The negative news threshold—An explanation for negative skewness in stock returns

Abstract

A vast literature documents negative skewness in stock index return distributions on several markets. In this paper the issue of negative skewness is approached from a different angle to previous studies by combining the Trueman's 1997 model of management disclosure practices with symmetric market responses in order to explain negative skewness in stock returns. Empirical tests reveal that returns for days when non-scheduled news items are disclosed are the source of negative skewness in stock returns, as predicted. These findings suggest that negative skewness in stock returns is induced by asymmetries in the news disclosure policies of firm management. Furthermore, it is found that the returns are negatively skewed only for non-scheduled firm-specific news disclosures for firms where the management is compensated with stock options.     

On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks

We find support for a negative relation between conditional expected monthly return and conditional variance of monthly return, using a GARCH-M model modified by allowing (1) seasonal patterns in volatility, (2) positive and negative innovations to returns having different impacts on conditional volatility, and (3) nominal interest rates to predict conditional variance. Using the modified GARCH-M model, we also show that monthly conditional volatility may not be as persistent as was thought. Positive unanticipated returns appear to result in a downward revision of the conditional volatility whereas negative unanticipated returns result in an upward revision of conditional volatility.     

The empirical relationship between risk and return: evidence from the UK stock market

Previous studies reach no consensus on the relationship between risk and return using data from one market. We argue that the world market factor should not be ignored in assessing the risk-return relationship in a partially integrated market. Applying a bivariate generalized autoregressive conditional heteroscedasticity in mean (GARCH-M) model to the weekly stock index returns from the UK and the world market, we document a significant positive relationship between stock returns and the variance of returns in the UK stock market after controlling for the covariance of the UK and the world market return. In contrast, conventional univariate GARCH-M models typically fail to detect this relationship. Nonnested hypothesis tests supplemented with other commonly used model selection criteria unambiguously demonstrate that our bivariate GARCH-M model is more likely to be the true model for UK stock market returns than univariate GARCH-M models. Our results have implications for empirical assessments of the risk-return relationship, expected return estimation, and international diversification.     

Asymmetric Price and Volatility Adjustments in Emerging Asian Stock Markets

This paper tests the hypothesis that stock returns in emerging stock markets adjust asymmetrically to past information. The evidence suggests that both the conditional mean and the conditional variance respond asymmetrically to past information. In agreement with studies dealing with developed stock markets, the conditional variance is an asymmetrical function of past innovations, rising proportionately more during market declines. More importantly, the conditional mean is also an asymmetrical function of past returns. Specifically, positive past returns are more persistent than negative past returns of an equal magnitude. This behaviour is consistent with an asymmetric partial adjustment price model where news suggesting overpricing (negative returns) are incorporated faster into current prices than news suggesting underpricing (positive returns). Furthermore, the asymmetric adjustment of prices to past information could be partially responsible for the asymmetries in the conditional variance if the degree of adjustment and the level of volatility are positively related.     

ON THE RATIONALITY OF COMMON STOCK RETURN VOLATILITY

This paper derives the relationship between the population unconditional variance of common stock returns and the variance of expected returns conditional on a well-specified information set. As a consequence, a lower bound is obtained for the variance of common stock returns. The sample counterpart of this bound is then empirically tested against the sample variance of returns. The paper's main conclusion can be stated as follows: the observed volatility of real (inflation-adjusted) common stock returns is not “irrationally” large. The paper admits of this conclusion because the point estimate of the lower-bound variance derived in this model is actually larger than the point estimate of common stock return volatility. However, since these point estimates are found to have a statistically insignificant difference, equality of the two variances cannot be ruled out. Hence, “rationality” of common stock returns—as implied by a utility-based valuation conditional on a specified information set—cannot be rejected.     

On the distribution and conditional heteroscedasticity in Taiwan stock prices

This paper studies the distribution and conditional heteroscedasticity in stock returns on the Taiwan stock market. Apart from the normal distribution, in order to explain the leptokurtosis and skewness observed in the stock return distribution, we also examine the Student-t, the Poisson–normal, and the mixed-normal distributions, which are essentially a mixture of normal distributions, as conditional distributions in the stock return process. We also use the ARMA (1,1) model to adjust the serial correlation, and adopt the GJR–generalized autoregressive conditional heteroscedasticity (GARCH (1,1)) model to account for the conditional heterscedasticity in the return process. The empirical results show that the mixed–normal–GARCH model is the most probable specification for Taiwan stock returns. The results also show that skewness seems to be diversifiable through portfolio. Thus the normal–GARCH or the Student-t–GARCH model which involves symmetric conditional distribution may be a reasonable model to describe the stock portfolio return process¹.     

