Empirical Asset Pricing Models Research Articles

A long-short dual-mode knowledge distillation framework for empirical asset pricing models in digital financial networks

The continuous combination of digital network technology and traditional financial services has given birth to digital financial networks, which explore massive economic data under the AI-driven models to achieve intelligent connections among financial institutions, markets, transactions, and instruments. Empirical asset pricing is a challenging task in financial analysis, which has attracted research attention. However, existing studies only focus on tackling the challenges of equity risk premium in the single stock market. Considering multiple economic linkages between the two countries, the transaction history of the US stock market as empirical knowledge is a powerful supplement to improve the prediction of equity risk premium in the China market. In this paper, we aim to fully leverage the prior information in two stock markets for empirical asset pricing models. Due to the rich financial domain knowledge, there may be various characteristic signals that partially overlap in different periods. To address these issues, we propose a framework based on long-short dual-mode knowledge distillation, termed as LSDM-KD, which incorporates US and China stock market models, and a shared characteristic signals model. The method effectively understands the relationships between assets and market behaviour, reducing reliance on expensive correlation databases and professional knowledge. Extensive experiments conducted on US and China stock market datasets demonstrate that our LSDM-KD can significantly improve the performance of empirical asset pricing.

The use of asset growth in empirical asset pricing models

We show that the performance of the new factor models of Hou et al. (2015) and Fama and French (2015) depends crucially on how their investment factor is constructed. Both models use growth in total assets to measure investment. Their ability to price the cross-section of returns decreases significantly when the investment factor is constructed using traditional investment measures, or measures that also account for investment in intangibles. In contrast, we find that factors based on growth in inventory and accounts receivable contain the bulk of the pricing information in the asset growth factor. We show evidence that the superior performance of the asset growth factor seems to be attributable to its ability to capture aggregate shocks to equity financing costs.

Empirical Asset Pricing Models: Evidence from the Chinese Stock Market

This study constructs conventional asset pricing models including the CAPM, the Fama and French three-factor model (FF3 hereafter), the Carhart four-factor model (FFC4 hereafter), and the Fama and French five-factor model (FF5 hereafter). Additionally, a six-factor model (FF5 model augments the Carhart momentum factor) is also constructed and it outperforms other conventional asset pricing models in the Chinese stock market while explaining the returns variation of cross-sectional indices and individual stocks. However, the explanatory power of models varies in explaining indices and individual stocks because of their own specificity. The models can capture most at 69.05% and least at 3.03% of the variation of the return in certain individual stocks. In light of indices, models account for the largest proportion of the variation of the return at 96.83% and the smallest proportion at 85.28%. Moreover, the predictive ability of the six-factor model is confirmed in this study, which implies the validity of constructed factors and the model.

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.

Empirical evaluation of overspecified asset pricing models

Empirical asset pricing models with possibly unnecessary risk factors are increasingly common. Unfortunately, they can yield misleading statistical inferences. Unlike previous studies, we estimate the identified set of SDFs and risk prices compatible with a given model’s asset pricing restrictions. We also propose tests that detect problematic situations with economically meaningless SDFs unrelated to the test assets. Empirically, we estimate linear subspaces of SDFs compatible with popular extensions of the traditional and consumption versions of the CAPM, which are typically two-dimensional. Moreover, we often find that all the SDFs in those linear spaces are uncorrelated with the test assets’ returns.

Empirical Asset Pricing with Functional Factors

Abstract We propose a methodology to use functional factors in empirical asset pricing models. We establish conditions under which it is possible to recover linear beta pricing. The proposed estimation approach allows us to use high-dimensional functional curves, such as the term structure of interest rates or the implied volatility smile, as factors. This framework enables the estimation of functional factor loadings as well as risk premium parameters of factor models. We derive estimation algorithms and establish the asymptotic consistency and normality of the parameter estimates. In an empirical application, we show that the implied variance smile of the S&P500 is a potential pricing factor for momentum-sorted portfolios. In particular, a positive risk premium is earned by the convexity of the implied variance curve.

