Beta,size, book-to-market equity and returns: A study based on UK data

This paper examines the role of beta, size and book-to-market equity as competing risk measurements in explaining the cross-sectional returns of UK securities for the period July 1980 through June 2000. The methodology of [Fama, E., French, K., 1992. The cross-section of expected stock returns. Journal of Finance 47, 427–467] and [Pettengill, G., Sundaram, S., Mathur, I., 1995. The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis 30, 101–116] is adopted. Results show that, when adopting the methodology of [Pettengill, G., Sundaram, S., Mathur, I., 1995. The conditional relation between beta and returns. Journal of Financial and Quantitative Analysis 30, 101–116], where data is segmented between up and down markets, a significant relationship is found between beta and returns even in the presence of size and book-to-market equity. Size is not found to be a significant risk variable, whereas book-to-market equity is found to be priced by the market and is thus a significant determinant of security returns. This is the case irrespective of the methodology adopted.     

Security returns, beta, size, and book-to-market equity: evidence from the Shanghai A-share market

The main purpose of this paper is to explore the cross-sectional relationship between security returns and beta, size and book-to-market equity in the Shanghai A-share market. This study takes place during the period January 1997–December 2006. The methodology of Fama and French (J Finance 51:55–84, 1992) and Pettengill et al. (J Financial Quant Anal 30:101–116, 1995) is adopted. The Results show no evidence of an unconditional relationship between beta and returns. However, a conditional relationship is found when the data is split into up and down markets. The relationship holds even in the presence of size and book-to-market equity. Both size and book-to-market equity is found to be priced by the market and thereby regarded as significant determinants of security returns.     

The relationship between size,book-to-market equity ratio,earnings–price ratio,and return for the Hong Kong stock market

In this paper, we investigate the relation between stock returns and β, size (ME), leverage, book-to-market equity ratio, and earnings–price ratio (E/P) in Hong Kong stock market using the Fama and French (FF) [J. Finance 47 (1992) 427] approach. FF find that two variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with β, size, leverage, book-to-market equity, and E/P ratios. In this paper, similar to previous studies in Hong Kong and US stock markets, we find that β is unable to explain the average monthly returns on stocks continuously listed in Hong Kong Stock Exchange for the period July 1984–June 1997. But three of the variables, size, book-to-market equity, and E/P ratios, seem able to capture the cross-sectional variation in average monthly returns over the period. The other two variables, book leverage and market, are also able to capture the cross-sectional variation in average monthly returns. But their effects seem to be dominated by size, book-to-market equity, and E/P ratios, and considered to be redundant in explaining average returns when size, book-to-market equity, and E/P ratios are also considered. The results are consistent across subperiods, across months, and across size groups. These suggest that the results are not driven by extreme observations or abnormal return behavior in some of the months or by size groups.     

Size,value and momentum in stock returns: evidence from India

This paper examines the effects of size, value and momentum on the cross-sectional relation between expected returns and risk in the Indian stock market. We find that the conditional Carhart four-factor model empirically describes the variation of cross-section of return better than the unconditional model. When size, book-to-market and momentum effects are controlled in the conditional model, the positive relation of market beta, book-to-market and momentum with expected returns remains economically and statistically significant. However, this evidence is found to be subject to characteristics of test portfolios. The expected returns are sensitive to changes in predictive macroeconomic variables.     

Liquidity and asset pricing: Evidence from the Hong Kong stock market

This study investigates the role of liquidity in pricing stock returns in the Hong Kong stock market. Our results show that liquidity is an important factor for pricing returns in Hong Kong after taking well-documented asset pricing factors into consideration. The results are robust to adding portfolio residuals and higher moment factor in the factor models. The results are also robust to seasonality, and conditional-market tests. We also compare alternative factor models and find that the liquidity four-factor model (market excess return, size, book-to-market ratio, and liquidity) is the best model to explain stock returns in the Hong Kong stock market, while the momentum factor is not found to be priced.     

Tests of the Relations Among Marketwide Factors,Firm-Specific Variables,and Stock Returns Using a Conditional Asset Pricing Model

In this article we generalize Harvey's (1989) empirical specification of conditional asset pricing models to allow for both time-varying covariances between stock returns and marketwide factors and time-varying reward-to-covariabilities. The model is then applied to examine the effects of firm size and book-to-market equity ratios. We find that the traditional asset pricing model with commonly used factors can only explain a small portion of the stock returns predicted by firm size and book-to-market equity ratios. The results indicate that allowing time-varying covariances and time-varying reward-to-covariabilities does little to salvage the traditional asset pricing models.     