Sensitivity of the bank stock returns distribution to changes in the level and volatility of interest rate: A GARCH-M model

The objective of this paper is to employ the generalized autoregressive conditionally heteroskedastic in the mean (GARCH-M) methodology to investigate the effect of interest rate and its volatility on the bank stock return generation process. This framework discards the restrictive assumptions of linearity, independence, and constant conditional variance in modeling bank stock returns. The model presented here allows for shifts in the volatility equation in response to the changes in monetary policy regime in 1979 and 1982 to be estimated. ARCH, GARCH, and volatility feed back effects are found to be significant. Interest rate and interest rate volatility are found to directly impact the first and the second moments of the bank stock returns distribution, respectively. The latter also affects the risk premia indirectly. The degree of persistence in shocks is substantial for all the three bank portfolios and sensitive to the nature of the bank portfolio and the prevailing monetary policy regime.     

Price Convexity and Skewness

This paper develops a model in which investors who are prohibited from short selling agree to disagree on the precision of a publicly observed signal. The model implies that the equilibrium price is a convex function of the public signal. The model predicts that (1) the stock price reacts more to good news than to bad news; (2) the skewness of stock returns is positively correlated with contemporaneous returns, but negatively correlated with lagged returns; (3) short sale constraints increase rather than decrease skewness; and (4) disagreement about information precision increases skewness. Empirical tests conducted find supportive evidence for all these predictions.     

Accounting Ratios and the Cross‐section of Expected Stock Returns

Under clean‐surplus accounting, the log return on a stock can be decomposed into a linear function of the contemporaneous log return on equity, the contemporaneous log dividend–price ratio (if the stock pays a dividend), and both the contemporaneous and lagged values of the log book‐to‐market equity ratio. This paper studies the implications of this decomposition for the cross‐section of conditional expected stock returns. The empirical analysis reveals that the log accounting ratios capture cross‐sectional variation in both the conditional mean and conditional variance of log stock returns, which is consistent with the decomposition. It also brings fresh insights to the relation between firm size (market equity) and conditional expected stock returns. The evidence indicates that the conditional median return increases with firm size, while the conditional return skewness decreases with firm size. Empirically, the skewness effect outweighs the median effect, leading to the well‐documented inverse relation between size and average returns. The results of out‐of‐sample tests suggest that investors could use the information provided by the observed values of the log accounting ratios to formulate more effective portfolio strategies.     

Variance Spillover and Skewness in Financial Asset Returns

Bond and stock returns have been observed in the literature to exhibit unconditional skewness and temporal persistence in conditional skewness. We demonstrate that observed persistence in conditional third central moments can be due to the spillover of conditional variance dynamics. The confounding of true skewness and a variance spillover effect is problematic for financial modeling. Using market data, we empirically demonstrate that a simple standardization approach removes the variance‐induced skewness persistence. An important implication is that more parsimonious return and asset pricing models result if skewness persistence need not be modeled.     

Whence GARCH? A Preference-Based Explanation for Conditional Volatility

We develop a preference-based equilibrium asset pricing modelthat explains low-frequency conditional volatility. Similarto Barberis, Huang, and Santos (2001), agents in our model careabout wealth changes, experience loss aversion, and keep a mentalscorecard that affects their level of risk aversion. A new featureof our model is that when perturbed by unexpected returns, investorsbecome temporarily more sensitive to news. Gradually investorsbecome accustomed to the new level of wealth, restoring priorlevels of risk aversion and news sensitivity. The state-dependentsensitivity to news creates the type of volatility clusteringfound in low-frequency stock returns. We find empirical supportfor our model's predictions that relate the scorecard to conditionalvolatility and skewness.     

Firm size and volatility analysis in the Spanish stock market

Using Spanish stock market data, this paper examines volatility spillovers between large and small firms and their impact on expected returns. By using a conditional capital asset pricing model (CAPM) with an asymmetric multivariate GARCH-M covariance structure, it is shown that there exist bidirectional volatility spillovers between both types of companies, especially after bad news. After estimating the model, a positive and significant price of risk is obtained. This result is consistent with the volatility feedback effect, one of the most popular explanations of the asymmetric volatility phenomenon, and explains why risk premiums are much more sensitive to negative return shocks coming from the whole market or other related markets.     

Time‐Varying Risk–Return Trade‐off in the Stock Market

We uncover a strong comovement of the stock market risk–return trade‐off with the consumption–wealth ratio (CAY). The finding reflects time‐varying investment opportunities rather than countercyclical aggregate relative risk aversion. Specifically, the partial risk–return trade‐off is positive and constant when we control for CAY as a proxy for investment opportunities. Moreover, conditional market variance scaled by CAY is negatively priced in the cross‐section of stock returns. Our results are consistent with a limited stock market participation model, in which shareholders require an illiquidity premium that increases with CAY, in addition to the risk premium that is proportional to conditional market variance.     