Digesting anomalies: A q-factor approach for the Thai market

We study the extent to which a q-factor approach explains other cross-sectional factor returns in the Thai market from 2000 to 2019. Univariate statistics of the q-factor premia show that the Thai factors have almost double the statistical and economic significance compared to US factors. While the q-factor model and the Fama-French six-factor model have similar performances in the US, they do not in Thailand. We find that the q-factor model reduces the t-statistics of the alphas for 13 out of 15 anomalies when compared to the six-factor model. Our findings suggest that the q-factor model is a better empirical asset pricing model in Thailand, showing external validity of the model even in an emerging market.

Analysis of Bitcoin prices using market and sentiment variables

AbstractThis paper proposes an empirical model for analysing the dynamics of Bitcoin prices. To do this, we consider a vector error correction model over two overlapping periods: 2010–17 and 2010–19. Price discovery is achieved through the Gonzalo–Granger permanent‐transitory decomposition. The pricing factors are endogenous linear combinations of the S&P 500 index, gold price, a Google search variable associated to Bitcoin and a fear index proxied by the FED Financial Stress Index. Our empirical analysis shows that during the first period, a linear combination of four pricing factors describes the efficient Bitcoin price. The S&P 500 index and Google searches have a positive effect whereas gold prices and the fear index have a negative effect. In contrast, during the second period, the efficient price behaves idiosyncratically and can be only rationalised by individuals' search for information on the cryptocurrency. These findings provide empirical evidence on the presence of a correction in Bitcoin prices during the period 2018–19 uncorrelated to market fundamentals. We also show that standard empirical asset pricing models perform poorly for explaining Bitcoin prices.

Empirical Asset Pricing with Functional Factors

We propose a methodology to use functional factors in empirical asset pricing models. The term structure of interest rates and the implied volatility smile are just two common examples. Functional factors usually incorporate investors risk preferences that could be priced in the cross-section of stock returns. We derive a theory for pricing functional factors that encompasses the usual one for scalar valued factors. We then provide estimation algorithms for betas, risk prices and risk premia and show that they are asymptotically Gaussian and suggest the bootstrap as method to carry out inference. We apply our approach to extract additional information embedded in the implied variance curve. We argue that changes in the shape of the implied variance curve provide information about fear and uncertainty and we distinguish between the two. We show that convexity can be seen as a proxy for volatility uncertainty. This uncertainty could explain the premium earned by momentum strategies, which is seen as pricing anomaly in literature. The empirical results show that the S&P500 3-month implied variance curve is a pricing factor for momentum sorted portfolios and a positive risk premium is earned by the convexity of the implied variance curve.

Exploring Breaks in the Distribution of Stock Returns: Empirical Evidence from Apple Inc.

We implement and test four leading families of unsupervised learning changepoint detection models to investigate the incidence, origins, and effects of breaks in the mean and variance of Apple’s stock returns distribution. These models reveal a sustained incidence of breaks, mainly in the variance. Empirical asset pricing models do not explain this result, even allowing for time-varying coefficients. The breaks occur in response to corporate events, particularly earnings releases and stock-related news. These findings have general implications beyond Apple. Estimation procedures for asset pricing models must address these breaks. Our findings also open event studies to new types of inquiry.

Analysis of Bitcoin Prices Using Market and Sentiment Variables

This paper proposes an empirical model for analyzing the dynamics of Bitcoin prices. To do this, we consider a vector error correction model over two overlapping periods: 2010-2017 and 2010-2019. Price discovery is achieved through the Gonzalo-Granger permanent-transitory decomposition. The pricing factors are endogenous linear combinations of the S&P 500 index, gold price, a Google search variable associated to Bitcoin, and a fear index proxied by the FED Financial Stress Index. Our empirical analysis shows that during the first period a linear combination of four pricing factors describes the efficient Bitcoin price. The S&P 500 index and Google searches have a positive effect whereas gold prices and the fear index have a negative effect. In contrast, during the second period, the efficient price behaves idiosyncratically and can be only rationalized by individuals’ search for information on the cryptocurrency. These findings provide empirical evidence on the presence of a correction in Bitcoin prices during the period 2018-2019 uncorrelated to market fundamentals. We also show that standard empirical asset pricing models perform poorly for explaining Bitcoin prices.

