Good News,Bad News,Volatility, and Betas

We investigate the conditional covariances of stock returns using bivariate exponential ARCH (EGARCH) models. These models allow market volatility, portfolio-specific volatility, and beta to respond asymmetrically to positive and negative market and portfolio returns, i.e., “leverage” effects. Using monthly data, we find strong evidence of conditional heteroskedasticity in both market and non-market components of returns, and weaker evidence of time-varying conditional betas. Surprisingly while leverage effects appear strong in the market component of volatility, they are absent in conditional betas and weak and/or inconsistent in nonmarket sources of risk.     

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.     

Estimation of conditional asset pricing models with integrated variables in the beta specification

We introduce a methodology which deals with possibly integrated variables in the specification of the betas of conditional asset pricing models. In such a case, any model which is directly derived by a polynomial approximation of the functional form of the conditional beta will inherit a nonstationary right hand side. Our approach uses the cointegrating relationships between the integrated variables in order to maintain the stationarity of the right hand side of the estimated model, thus, avoiding the issues that arise in the case of an unbalanced regression. We present an example where our methodology is applied to the returns of funds-of-funds which are based on the Morningstar mutual fund ranking system. The results provide evidence that the residuals of possible cointegrating relationships between integrated variables in the specification of the conditional betas may reveal significant information concerning the dynamics of the betas.     

Bias in estimating the systematic risk of extreme performers: Implications for financial analysis, the leverage effect, and long-run reversals

We show how bias can arise systematically in the beta estimates of extreme performers when long-run return reversals are present and partly, or wholly, due to sign changes in unanticipated factor realizations. Our evidence is consistent with this bias being responsible for the large shifts in the beta estimates of extreme performers, more so than the leverage effect, which has been the predominant explanation in prior literature. Bias in these contemporaneous realized betas, estimated with the same returns that are to be risk adjusted, arises due to the general problem of “overconditioning,” where betas are estimated conditional on information that is not yet known. Several methods for conditioning betas on out-of-sample returns are evaluated and found to be lacking, although some offer improvement under certain circumstances. We also show evidence of this bias in the Fama-French Three-factor loadings of extreme performers. Our findings indicate not only that previous studies of long-run reversals understate contrarian profits but that bias is prevalent in the OLS beta estimates of extreme performers, and this has implications for estimating the cost of capital and measuring long-run performance. We offer recommendations for identifying when this bias is likely present, as well as general methods to correct for it.     

Oil and stock market activity when prices go up and down: the case of the oil and gas industry

We examine the asymmetric effects of daily oil price changes on equity returns, market betas, oil betas, return variances, and trading volumes for the US oil and gas industry. The responses of stock returns associated with negative changes in oil prices are higher than that associated with positive changes in oil prices. Stock risk measured by market beta is influenced more due to oil price decreases than due to oil price increases. On the other hand, oil risk exposures (oil betas) and return variances are more influenced by oil price increases than oil price decreases. The results of our study indicate that oil and gas firm returns, market betas, oil betas, return variances respond asymmetrically to oil price changes. We also find that relative changes in oil prices along with firm-specific factors such as firm size, ROA, leverage, market-to-book ratio (MBR) are important in determining the effects of oil price changes on oil and gas firms’ returns, risks, and trading volumes.     

Estimating Systematic Risk Using Time Varying Distributions

This article proposes a dynamic vector GARCH model for the estimation of time-varying betas. The model allows the conditional variances and the conditional covariance between individual portfolio returns and market portfolio returns to respond asymmetrically to past innovations depending on their sign. Covariances tend to be higher during market declines. There is substantial time variation in betas but the evidence on beta asymmetry is mixed. Specifically, in 50% of the cases betas are higher during market declines and for the remaining 50% the opposite is true. A time series analysis of estimated time varying betas reveals that they follow stationary mean-reverting processes. The average degree of persistence is approximately four days. It is also found that the static market model overstates non-market or, unsystematic risk by more than 10%. On the basis of an array of diagnostics it is confirmed that the vector GARCH model provides a richer framework for the analysis of the dynamics of systematic risk.     

Is unlevered firm volatility asymmetric?