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.     

The Comovement of US and UK Stock Markets

US and UK stock returns are highly positively correlated over the period 1918–99. Using VAR‐based variance decompositions, we investigate the nature of this comovement. Excess return innovations are decomposed into news about future dividends, real interest rates, and excess returns. We find that the latter news component is the most important in explaining stock return volatility in both the USA and the UK and that stock return news is highly correlated across countries. This is evidence against Beltratti and Shiller's (1993) finding that the comovement of US and UK stock markets can be explained in terms of a simple present value model. We interpret the comovement as indicating that equity premia in the two countries are hit by common real shocks.     

Intraday Seasonalities and Macroeconomic News Announcements

Using a data set consisting of more than five years of 5‐minute intraday stock index returns for major European stock indices and US macroeconomic surprises, conditional means and volatility behaviour in European markets were investigated. The findings suggest that the opening of the US stock market significantly raises the level of volatility in Europe, all markets responding in an identical fashion. Furthermore, US macroeconomic surprises exert an immediate and major impact on both the European stock markets’ intraday returns and volatilities. Thus, high frequency data appear to be critical for the identification of news impacting the markets.     

Do Accruals Drive Firm‐Level Stock Returns? A Variance Decomposition Analysis

This paper extends the variance decomposition framework of Campbell [1991], Campbell and Ammer [1993], and Vuolteenaho [2002] to address the relative value relevance of accrual news, cash flow news, and expected-return news in driving firm-level equity returns. The extension is based on the Feltham-Ohlson [1995, 1996] clean surplus relations. Using three models, this study shows that all three factors, accruals, cash flows, and expected future discount rates are value relevant. Moreover, accrual news is found to significantly dominate expected-return news in driving firm-level stock returns. Operating income news is also found to significantly dominate both expected-return news and free cash flow news in driving firm-level stock returns. Furthermore, after splitting net income into cash flow and accrual earnings components in the Vuolteenaho model, accrual earnings news and cash flow earnings news are found to equally drive firm-level stock returns and to dominate expected-return news. Further disaggregation of the data yields some evidence that accrual earnings news is a more important factor than cash flow earnings news in driving current stock returns. Overall, the three models indicate that changes in expected future accruals are a primary driver, if not the primary driver, of current stock returns.     

Short-term Dynamics in the Cyprus Stock Exchange

Abstract

This paper investigates the short-term dynamics of stock returns in an emerging stock market namely, the Cyprus Stock Exchange (CYSE). Stock returns are modelled as conditionally heteroscedastic processes with time-dependent serial correlation. The conditional variance follows an EGARCH process, while for the conditional mean three nonlinear specifications are tested, namely: (a) the LeBaron exponential autoregressive model; (b) the Sentana and Wadhwani positive feedback trading model; and finally (c) a model that nests both (a) and (b). There is an inverse relationship between volatility and autocorrelation consistent with the findings from several other stock markets, including the US. This pattern could be the manifestation of a certain form of noise trading namely positive feedback trading or, momentum trading strategies. There is little evidence that market declines are followed with higher volatility than market advances, the so-called ‘leverage effect’, that has been observed in almost all developed stock markets. In out of sample forecasts, the nonlinear specifications provide better results in terms of forecasting both first and second moments of the distribution of returns.     

Non-linear dependence and conditional heteroscedasticity in stock returns evidence from the norwegian thinly traded equity market

Abstract

The paper investigates the presence of non-linear dependencies in stock returns for the Norwegian equity market as it is very difficult to interpret the unconditional distribution of stock returns and its economic implications if the i.i.d. assumption is violated. Standard tests of non-linear dependence give strong evidence for the presence of non-linearity in raw returns. Modelling non-linear dependence must distinguish between models that are non-linear in mean and hence depart from the Martingale hypothesis, and models that are non-linear in variance and hence depart from independence but not from the Martingale hypothesis. Therefore, three non-linear models of asset returns are formulated applying ARMA-GARCH specifications for the conditional mean and variance equations. The paper goes on to answer which model has the necessary characteristics that are sufficient to account for most of the non-linear dependence. In the Norwegian equity market most of the non-linear dependence seems to be conditional heteroscedasticity. However, the most thinly traded assets still report significant non-linear dependence for all non-linear specifications. These results imply that the independence hypothesis can be rejected for all assets, portfolios and indices. Moreover, for thinly traded assets the Martingale hypothesis can also be rejected. The economic implications from the unconditional distributions of thinly traded assets are therefore very difficult to interpret and are unfamiliar territory for those who are accustomed to thinking analytically, intuitively and linearly.     

Option pricing under regime switching

Abstract

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.