investments has potential distorting effects on factor investing based on book-to-market, investment, and profitability. Incorporating intangible investment/capital into the conceptual frameworks and empirical factor models of Fama and French (1993, 2015) and Hou, Xue and Zhang (2015) highlights the importance of separating tangible from intangible investments and addressing the effects of intangible investment on profitability and other valuation metrics. We show that existing empirical factor models grossly understate the relative importance of the value factor. Incorporating intangibles significantly improves these factor models, especially over recent decades during which intangible investments have become increasingly important.

Factor Forestry: Pruning using an Economic Chainsaw

Hundreds of anomalies, factors, or characteristic portfolios have been discovered whose risk-return spread is not explained by benchmark empirical factor models. Each of these is a potential candidate as a factor in such models. Efforts to narrow down this plethora of candidates to a parsimonious set has mainly relied on econometric and statistical tools. Standard textbooks, however, emphasize that factors in models proxy for the marginal utility of aggregate consumption growth. Imposing the economic restrictions that this link implies, we find that only 10-20 per cent of this forest of factors impound news about future consumption growth, the low-frequency risk of consumption growth or its extreme tails i.e. bad times. Interestingly, new factors used in models that perform better than the benchmark models do better in passing economically motivated hurdles. Our results imply that imposing theoretical restrictions, on this forest of potential factors can impose discipline, in the search for an ex-post MV efficient portfolios. In addition, applying an economic chainsaw to yet to be discovered anomalies could curb the growth of this forest.

How Robust are Empirical Factor Models to the Choice of Breakpoints?

How Robust are Empirical Factor Models to the Choice of Breakpoints?

Firm Characteristics and Empirical Factor Models: A Model Mining Experiment

Abstract In a novel model mining experiment, we data mine hundreds of randomly constructed three-factor models and find that many outperform well-known models from the literature, including those with four and five factors. The results provide compelling evidence that the threshold of factor model success needs to be raised. Confidence intervals for model rankings, derived from a bootstrap simulation, offer new insights into the consistency of a model’s pricing ability. Rankings for some well-known models are unusually volatile, which have wider confidence intervals than that of most of the random factor models.

Betting Against Other Betas

Using several multi-factor models, I find strong against beta'' effects - flat relations between betas and expected returns - for most non-market factors in US and international stock markets. Arbitrage portfolios'' designed to profit from these effects earn average returns similar to those of the factors, with substantially reduced risk. Betas are persistent, indicating that the factor models successfully capture important dimensions of co-variation in returns. Previously-proposed explanations for the betting against market beta effect do not explain these results. These findings raise questions about the economic content of existing empirical factor models and the co-variance-based expected return paradigm.

Carry trades and commodity risk factors

This paper investigates the importance of commodity prices for the returns of currency carry trade portfolios. We adopt a recently developed empirical factor model to capture commodity commonalities and heterogeneity. Agricultural material and metal price risk factors are found to have explanatory power on the cross-section of currency returns, while commodity common and oil factors do not. Although stock market risk is strongly linked to currencies in developed countries, the agricultural material factor is more important for emerging currencies compared to the stock market factor. This suggests that emerging currencies are somewhat segmented from a common financial market shock.

Term Structure Models During the Global Financial Crisis: A Parsimonious Text Mining Approach

This work develops and estimates a three-factor term structure model with explicit sentiment factors in a period including the global financial crisis, where market confidence was said to erode considerably. It utilizes a large text data of real time, relatively high-frequency market news and takes account of the difficulties in incorporating market sentiment into the models. To the best of our knowledge, this is the first attempt to use this category of data in term-structure models. Although market sentiment or market confidence is often regarded as an important driver of asset markets, it is not explicitly incorporated in traditional empirical factor models for daily yield curve data because they are unobservable. To overcome this problem, we use a text mining approach to generate observable variables which are driven by otherwise unobservable sentiment factors. Then, applying the Monte Carlo filter as a filtering method in a state space Bayesian filtering approach, we estimate the dynamic stochastic structure of these latent factors from observable variables driven by these latent variables. As a result, the three-factor model with text mining is able to distinguish (1) a spread-steepening factor which is driven by pessimists’ view and explaining the spreads related to ultra-long term yields from (2) a spread-flattening factor which is driven by optimists’ view and influencing the long and medium term spreads. Also, the three-factor model with text mining has better fitting to the observed yields than the model without text mining. Moreover, we collect market participants’ views about specific spreads in the term structure and find that the movement of the identified sentiment factors are consistent with the market participants’ views, and thus market sentiment.

Carry Trades and Commodity Risk Factors

This paper investigates the importance of commodity prices for the returns of currency carry trade portfolios. We adopt a recently developed empirical factor model to capture commodity commonalities and heterogeneity. Agricultural material and metal price risk factors are found to have explanatory power on the cross-section of currency returns, while commodity common and oil factors do not. Although stock market risk is strongly linked to currencies in developed countries, the agricultural material factor is more important for emerging currencies compared to the stock market factor. This suggests that emerging currencies are somewhat segmented from a common financial market shock.