Asymmetric volatility refers to the stylized fact that stock volatility is negatively correlated to stock returns. Traditionally, this phenomenon has been explained by the financial leverage effect. This explanation has recently been challenged in favor of a risk premium based explanation. We develop a new, unlevering approach to document how well financial leverage, rather than size, beta, book-to-market, or operating leverage, explains volatility asymmetry on a firm-by-firm basis. Our results reveal that, at the firm level, financial leverage explains much of the volatility asymmetry. This result is robust to different unlevering methodologies, samples, and measurement intervals. However, we find that financial leverage does not explain index-level volatility asymmetry. We show that this difference between index-level asymmetry and firm-level asymmetry is driven by the asymmetry of the unlevered covariance component of index volatility.     

An Empirical Re-Examination of the Cross-Section of Expected Returns: UK Evidence

This paper is a study of the Fama and French (1992) analysis in the UK context. Consistent with their findings, our results do not support a positive relationship between beta and average monthly returns. We find that book-to-market equity and market leverage are consistently significant in explaining UK average returns. Contrary to the Fama-French evidence, size has an insignificant effect on average returns. A puzzling negative beta-returns relationship is found in some monthly regressions,and results based on annual data reveal a reversal of betas for the smallest-size portfolios. Some possible explanations are offered for these findings.     

Predicting systematic risk: Implications from growth options

In accordance with the well-known financial leverage effect, decreases in stock prices cause an increase in the levered equity beta for a given unlevered beta. However, as growth options are more volatile and have higher risk than assets in place, a price decrease may decrease the unlevered equity beta via an operating leverage effect. This is because price decreases are associated with a proportionately higher loss in growth options than in assets in place. Most of the existing literature focuses on the financial leverage effect: This paper examines both effects. We show, with a simple option pricing model, the opposing effects at work when the firm is a portfolio of assets in place and growth options. Our empirical results show that, contrary to common belief, the operating leverage effect largely dominates the financial leverage effect, even for initially highly levered firms with presumably few growth options. We then link variations in betas to measurable firm characteristics that proxy for the fraction of the firm invested in growth options. We show that these proxies jointly predict a large fraction of future cross-sectional differences in betas. These results have important implications on the predictability of equity betas, hence on empirical asset pricing and on portfolio optimization that controls for systematic risk.     

ASYMMETRIC COVARIANCE,VOLATILITY, AND THE EFFECT OF NEWS

We propose that covariance (rather than beta) asymmetry provides a superior framework for examining issues related to changing risk premiums. Accordingly, we investigate whether the conditional covariance between stock and market returns is asymmetric in response to good and bad news. Our model of conditional covariance accommodates both the sign and magnitude of return innovations, and we find significant covariance asymmetry that can explain, at least in part, the volatility feedback of stock returns. Our findings are consistent across firm size, firm leverage, and temporal and cross‐sectional aggregations.     

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.     

The Conditional Beta and the Cross-Section of Expected Returns

We examine the cross-sectional relation between conditional betas and expected stock returns for a sample period of July 1963 to December 2004. Our portfolio-level analyses and the firm-level cross-sectional regressions indicate a positive, significant relation between conditional betas and the cross-section of expected returns. The average return difference between high- and low-beta portfolios ranges between 0.89% and 1.01% per month, depending on the time-varying specification of conditional beta. After controlling for size, book-to-market, liquidity, and momentum, the positive relation between market beta and expected returns remains economically and statistically significant.     

On Stable Factor Structures in the Pricing of Risk: Do Time-Varying Betas Help or Hurt?

There is now considerable evidence suggesting that estimated betas of unconditional capital asset pricing models (CAPMs) exhibit statistically significant time variation. Therefore, many have advocated the use of conditional CAPMs. If we succeed in capturing the dynamics of beta risk, we are sure to outperform constant beta models. However, if the beta risk is inherently misspecified, there is a real possibility that we commit serious pricing errors, potentially larger than with a constant traditional beta model. In this paper we show that this is indeed the case, namely that pricing errors with constant traditional beta models are smaller than with conditional CAPMs.     

Multi-Period Lead Relations between Price-to-Book Ratios and Accounting Rates-of-Returns: Korean Evidence

Using a sample of Korean firms, this paper investigates the relations between price-to-book ratios and their determinants identified by Ohlson's (1995) accounting-based valuation model. A particular emphasis is placed on thequestion of whether and how the impact of future accounting rates-of-returns on current price-to-book ratios decays within a finite time horizon. Our results reveal that any current price-to-book ratio is significantly relatedto current and future accounting rates-of-returns over the five subsequent years.The relation between the two is stronger when accrual earnings are used for measuring accounting rates-of-returns than it is when cash flows or dividend flows are used. Further, the strength of this multi-period lead relation tends to decrease substantially in magnitude and significance with the time horizon, and becomes insignificant beyond a certain time horizon.     

