Fama-French Size Research Articles

What Drives the Size and Value Factors?

Abstract I find that approximately 30% of price fluctuations in the Fama-French size and value factors are nonfundamental price pressures driven by correlated fund flows, which generate price movements that revert over time. Is this really demand-based price pressure? I show that the price effects happen exclusively in periods when mutual funds place trades, a fact that is difficult to explain using traditional mechanisms such as unobserved investor preference changes. The estimated price elasticity is also consistent with other studies. Overall, my findings show that a sizable fraction of size and value factor movements do not represent economic risk. (JEL G10, G12, G23, G40)

Fragile Factor Premia

We demonstrate that returns and volatilities of the Fama-French size and value factors are significantly determined by non-fundamental flow-induced trading from actively managed equity mutual funds. Mutual fund flows are largely ignorant about systematic risks. These non-fundamental shifts in demand induce large return heterogeneity within and across the Fama-French size and book-to-market portfolios. We show that aggregate mutual fund flow- induced trades across the size and book-to-market spectrum significantly influence the size and value premia, followed by large subsequent reversals. We also find that the expected volatilities of mutual funds’ flow-induced trades strongly predict future factor volatilities. Our results highlight the importance of non-fundamental demand shocks in determining factor premia and factor volatilities.

Additional tests of multi-index asset pricing models: evidence from an emerging market

ABSTRACTThis study provides comprehensive evidence on the performance of asset pricing models in an emerging market setting. Tests are conducted on portfolios formed based on Fama–MacBeth betas, Fama–French size and book-to-market (B/M) factors, Carhart’s short- and long-term past returns and Pastor and Stambaugh’s liquidity beta. This is one of the first studies to provide emerging market evidence on Pastor and Stambaugh’s liquidity beta measuring a firm’s sensitivity to changing levels of market-wide liquidity. Results of the study are supported by metrics such as confidence intervals around the R2 values and the Gibbons-Ross-Shanken test. Similar to previous findings, the market factor is positive and significant even when models are augmented by the size and B/M factors that are themselves consistently significant and positive. Contrary to evidence from developed markets, contrarian, not momentum, strategies are preferred among the investors, especially for larger firms. Larger firms also are perceived to be less vulnerable when market-wide liquidity decreases.

Additional Tests of Multi-Index Asset Pricing Models: Evidence from an Emerging Market

This study provides comprehensive evidence on the performance of asset pricing models in an emerging market setting. Tests are conducted on portfolios formed based on Fama-MacBeth betas, Fama-French size and book-to-market factors, Carhart’s short- and long-term past returns and Pastor and Stambaugh’s (2003) liquidity beta. This is one of the first studies to provide emerging market evidence on Pastor and Stambaugh’s liquidity beta measuring a firm’s sensitivity to changing levels of market-wide liquidity. Results of the study are supported by metrics such as confidence intervals around the R2 values and the Gibbons-Ross-Shanken (1989) test. Similar to previous findings, the market factor is positive and significant even when models are augmented by the size and book-to-market factors that are themselves consistently significant and positive. Contrary to evidence from developed markets, contrarian, not momentum, strategies are preferred among the investors, especially for larger firms. Larger firms also are perceived to be less vulnerable when market-wide liquidity decreases.

