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.     

Heteroskedasticity in Stock Returns

We use predictions of aggregate stock return variances from daily data to estimate time-varying monthly variances for size-ranked portfolios. We propose and estimate a single factor model of heteroskedasticity for portfolio returns. This model implies time-varying betas. Implications of heteroskedasticity and time-varying betas for tests of the capital asset pricing model (CAPM) are then documented. Accounting for heteroskedasticity increases the evidence that risk-adjusted returns are related to firm size. We also estimate a constant correlation model. Portfolio volatilities predicted by this model are similar to those predicted by more complex multivariate generalized-autoregressive-conditional-heteroskedasticity (GARCH) procedures.     

Measuring performance in a dynamic world: Conditional mean–variance fundamentals

We develop conditional alpha performance measures that are consistent with conditional mean–variance analysis and the magnitude and sign of the implied true conditional time-varying alphas. The sequence of conditional alphas and betas is estimable from surprisingly simple unconditional regressions. Other common performance measures are derivable from the conditional investment opportunity set based on its conditional asset return moments. Our bootstrap analysis of Morningstar mutual fund returns data demonstrates that the differences between existing conditional alpha measures and our proposed alpha are substantive for typical parameterizations.     

Efficiency in the Pricing of the FTSE 100 Futures Contract

This paper studies the pricing efficiency in the FTSE 100 futures contract by linking the predictable movements in futures returns to the time-varying risk and risk premia associated with prespecified factors. The results indicate that the predictability of the FTSE 100 futures returns is consistent with a conditional multifactor model with time-varying moments. The dynamics of the factor risk premia, combined with the variation in the betas, capture most of the predictable variance of returns, leaving little variation to be explained in terms of market inefficiency. Hence the predictive power of the instruments does not justify a rejection of market efficiency.     

Volatility and information flows in emerging equity market: A case of the Korean Stock Exchange

Applying the generalized autoregressive conditional heteroskedasticity (GARCH) model to the Korean Stock Exchange, this study examines: (1) the statistical property of time-varying volatility in returns and trading volume data found in an emerging capital market, and (2) the property of the conditional variances of returns in predicting the flow patterns of information across the firms of different sizes. The results find that current trading volume as a proxy of information arrival dramatically reduces the persistence of the conditional variance, meaning that the arrival of information is a source of the ARCH effect in the emerging market just as it is in the U.S. The results also show that just as the volatility of larger firms can be predicted by shocks to smaller firms, the volatility of smaller firms can be predicted by shocks to larger firms. However, the volatility spillover effect from larger to smaller firms is more significant than that from smaller to larger firms.     

Are the Latent Variables in Time-Varying Expected Returns Compensation for Consumption Risk?

Multibeta asset pricing models are examined using proxies for economic state variables in a framework which exploits time-varying expected returns to estimate conditional betas. Examples include multiple consumption-beta models and models where asset returns proxy for the state variables. When the state variables are not specified, the tests indicate two or three time-varying expected risk premiums in the sample of quarterly asset returns. Conditional betas relative to consumption generate less striking evidence against the model than betas relative to asset returns, but both the consumption and the market variables fail to proxy for the state variables.     

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.     

CAPM over the long run: 1926–2001

A conditional one-factor model can account for the spread in the average returns of portfolios sorted by book-to-market ratios over the long run from 1926 to 2001. In contrast, earlier studies document strong evidence of a book-to-market effect using OLS regressions over post-1963 data. However, the betas of portfolios sorted by book-to-market ratios vary over time and in the presence of time-varying factor loadings, OLS inference produces inconsistent estimates of conditional alphas and betas. We show that under a conditional CAPM with time-varying betas, predictable market risk premia, and stochastic systematic volatility, there is little evidence that the conditional alpha for a book-to-market trading strategy is different from zero.     

Expected Returns,Time-varying Risk,and Risk Premia

A new empirical model for intertemporal capital asset pricing is presented that allows both time-varying risk premia and betas where the latter are identified from the dynamics of the conditional covariance of returns. The model is more successful in explaining the predictable variations in excess returns when the returns on the stock market and corporate bonds are included as risk factors than when the stock market is the single factor. Although changes in the covariance of returns induce variations in the betas, most of the predictable movements in returns are attributed to changes in the risk premia.     