Delayed Reaction to Good News and the Cross-Autocorrelation of Portfolio Returns

We document a directional asymmetry in the small stock concurrent and lagged response to large stock movements. When returns on large stocks are negative, the concurrent beta for small stocks is high, but the lagged beta is insignificant. When returns on large stocks are positive, small stocks have small concurrent betas and very significant lagged betas. That is, the cross-autocorrelation puzzle documented by Lo and MacKinlay (1990a) is associated with a slow response by some small stocks to good, but not to bad, common news. Time series portfolio tests and cross-sectional tests of the delay for individual securities suggest that existing explanations of the cross-autocorrelation puzzle based on data mismeasurement, minor market imperfections, or time-varying risk premiums fail to capture the directional asymmetry in the data.     

Corporate Investment and Asset Price Dynamics: Implications for the Cross-section of Returns

We show that corporate investment decisions can explain the conditional dynamics in expected asset returns. Our approach is similar in spirit to Berk, Green, and Naik (1999) , but we introduce to the investment problem operating leverage, reversible real options, fixed adjustment costs, and finite growth opportunities. Asset betas vary over time with historical investment decisions and the current product market demand. Book‐to‐market effects emerge and relate to operating leverage, while size captures the residual importance of growth options relative to assets in place. We estimate and test the model using simulation methods and reproduce portfolio excess returns comparable to the data.     

Information asymmetry,leverage and firm value: Do crisis and growth matter?

Drawing on pecking order and agency cost theories, we assess the extent to which information asymmetry is an important determinant of firm value and the extent to which this relationship is conditional on the leverage level of firms. We also assess the impact of information asymmetry on firm value during the pre and post 2007/09 financial crisis period and for high and low growth opportunity firms. Using a large sample of UK firms, our empirical findings suggest that information asymmetry adversely impacts firm value, and that this effect decreases with firm's leverage. We also find that leverage has a negative effect on firm value, and that the marginal effect of leverage is lower for information asymmetric firms. Further, we find that the relation between information asymmetry and firm value is more pronounced in the post-crisis period than the pre-crisis period. Finally, we show that the impact of information asymmetry on firm value is higher (lower) for firms with high (low) growth opportunities.     

Equilibrium "Anomalies"

Many empirical “anomalies” are actually consistent with the single beta capital asset pricing model if the empiricist utilizes an equity‐only proxy for the true market portfolio. Equity betas estimated against this particular inefficient proxy will be understated, with the error increasing with the firm's leverage. Thus, firm‐specific variables that correlate with leverage (such as book‐to‐market and size) will appear to explain returns after controlling for proxy beta simply because they capture the missing beta risk. Loadings on portfolios formed on relative leverage and relative distress completely subsume the powers of the Fama and French (1993) returns to small minus big market capitalization (SMB) portfolios and returns to high minus low book‐to‐market (HML) portfolios factors in explaining cross‐sectional returns.     

Unconditional Tests of Linear Asset Pricing Models with Time‐Varying Betas

In conditional affine factor models, estimated risk prices should satisfy certain unconditional constraints. Specifically, a cross‐sectional estimate of the unconditional slope associated with a risk factor should equal the average price of risk of the factor. The estimated slope associated with the product of a risk factor and an instrument should be equal to the covariance of the factor risk premium with the instrument. We show that the constraints only apply to the conditional models with time‐varying betas. We identify an unconditional constraint on unconditional betas for time‐varying beta models and incorporate it into model tests. We show that imposing this unconditional constraint changes estimates of unconditional betas and risk prices significantly.     

Size,time-varying beta,and conditional heteroscedasticity in UK stock returns

The purpose of this study is to examine the relationship between firm size and time-varying betas of UK stocks. We extend the Schwert and Seguin (1990)(Journal of Finance 45, 1120–1155) methodology by explicitly modeling conditional heteroscedasticity in the market model residual returns. Our results show that the time-varying coefficient is not statistically significant for both small and large firm stock indexes. We also find that accounting for GARCH effects in the Schwert-Seguin market model yields beta estimates that are markedly differently from those when conditional heteroscedasticity is ignored. Event studies that ignore conditional heteroscedasticity may bias the abnormal returns of small and large firms, thereby leading to a different conclusion regarding the significance of an information event.