Volatility, distress risk, and the cross-section of portfolio returns

Purpose – This paper aims to examine the nexus between the pricing of market-wide volatility risk and distress risk in the cross-section of portfolio returns for the 1990-2011 time period. The author expands upon prior research by constructing an ex post factor that mimics aggregate volatility risk based on the new VIX index of the Chicago Board Options Exchange, termed FVIX, as well as focuses on volatility risk in crisis versus non-crisis time periods. Design/methodology/approach – The author investigates the relationship between volatility and distress risk using several techniques in the empirical finance literature. Specifically, the author investigates the behavior of correlations between risk factors as well as the correlations between factor loadings when using the Fama and French research portfolios as our test assets for different time periods. Additionally, the author examines the variation in the volatility factor loadings across the size- and value-sorted portfolios and assesses whether augmenting conventional pricing models with a volatility factor leads to a higher goodness-of-fit in pricing the 25 size- and value-sorted portfolios. Findings – The author’s results suggest that factor volatilities are high during periods of market turmoil. In addition, the author presents evidence indicating that a factor mimicking innovation in volatility (based on the new VIX) is correlated with the market and momentum factors, while exhibiting the uncorrelated behavior with respect to the size, value and liquidity factors when using data from 1990 through 2011. In this paper, the author finds that the aggregate volatility factor’s correlation with the market and momentum factors increases during crisis periods. In periods of relative market tranquility, correlations decrease significantly. In examining multivariate factor loadings for the test assets, the results provide no clear pattern with regard to the variation of the volatility loadings across the book-to-market and size dimensions. Furthermore, the author finds that conventional pricing models are comparable to FVIX-augmented pricing models, in terms of goodness-of-fit, when pricing the 25 Fama-French size- and value-sorted portfolios. Additionally, when using the FVIX volatility factor to proxy for aggregate volatility risk, the coefficients are never significant statistically, thus revealing that innovations in aggregate volatility based on the new VIX index do not constitute a priced risk factor in the cross-section of returns. Originality/value – The author’ finding indicates an absence of strong variation of the volatility factor loadings across the Fama-French research portfolios. In particular, the asset pricing results cast doubt on whether a factor mimicking innovations in aggregate volatility based on the new VIX index is priced. In agreement with prior research, the author believes that the inseparability of volatility and jump risk in the VIX can be a possible explanation of the current findings in this paper.

Insights on the global macro-finance interface: Structural sources of risk factor fluctuations and the cross-section of expected stock returns

Abstract This study contributes to the investigation of the macro-finance interface by assessing the economic content and risk-based interpretation of widely employed risk factors in the specification of empirical asset pricing models, i.e., Fama–French size and value, Carhart momentum, as well as the more recent Pastor–Stambaugh liquidity and Adrian–Etula–Muir leverage factors. Strong support for their risk-based interpretation, encompassing evidence on cause, persistence and direction of the size, value and momentum effects, and new insights on the specification of systematic risk, are provided.

Insights on the Global Macro-Finance Interface: Structural Sources of Risk Factors Fluctuations and the Cross-Section of Expected Stock Returns

This study contributes to the investigation of the macro- finance interface by assessing the economic content and risk based interpretation of widely employed risk factors in the specifi cation of empirical asset pricing models, i.e., Fama-French size and value, and Carhart momentum factors, as well as the more recent Pastor-Stambaugh liquidity and Adrian-Etula-Muir leverage factors. Strong support for their risk based interpretation, encompassing evidence on causes, persistence and direction of the size, value and momentum effects, and new insights on the specifi cation of systematic risk, are provided.

Business Cycle Implication of Long-Run Risk Consumption CAPM: Korean Stock Market Evidence

This paper examines long-run consumption based asset pricing models by studying sixteen Fama-French size and book-to-market portfolios in KRX (Korea Exchange) as test assets. In our empirical implementation, we follow both models of Hansen, Heaton and Li (2008) and Parker and Julliard (2005). Hansen, Heaton and Li (2008) used recursive utility framework. The stochastic discount factor for this model depends on the present value of expectations about future consumption growth rates. In the empirical specification for this model, we follow Malloy, Moskowiz and Vissing-Jørgensen (2008). Meanwhile, Parker and Julliard (2005) proposed a model based upon the power utility framework and explicitly considers the consumption adjustment period. Our main results are surprisingly consistent with the results of existing literatures. By assessing both of these models, we find that the significance of the excess returns of the test assets in predicting consumption growth peaks at the horizon of 2.5 years. These empirical results partly proves the existence of long-run consumption risk in Korean economy. We can relate stock returns to long-run consumption risk and business cycle. Specifically, the stochastic discount factor of Parker and Julliard’s model captures the financial crises in the years of 1997 and 2003. Moreover, it catches the business cycle pattern of composite leading index in Korea.