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.     

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.     

Smooth Transition ARCH Models: Estimation and Testing

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.     

Common stochastic trends and volatility in Asian-Pacific equity markets

This paper uses Johansen's cointegration test and a modified cointegration test with generalized autoregressive conditional heteroskedasticity (GARCH) effects to examine linkages between the U.S. and five Asian-Pacific stock markets (Australia, Hong Kong, Japan, Malaysia, and Singapore) during the period from 1988 to 1994. The modified cointegration test with GARCH effects is used to assess whether these stock price series share common time-varying volatility. The results indicate that the six stock markets are highly integrated through the second moments of stock returns but not the first moments.     

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.     

A semiparametric conditional capital asset pricing model

This paper proposes using a functional coefficient regression technique to estimate time-varying betas and alpha in the conditional capital asset pricing model (CAPM). Functional coefficient representation relaxes the strict assumptions regarding the structure of betas and alpha by combining the predictors into an index. Appropriate index variables are selected by applying the smoothly clipped absolute deviation penalty. In such a way, estimation and variable selection can be done simultaneously. Based on the empirical studies, the proposed model performs better than the alternatives in explaining asset returns and we find no strong evidence to reject the conditional CAPM.     

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.     

S&P 500 trading strategies and stock betas

This paper shows that S&P 500 stock betas are overstatedand the non-S&P 500 stock betas are understated becauseof liquidity price effects caused by the S&P 500 tradingstrategies. The daily and weekly betas of stocks added to theS&P 500 index during 1985-1989 increase, on average, by0.211 and 0.130. The difference between monthly betas of otherwisesimilar S&P 500 and non-S&P 500 stocks also equals 0.125during this period. Some of these increases can be explainedby the reduced nonsynchroneity of S&P 500 stock prices,but the remaining increases are explained by the price pressureor excess volatility caused by the S&P 500 trading strategies.I estimate that the price pressures account for 8.5 percentof the total variance of daily returns of a value-weighted portfolioof NYSE/AMEX stocks. The negative own autocorrelations in S&P500 index returns and the negative cross autocorrelations betweenS&P 500 stock returns provide further evidence consistentwith the price pressure hypothesis.     

Beta Asymmetry in the Global Stock Markets Following the Subprime Mortgage Crisis

I set out in this study to examine the asymmetry in beta responses using the dynamic conditional correlation threshold generalized autoregressive conditional heteroskedasticity (DCC-GJR-GARCH) model. The empirical results reveal that asymmetry is discernible in both volatility and betas in the global stock markets. Furthermore, when leverage is linked with the price-to-book ratio, the results indicate that the beta asymmetry is attributable to the leverage effect. The results of this study also reveal that the declines in the price-to-book ratio following the subprime mortgage crisis have led to an overall increase in betas.     

Is asymmetric mean-reverting pattern in stock returns systematic? Evidence from Pacific-basin markets in the short-horizon

This paper applies asymmetric nonlinear smooth transition generalized autoregressive conditional heteroskedasticity (ANST-GARCH) models to the analysis of mean-reversion and time-varying volatility in weekly index returns of the stock markets of nine countries in the Pacific-basin. It finds that the returns exhibit an asymmetric pattern of return reversals, viz., on average, a negative return reverts more quickly, with a greater magnitude, to a positive return than a positive return reverting to a negative one. The asymmetric pattern of return reversals is directly associated with the unequal pricing behavior on the part of investors. Following a negative return shock, investors do not appear to require any additional premium to the leverage effect; instead they actually neutralize the risk in the form of a reduced premium! The reduction in risk premium causes not only the current stock price to rise but also the realized negative return to revert faster with a greater magnitude.     

Changes in Expected Security Returns,Risk, and the Level of Interest Rates

Regressions of security returns on treasury bill rates provide insight about the behavior of risk in rational asset pricing models. The information in one-month bill rates implies time variation in the conditional covariances of portfolios of stocks and fixed-income securities with benchmark pricing variables, over extended samples and within five-year subperiods. There is evidence of changes in conditional “betas” associated with interest rates. Consumption and stock market data are examined as proxies for marginal utility, in a general framework for asset pricing with time-varying conditional covariances.