The risk–return relations in the Singapore stock market

This paper examines the risk–return relations in the Singapore stock market for the period April 1986 to December 1998. Though beta is significantly related to realized returns, the explanatory power is low. Adding other stock characteristics such as skewness and kurtosis provides limited incremental benefits. However, when a conditional framework based on up and down markets is introduced, the explanatory power increases more than 100 times and there is a significant positive (negative) relation between beta and returns when the market excess returns are positive (negative). The same relation applies when unsystematic risk, total risk and kurtosis are added separately to the beta–return relation during up and down markets with increased explanatory power. Our results indicate that other stock characteristics in addition to beta are also important in pricing risky assets and investors do not hold diversified portfolios. Our results are also checked and compared with another conditional model with time-varying betas conditional on a set of economic variables.     

The Cross-Section of Stock Returns on The Shanghai Stock Exchange

This study explores the cross-sectional stock return behavior on the A-share market of the Shanghai Stock Exchange (SSE), which is segmented from world's other equity markets. We estimate the effects of beta, firm size, book-to-market equity ratio and a variable unique to the Chinese stock markets, the proportion of firm's floating (tradable) equity over total equity on SSE stocks over the period 1993–2002. We find that smaller firms and value stocks perform better. Systematic risk is negatively significant in down markets. The proportion of floating equity has no direct effect on stock returns. JEL Classification: G14, G15     

Cross-sectional analysis of Swedish stock returns with time-varying beta: the Swedish stock market 1983–96

This paper analyses the ability of beta and other factors, like firm size and book-to-market, to explain cross‐sectional variation in average stock returns on the Swedish stock market for the period 1983–96. We use a bivariate GARCH(1,1) process to estimate time-varying betas for asset returns. The estimated variances of these betas, derived from a Taylor series approximation, are used for correcting errors in variables. An extreme bound analysis is utilized for testing the sensitivity of the estimated coefficients to changes in the set of included explanatory variables.
Our results show that the estimated conditional beta is a more accurate measure of the true market beta than the beta estimated by OLS. The coefficient for beta is not significantly different from zero, while the variables book-to-market and leverage have significant coefficients, and the latter coefficients are also robust to model specification. Excluding the down turn 1990–92 from the sample shows that the significance of the risk premium for leverage might be considered as an industry effect during this extreme period. Finally, we find a close dependence between the risk premium for beta and that for size and book-to-market. The omission of each of these variables may cause statistical bias in the estimated coefficient for beta.     

Macroeconomic risk and the cross-section of stock returns

We develop a conditional version of the consumption capital asset pricing model (CCAPM) using the conditioning variable from the cointegrating relation among macroeconomic variables (dividend yield, term spread, default spread, and short-term interest rate). Our conditioning variable has a strong power to predict market excess returns in the presence of competing predictive variables. In addition, our conditional CCAPM performs approximately as well as Fama and French’s (1993) three-factor model in explaining the cross-section of the Fama and French 25 size and book-to-market sorted portfolios. Our specification shows that value stocks are riskier than growth stocks in bad times, supporting the risk-based story.     

The Cross-Section of Expected Stock Returns

Two easily measured variables, size and book-to-market equity, combine to capture the cross-sectional variation in average stock returns associated with market β, size, leverage, book-to-market equity, and earnings-price ratios. Moreover, when the tests allow for variation in β that is unrelated to size, the relation between market β and average return is flat, even when β is the only explanatory variable.     

The conditional relation between dispersion and return

The main goal of this paper is to examine the conditional pricing effect of return dispersion on the cross section of returns. We observe a systematic conditional relation between dispersion and return even after controlling for market, size and book-to-market factors. However, we find that return dispersion risk is asymmetrically priced with a significantly positive premium observed during periods of large market gains only. The findings are found to be robust to alternative conditional specifications of market returns, suggesting asymmetric pricing effect of the return dispersion factor. We provide alternative explanations for the systematic risk captured by the return dispersion factor and discuss implications for portfolio management and corporate decisions.     

THE EFFECT OF SIZE,BOOK-TO-MARKET EQUITY,PRIOR RETURNS,AND BETA ON STOCK RETURNS: JANUARY VERSUS THE REMAINDER OF THE YEAR

Size and book-to-market equity are shown to transcend beta in explaining stock returns. One possible explanation of the book-to-market equity effect is overreaction. We investigate the effect of size, book-to-market equity, prior returns, and beta on stock returns. We find significant reversals in January consistent with overreaction. We find a strong positive relation between returns and prior returns for February through December. Both patterns are distinct from either a size or book-to-market equity effect. Book-to-market equity is significantly related to returns, with some evidence of a stronger effect in January.     