Human Capital and Asset Pricing

From the optimal behavior of arbitrary number of consumer-investors who act as to maximize their life-time utility of consumption and leisure, this paper derives a continuous-time intertemporal asset pricing model with stochastic human capital, leisure, consumption, and investment opportunities. Explicit demand functions for assets are derived and it is shown that, with heterogeneous human capital, the classic fund separation results may no longer hold. The human capital is modeled to include not only its marketed benefits but also its non-market benefits by the use of aggregate labor income and three macro variables in labor statistics: the average weekly employment hours, the unemployment rate, and the labor participation rate. Three flexibility parameters are introduced to explicitly account for the hidden unemployment, the self-employment, and the time spent on job-related activity such as work-commute and so on. Although a formal and comprehensive test is left as a future research task, two pieces of evidence are provided. First, a quick revisit of the equity premium puzzle shows that my model is plausible to explain the observed equity premium with the actual data. Then a preliminary test using returns of the 25 Fama-French size B/M portfolios shows that my model captures about 75% of the total variation in the cross-section returns and that the unemployment rate plays a critical role in explaining the cross-section returns.

Cross-section of Equity Returns Motivated by Fama and French

The market β has been at the core of finance texts for decades. Fama and French (1992) find startling results that decry the importance of the β as a major explanatory variable for stock returns. We continue in that fashion, and attempt to discover other variables that may have an importance in explaining stock returns. We also run the Fama-French size and book-to-market ratios tests on our dataset in order to have a point of comparison for our model.

Tracking down distress risk

This paper shows that exposure to aggregate distress risk is the underlying source of the premiums for the Fama-French size (SMB) and value (HML) factors. Using a unique data set of aggregate business failures of both private and public firms from 1926 to 1997, I build portfolios that track news about future firm failures. These tracking portfolios optimally hedge aggregate distress risk and earn a Capital Asset Pricing Model (CAPM) alpha of approximately −4% a year. Both HML and SMB predict changes in future failure rates. Small stocks have lower returns than large stocks and value stocks have lower returns than growth stocks when the market expects an increase in future failure rates. Finally, a two-factor model with the market and the tracking portfolio for aggregate distress as factors does as well as the Fama-French three-factor model in pricing the 25 size and book-to-market sorted portfolios.

The link between macro-economic factors and style returns

Though the size premium and value premium have been well recognized, the risk-based explanations behind them have not yet been extensively exploited. This article examines the economic nature of the Fama-French size and book-to-price factors and establishes a significant link between the style factors and macro-economic state variables using two different approaches: (i) discrete state analysis, and (ii) threshold regression. The results from these two methods support the same conclusions. Firstly, value and small caps have performed best in periods of higher GDP growth; secondly, there exists a positive relationship between unexpected inflation and the value premium, and a negative relationship between unexpected inflation and the size premium; thirdly, value and smaller stocks perform better when short-term interest rates are low; finally, we find a positive relationship between the return premiums and the term spread.

Realized betas and the cross-section of expected returns

What explains the cross section of expected returns for the 25 size/value Fama–French (FF) portfolios? It is found that modelling time-varying betas is important to explain the cross section of expected returns, as well as to comply with the time series restriction on Jensen-alpha. Support for a modified version of the conditional Jagannathan and Wang's (1996) Capital Asset Pricing Model (CAPM) is found, where implementation is carried out in the realized beta framework proposed in this article. About 63% of the cross-sectional variability of the expected returns for the 25 FF size and value sorted portfolios is then found to be explained by this parsimonious two-variable model.

Tracking Down Distress Risk

This paper shows that exposure to aggregate distress risk is the underlying source of the premiums for the Fama-French size (SMB) and value (HML) factors. Using a unique dataset of aggregate business failures of both private and public firms from 1926 to 1997, I build portfolios that track news about future firm failures. These tracking portfolios optimally hedge aggregate distress risk and earn a CAPM alpha of approximately -4% a year. Both HML and SMB predict changes in future failure rates. Small stocks have lower returns than large stocks and value stocks have lower returns than growth stocks when the market expects an increase in future failure rates. Finally, a two-factor model with the market and the tracking portfolio for aggregate distress as factors does as well as the Fama-French three-factor model in pricing the 25 size and book-to-market sorted portfolios and 30 industry sorted portfolios.