Term Structure Models During the Global Financial Crisis: A Parsimonious Text Mining Approach

This work develops and estimates a three-factor term structure model with explicit sentiment factors in a period including the global financial crisis, where market confidence was said to erode considerably. It utilizes a large text data of real time, relatively high-frequency market news and takes account of the difficulties in incorporating market sentiment into the models. To the best of our knowledge, this is the first attempt to use this category of data in term-structure models. Although market sentiment or market confidence is often regarded as an important driver of asset markets, it is not explicitly incorporated in traditional empirical factor models for daily yield curve data because they are unobservable. To overcome this problem, we use a text mining approach to generate observable variables which are driven by otherwise unobservable sentiment factors. Then, applying the Monte Carlo filter as a filtering method in a state space Bayesian filtering approach, we estimate the dynamic stochastic structure of these latent factors from observable variables driven by these latent variables. As a result, the three-factor model with text mining is able to distinguish (1) a spread-steepening factor which is driven by pessimists’ view and explaining the spreads related to ultra-long term yields from (2) a spread-flattening factor which is driven by optimists’ view and influencing the long and medium term spreads. Also, the three-factor model with text mining has better fitting to the observed yields than the model without text mining. Moreover, we collect market participants’ views about specific spreads in the term structure and find that the movement of the identified sentiment factors are consistent with the market participants’ views, and thus market sentiment.

Expected Investment Growth and the Cross Section of Stock Returns

Expected investment growth (EIG) is a strong predictor for cross-sectional stock returns. Between July 1953 and December 2015 in the US, an investment strategy that takes a long position in firms with high EIG and a short position in firms with low EIG generates an average annual return of more than 20%, with a Sharpe ratio of 1.01. This return predictability holds both in subperiods and in different subsamples of firms, as well as in all other G7 countries. Leading empirical factor models including CAPM, Fama-French three-factor model, Carhart four-factor model, and the recent Hou, Xue, and Zhang four-factor model and Fama and French five-factor model all fail to fully capture the profitability of this investment strategy. Further analyses suggest that EIG is closely related to financial distress risk, especially at a short horizon up to one year, and is a better predictor of stock returns than failure probability from Campbell, Hilscher, and Szilagyi (2008). We provide supporting evidence for both risk-based explanation and behavioral explanation for this large EIG premium.

Macroeconomic Fundamentals, Expected Returns and the Pricing of Anomaly Portfolios

Recent research has identified more than three hundred factors that have statistically significant prices of risk in asset pricing tests. This evidence is disconcerting and more parsimonious factor pricing models are required. Our work contributes to the effort of reducing this “zoo of factors”. We propose a set of empirical factors that mimic macroeconomic sources of risk in the economy. Our three factor model does well in explaining the cross-section of a number of common benchmark portfolios and other ‘anomaly’ spreads relative to standard empirical factor models.

Firm Characteristics and Empirical Factor Models: A Data-Mining Experiment

A three-factor model using the standardized-unexpected-earnings and cashflow-to-price factors explains 15 well-known asset pricing anomalies. Our data-mining experiment provides a backdrop against which such claims can be evaluated. We construct three-factor linear pricing models that match return spreads associated with as many as 15 out of 27 commonly used firm characteristics over the 1971-2011 sample. We form target assets by sorting firms into ten portfolios on each of the chosen characteristics and form candidate pricing factors as long-short positions in the extreme decile portfolios. Our analysis exhausts all possible 351 three-factor models, consisting of two characteristic-based factors in addition to the market portfolio. 65% of the examined factor models match a larger fraction of the target return cross-sections than the CAPM or the Fama-French three-factor model. We find that the relative performance of the complete set of three-factor models is highly sensitive to the sample choice and the factor construction methodology. Our results highlight the challenges of evaluating empirical factor models.

Firm Characteristics and Empirical Factor Models: A Data-Mining Experiment

A three-factor model using the standardized-unexpected-earnings and cashflow-to-price factors explains 15 well-known asset pricing anomalies. Our data-mining experiment provides a backdrop against which such claims can be evaluated. We construct three-factor linear pricing models that match return spreads associated with as many as 15 out of 27 commonly used firm characteristics over the 1971-2011 sample. We form target assets by sorting firms into ten portfolios on each of the chosen characteristics and form candidate pricing factors as long-short positions in the extreme decile portfolios. Our analysis exhausts all possible 351 three-factor models, consisting of two characteristic-based factors in addition to the market portfolio. 65% of the examined factor models match a larger fraction of the target return cross-sections than the CAPM or the Fama-French three-factor model. We find that the relative performance of the complete set of three-factor models is highly sensitive to the sample choice and the factor construction methodology. Our results highlight the challenges of evaluating empirical factor models.