Default Risk and Equity Returns: Evidence from the Taiwan Equities Market

Studies of risk and return characteristics of different portfolios have recently gained enormous attention. Differing from past studies, this paper uses a compound option model to build the proxy of default risk and evaluate the relationship between default risk effect and equity returns. The primary goal of this paper is to evaluate the relationship among default risk, size, book-to-market, and equity returns, using data drawn from the Taiwan equities market, and to also examine whether size and book-to-market are proxies for default risk. The results show that the effects of size and book-to-market exist in different default portfolios when default risks are controlled. If size or book-to-market is controlled, there are no default effects. In the regression analysis, when default risk is included in Fama and French’s Three Factor Model, it shows that size, book-to-market and default risk have significant influence on equity returns and default risk is a systematic risk. Default risk is also more powerful in explaining returns when the compound option model is adopted for estimating default risks.     

Using Expectations to Test Asset Pricing Models

Asset pricing models generate predictions relating assets' expected rates of return and their risk attributes. Most tests of these models have employed realized rates of return as a proxy for expected return. We use analysts' expected rates of return to examine the relation between these expectations and firm attributes. By assuming that analysts' expectations are unbiased estimates of market-wide expected rates of return, we can circumvent the use of realized rates of return and provide evidence on the predictions emanating from traditional asset pricing models. We find a positive, robust relation between expected return and market beta and a negative relation between expected return and firm size, consistent with the notion that these are risk factors. We do not find that high book-to-market firms are expected to earn higher returns than low book-to-market firms, inconsistent with the notion that book-to-market is a risk factor.     

Do zero-cost portfolios have the ability to predict economic growth? Evidence from Hong Kong, South Korea and Taiwan

In this paper we investigate the relationship between growth in future Gross Domestic Product (GDP) and Industrial Production (IDP) and the performance of SMB (small stocks minus big stocks) and HML (High book-to-market stocks minus low book-to-market stocks) portfolios for equities listed in Hong Kong, South Korea and Taiwan.We find evidence to suggest that: (a) the excess market return is positively related to future GDP or IDP growth in South Korea and Taiwan; (b) contrary to most European markets, Australia, Japan and the US, future economic growth is in general significantly negatively related to SMB in Hong Kong and South Korea; and, (c) a negative relationship between future economic growth and HML for Hong Kong. Our results cast doubt if SMB and HML portfolios are positive risk factors in the Fama and French (Fama, E. F., and French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33, 3-56) three-factor asset pricing model for Hong Kong, South Korea and Taiwan.     

The Risk and Predictability of International Equity Returns

We investigate predictability in national equity market returns,and its relation to global economic risks. We show how to consistentlyestimate the fraction of the predictable variation that is capturedby an asset pricing model for the expected returns. We use amodel in which conditional betas of the national equity marketsdepend on local information variables, while global risk premiadepend on global variables. We examine single- and multiple-betamodels, using monthly data for 1970 to 1989. The models capturemuch of the predictability for many countries. Most of thisis related to time variation in the global risk premia.     

Can stochastic discount factor models explain the cross-section of equity returns?

We propose a multivariate test of the capital asset pricing model (C-CAPM) of the cross-sectional variation in equity returns in which we compare cross-sectional variation in equity returns to the cross-sectional variation in their conditional covariance with stochastic discount factors. We use a multivariate generalized heteroskedasticity in mean model to estimate 25 portfolios that are formed on size and the book-to-market ratio. Each portfolio is allowed to have its own no-arbitrage condition. We find that although the conditional covariances of returns with consumption exhibit negative variation across size, they do not vary across the book-to-market ratio. Thus, C-CAPM can capture the size effect, but not the value effect. The fit is, however, improved by allowing the coefficients on the consumption covariances to be different. The value effect appears to be associated with the book-to-market ratio as well as size. On its own the book-to-market ratio does not generate additional information about average returns to C-CAPM. A possible explanation for these findings is that both small and low book-to-market ratio firms are expected to have higher rates of growth.     

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.     

Conditional Equity Premium and Aggregate Corporate Investment

We document a strong negative relation between aggregate corporate investment and conditional equity premium estimated from direct stock market risk measures. Consistent with the investment-based asset pricing model, the comovement with conditional equity premium fully accounts for aggregate investment's market return predictive power. Similarly, conditional equity premium is a significant determinant of classic Tobin's q measure, although q has much weaker explanatory power for aggregate investment possibly because of its measurement errors. Moreover, the positive relation between aggregate investment and investor sentiment documented in previous studies reflects the fact that both variables correlate closely with conditional equity premium.