Asset Liquidity, Business Risk, and Beta

Ferguson and Shockley (2003) demonstrate that by utilizing an equity-only proxy for the market index, an empirical single factor capital asset pricing model can lead to anomalies. As most extant studies, they show that information from firms' liabilities-equity structures, per se, leverage and distress, can improve factor pricing models. We show that information about asset structure, per se, firm's asset liquidity (i.e. cash holdings) and business risk, can be as important. We complement Ferguson and Shockley's (2003) leverage based-theory with a liquidity based-theory. We show that since by adding cash to the asset mix, a firm can substantially change the investment opportunity set, asset liquidity and business risk should affect asset prices. We first explore the pertinence of cash holdings theoretically. In our economy, the capital asset pricing model holds in theory. True betas are calculated with respect to aggregate wealth, and proxy betas might not take into account the cash holdings of the firms. We show that the true beta of the firm's assets is higher than a proxy beta of the firm's assets that 'forgets' the riskless assets of the economy. The true stock beta of a firm is also higher than the proxy stock beta that does not take into account the riskless assets held by the firms. By other words, systematic risk is underestimated when the economy's aggregate cash holdings are not recognized as a valuable asset. Our empirical analysis shows that asset liquidity and business risk are priced factors in an extended asset pricing framework of Fama and French. In the cross-section of firms, we regress the observed returns on the erroneous proxy betas and then show that the alpha and beta coefficient estimates from a one-factor model would be different from the CAPM pricing error and market price of risk, respectively. Furthermore, we also show that well-known pricing factors such as size, book-to-market, leverage, and distress could serve as instruments that capture asset liquidity (i.e. cash holdings) and business risk. We show that the asset liquidity or cash holdings and business risk have significant risk premiums. We also show that while our asset liquidity and business risk factors partly correlate with the Fama-French size and book-to-market factors, and the Ferguson-Shockley leverage and distress factors, they still represent uncaptured risk that significantly affects equity betas.

Real Estate Risk in Equity Returns

In this paper, we investigate whether shocks to real estate markets constitute an important state variable in the context of the Intertemporal Capital Asset Pricing Model (ICAPM) and, hence, explain the cross-sectional variation in average returns of the 25 Fama-French portfolios sorted on size and book-to-market. We document that a real estate factor can explain much of the underlying risk inherent in the Fama-French size- and value-factors. In comparison to the Fama-French three-factor model, our alternative two-factor model including the real estate factor next to the market factor performs quite well in pricing the cross section of equity returns. Moreover, we provide evidence that the real estate factor is not captured by other sources of risk applied in the context of the ICAPM, such as shifts in credit market conditions and the stance of monetary policy, aggregate distress risk, and news related to future GDP growth.

Evaluating Asset Pricing Models Using the Second Hansen-Jagannathan Distance

We develop a systematic approach for evaluating asset pricing models based on the second Hansen-Jagannathan distance (HJD), which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our approach includes a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models. While the former can test whether a given model is correctly specified, the latter can compare relative performances of potentially misspecified models. Our methods are more powerful than existing ones in (i) detecting misspecified models that have small pricing errors but are not arbitrage free; and (ii) differentiating models that have similar pricing errors of a given set of test assets. Simulation studies show that our tests have reasonably good finite sample performances for typical sample sizes considered in the literature. Using the Fama-French size and book-to-market portfolios or hedge fund portfolios that exhibit option-like returns, we reach dramatically different conclusions on model performances based on our approach and existing methods.

Noise, Capm and the Size and Value Effects

We model a continuous time one factor economy where stock prices are noisy proxies of the informationally efficient values. The pricing error process is modeled as a mean-reverting process; this gives us a well defined notion of over-pricing and under-pricing in the market, and stocks fluctuates between being over-priced and under-priced. We show that in this economy, cap-weighting is a sub-optimal portfolio strategy. A non-cap-weighted portfolio outperforms a cap-weighted portfolio with the same factor exposure. This is because, in a cap-weighting scheme, portfolio weights are driven by market prices; as such, more weights are allocated to overvalued stocks and less weight to undervalued stocks. Following the same intuition, we show that in the cross-section, large cap stocks tend to underperform small cap stocks and high price-to-book stocks (growth stocks) tend to underperform low price-to-book stocks (value stocks). In this economy, if we proxy the hidden risk factor with the market clearing portfolio and regress stock returns against market returns (a CAPM regression), a non-cap-weighted portfolio exhibits significant alpha! However, when we regress the same non-cap-weighted portfolio against market, size and value, the Fama-French style regression exhibits factor loadings on value and size with insignificant alpha. Clearly, value and size are not risk factors in our economy! Value and size shows up in our regressions because the market portfolio is a poorly constructed proxy for the hidden risk factor. The paper contributes to the anomalies literature by showing that mean-reversion in stock returns and the Fama-French size and value effects are driven by the same market defect - pricing noise! This suggests that models, such as disposition effects and information herding, which can generate stock price over-reaction and therefore mean-reversion in stock prices, can also explain the value and size puzzle.