Size and Book-to-Market: Comparing Factor Loadings, Characteristics, Methodologies, and Time Periods

We show new evidence of firm size and book-to-market as priced risk factors in an empirical asset pricing model. A robust size and value premium persists across 1963-1991 and 1992-2017 sub-samples. Characteristics-based models do a better job explaining variation in stock returns than models based on factor loadings. An instrumental variable approach using individual stocks as test assets performs better than one using portfolios. We also present a decile-based measure of size and value with risk premium estimates that are intuitive to interpret. Results have implications for how investors might better understand exposure to systematic risk factors.

An Empirical Asset Pricing Model Accommodating the Sector-Heterogeneity of Risk

Stock returns are generally difficult to explain, as they are comprised of many discrete channels of risk. Empirical asset pricing models (EAPM), such as the Fama-French five-factor model (FF5), have been used to partition these channels across a series of systematic risk factors, such as company size (total market equity), value (book-to-market ratio), investment, and operating profitability. Prior EAPMs only accounted for how such factors contributed to risk at the market-level, ignoring any potential variation across sector. This study developed a sector-heterogenous model (SHM) which directly accounts for this variation by generalizing the Fama-French methodology to sector-subsets of stocks. The results demonstrated that risk is meaningfully heterogenous across sectors for each of the factors in the FF5, with different subgroups of factors being statistically significant within each sector. In a direct comparison of explanatory power, the SHM outperformed the FF5 and improved adjusted R2 by an average of 5% for stocks across all sectors. Several applications of sector-heterogeneity were then demonstrated for stock-picking purposes, including a high-beta portfolio strategy using the SHM-beta which outperformed the S&P 500 in backtesting. This study concludes that meaningful sector-heterogeneity exists in market risk. This information is materially useful to investors.

FIRM SIZE AND STOCK RETURNS: A QUANTITATIVE SURVEY

AbstractFirm size is commonly used in numerous empirical asset pricing models as a determinant of expected stock returns. Yet there is little consensus over the magnitude and stability of the size premium. In fact, some researchers even question whether firm size should be used as a pricing factor. We collect 1746 estimates of the slope coefficients capturing the association between firm size and stock returns reported in 102 published studies and conduct the first meta‐analysis on the size premium. We find evidence of a strong bias toward publishing statistically significant negative slope coefficients. After correcting for the bias, we find that the literature implies a difference in annual stock returns on the smallest and the largest New York Stock Exchange (NYSE) market capitalization quintiles of 1.72%. For the time periods covered in the sampled articles, we find that the size premium was larger in earlier years and that the intensity of publication bias has been decreasing over time.

Explaining Equity Anomalies in Frontier Markets: A Horserace of Factor Pricing Models

ABSTRACT We are the first to compare the explanatory power of the major empirical asset pricing models over equity anomalies in the frontier markets. We replicate over 160 stock market anomalies in 23 frontier countries for years 1996–2017 and evaluate their performance with the factor models. The Carhart’s four-factor model outperforms both the recent Fama and French five-factor model and the q-model by Hou, Xue, and Zhan. Its superiority is driven by the ability to explain the momentum-related anomalies. Inclusion of additional profitability and investment factors lead to no further major improvement in the performance. Nonetheless, none of the models is able to fully explain the abnormal returns on all of the anomaly portfolios.