Factor Multivariate Stochastic Volatility via Wishart Processes

This paper proposes a high dimensional factor multivariate stochastic volatility (MSV) model in which factor covariance matrices are driven by Wishart random processes. The framework allows for unrestricted specification of intertemporal sensitivities, which can capture the persistence in volatilities, kurtosis in returns, and correlation breakdowns and contagion effects in volatilities. The factor structure allows addressing high dimensional setups used in portfolio analysis and risk management, as well as modeling conditional means and conditional variances within the model framework. Owing to the complexity of the model, we perform inference using Markov chain Monte Carlo simulation from the posterior distribution. A simulation study is carried out to demonstrate the efficiency of the estimation algorithm. We illustrate our model on a data set that includes 88 individual equity returns and the two Fama–French size and value factors. With this application, we demonstrate the ability of the model to address high dimensional applications suitable for asset allocation, risk management, and asset pricing.

Modeling and Estimating a Higher Systematic Co-Moment Asset Pricing Model in the Brazilian Stock Market

ABSTRACT Many asset pricing models assume that only the second-order systematic co-moment (CAPM beta) should be priced by investors. However, since asset returns are not normal, investors are also concerned about higher moments and systematic co-moments (co-skewness, co-kurtosis, and so on). This paper examines the determinants of Brazilian stock returns from the CAPM beta, and Fama-French size and value factors, using higher-order systematic co-moments that encompass risks above the traditional CAPM beta. Our results indicate that the CAPM beta, and the Fama-French size and value factors appear to be important for explaining returns in Brazil, and they jointly provide statistically significant explanatory power across almost all the sample return periods. In general, adding a set of higher-order systematic co-moments has moderate explanatory power. RESUMEN. Muchos modelos para determinar el precio patrimonial presuponen que únicamente el co-momento sistémico de segundo orden (CAPM beta) debería tener su precio determinado por los inversores. Sin embargo, como los retornos patrimoniales no son normales, los inversores también están preocupados con los momentos más altos y co-momentos sistemáticos (co-sesgos, co-kurtosis, y así sucesivamente). Este docu-mento examina las determinantes del retorno del capital accionario brasileño del CAPM beta, con factores de tamaño y valor Fama-French, utilizando co-momentos sistemá ticos de orden más alto que agrupan los riesgos sobre el CAPM beta tradicional. Nuestros resultados indican que el CAPM beta y los factores de tamaño y valor Fama-French parecen ser importante para explicar los retornos en el Brasil y, juntos, suministran el poder explanatorio estadísticamente importante a lo largo de todos los períodos de retorno muestra, adicionando en general un conjunto de co-momentos sistemáticos de alto orden tiene un poder explanatorio moderado. RESUMO. Muitos modelos de precificação de ativos assumem que apenas o segundo co-momento (beta do CAPM) deve ser considerado pelos investidores. No entanto, como os retornos dos ativos não são normais, os investidores devem se preocupar também com momentos e co-momentos de ordem superior (co-assimetria, co-curtose etc). Esse artigo analisa os determinantes dos retornos das ações brasileiras a partir do beta do CAPM, dos fatores tamanho e valor de Fama-French eusando co-momentos de ordem superior que abrangem riscos além do tradicional beta do CAPM. Osresultados indicam que o beta do CAPM e os fatores de Fama-French são importantes para explicar os retornos no Brasil, e possuem poder explanatório conjunto estatisticamente significativo em quase todos os períodos. Em geral, os co-momentos de ordem superior possuem poder explanatório moderado.