Using Accounting Earnings and Aggregate Economic Indicators to Estimate Firm-level Systematic Risk

We revisit the literature on using accounting earnings to estimate firm-level systematic risk, using macroeconomic indicators rather than listed-firm indexes to measure aggregate risk. Conventional listed-firm indexes reflect an unrepresentative subset of aggregate assets and thus are expected to substantially mis-measure aggregate and systematic risk (Roll, 1977). That choice dictates using earnings rather than returns to measure firm-level outcomes. Earnings and macroeconomic indicators both are primarily realized annual outcomes and thus are better aligned in time than forward-looking returns for capturing the contemporaneous co-movements that underlie systematic risk. Our macroeconomic indicators are chosen to reflect shocks to aggregate supply and demand, providing a parsimonious model incorporating the two fundamental determinants of aggregate risk. We find that firms' earnings-based sensitivities (betas) to aggregate supply and demand shocks are negatively correlated, and explain the cross-section of returns better than conventional index betas. They are correlated with firm characteristics employed in empirical asset pricing models, and explain one quarter of the explanatory power of those characteristics.

Q‐FACTORS IN EMPIRICAL ASSET PRICING: A REVIEW AND SYNTHESIS

AbstractThe latest development in the asset pricing literature is the emergence of empirical asset pricing models comprising q‐factors (profitability and investment factors) in conjunction with other factors. However, as in the case of the older empirical models, there is scepticism regarding the application of these newer factor models consisting of q‐factors because of the debate surrounding the explanatory power of these empirically inspired asset pricing models. This review attempts to synthesize studies pertaining to the four alternative explanations of the asset pricing models comprising the q‐factors (profitability and investment) – the data snooping hypothesis, the risk‐based explanation, the irrational investor behaviour explanation and the interpretation that suggest that the combination of the risk‐free asset and the factors comprising the model span the mean‐variance efficient tangency portfolio that prices the universe of assets.

Cross-Section of Returns in Frontier Markets: Evidence from the GCC Markets

ABSTRACT Many variables have been used to explain a significant proportion of the cross-section of returns, mainly size and book-to-market. We investigate whether stock returns in the frontier markets of the GCC are driven by the same drivers. Additionally, we test other variables, such as β, leverage, momentum, and the price-to-earnings ratio. We conclude by examining which of the empirical asset pricing models (CAPM or three-factor) best describes returns in the GCC markets.

The nexus of anomalies-stock returns-asset pricing models: The international evidence

We study the international stock returns across Europe, Asia Pacific, North America, US, Japan, Global, and Global excluding US. We find there are value premiums in average stock returns across the regions. There is momentum return in all the regions except for Japan. With the exception of Japan, profitability and investment premiums in average stock returns exist across the regions. Further, the value, momentum, and profitability premiums vary with the firm size and premiums decrease from smaller to bigger stocks excluding Japan. We examine whether empirical asset pricing models capture the value, momentum, profitability, and investment pattern in international average returns, and the integration of the asset prices across the regions. We reject the global integrated pricing approach. The performance of local Carhart four-factor model is relatively better than the variant models in approximating the returns on Japanese size-B/M and size-momentum portfolios. Similarly, the FF five-factor model performs better than the variant models in approximating the returns on Asia Pacific, North American, and Japanese size-profitability portfolios. In addition, FF five-factor model performs relatively better in approximating the returns on European and Japanese size-investment portfolios.

Long-Run Return-Risk Trade-Off of Industry Portfolios and Performance of Maximum Diversification Strategy

Capital mobility may equalize investment opportunities across industries and cause the return-risk trade-offs of industry portfolios to converge. We show that over a long sample period, value-weighted industry portfolios have Sharpe ratios statistically indistinguishable from each other. We further show that industry Sharpe ratios exhibit mean-reversion that can be attributed to cross-industry capital mobility. An investment strategy explicitly based on equalized industry Sharpe ratios significantly outperforms the market. Its performance cannot be explained by the traditional empirical asset pricing models but is readily explained by the q-factor model. Our findings suggest that capital mobility and investment-based asset pricing have important implications on the long-run return-risk tradeoff in the financial market.