SKEWNESS AND KURTOSIS IN JAPANESE EQUITY RETURNS: EMPIRICAL EVIDENCE

In this paper, the distribution of equity returns on the Tokyo Stock Exchange is examined from 1965 to 1984, and significant and persistent skewness and kurtosis are found. The deviation of security returns from normality declines with increasing portfolio size and appears to be greater than the non-normality evidenced in U.S. security returns. Further, these deviations from normality persist even after controlling for January and firm size effects.     

The Analytics of the Intervaling Effect on Skewness and Kurtosis of Stock Returns

This paper analyzes how the skewness and kurtosis of securities' returns are affected by the length of the differencing interval over which returns are measured. Hawawini's previous analysis of this “intervaling effect” on log returns is shown to be incorrect, and the correct effects are derived. While Hawawini only considered log returns, we also derived the intervaling effect on the skewness and kurtosis of “simple” returns. Our results show that the length of differencing interval has very different effects on log and simple returns, but in both cases the effects on the returns' skewness and kurtosis are substantial and also quite tractable. These results also enable us to reconcile some of the contradictory results published earlier on the intervaling effect.     

The information content of implied skewness and kurtosis changes prior to earnings announcements for stock and option returns

We use option prices to examine whether changes in stock return skewness and kurtosis preceding earnings announcements provide information about subsequent stock and option returns. We demonstrate that changes in jump risk premiums can lead to changes in implied skewness and kurtosis and are also associated with the mean and variability of the stock price response to the earnings announcement. We find that changes in both moments have strong predictive power for future stock returns, even after controlling for implied volatility. Additionally, changes in both moments predict call returns, while put return predictability is primarily linked to changes in skewness.     

The Empirical Distribution of UK and US Stock Returns

There is now substantial evidence that daily equity returns are not normally distributed but instead display significant leptokurtosis and, in many cases, skewness. Considerable effort has been made in order to capture these empirical characteristics using a range of ad hoc statistical distributions. In this paper, we investigate the distribution of daily, weekly and monthly equity returns in the UK and US using two very flexible families of distributions that have been recently introduced: the exponential generalised beta (EGB) and the skewed generalised- t (SGT). These distributions permit very diverse levels of skewness and kurtosis and, between them, nest many of the distributions previously considered in the literature. Both the EGB and the SGT provide a very substantial improvement over the normal distribution in both markets. Moreover, for daily returns, we strongly reject the restrictions on the EGB and SGT implied by most of the distributions that are commonly used for modelling equity returns, including the student- t , the power exponential and the logistic distributions. Instead, our preferred distributions for daily returns are the generalised- t for the US and the skewed- t for the UK, both of which are members of the SGT family. For weekly returns, our preferred distributions are the student- t for the UK and the skewed- t for the US, while for monthly returns, our preferred distributions are the EBR12 for the UK and the logistic for the US. We consider the implications of our findings for the implementation of value-at-risk, a risk management methodology that rests heavily on the distributional characteristics of returns.     

Implied volatility skews and stock return skewness and kurtosis implied by stock option prices

The Black-Scholes* option pricing model is commonly applied to value a wide range of option contracts. However, the model often inconsistently prices deep in-the-money and deep out-of-the-money options. Options professionals refer to this well-known phenomenon as a volatility ‘skew’ or ‘smile’. In this paper, we examine an extension of the Black-Scholes model developed by Corrado and Su that suggests skewness and kurtosis in the option-implied distributions of stock returns as the source of volatility skews. Adapting their methodology, we estimate option-implied coefficients of skewness and kurtosis for four actively traded stock options. We find significantly nonnormal skewness and kurtosis in the option-implied distributions of stock returns.     

SKEWNESS AND KURTOSIS IN S&P 500 INDEX RETURNS IMPLIED BY OPTION PRICES

The Black-Scholes (1973) model frequently misprices deep-in-the-money and deep-out-of-the-money options. Practitioners popularly refer to these strike price biases as volatility smiles. In this paper we examine a method to extend the Black-Scholes model to account for biases induced by nonnormal skewness and kurtosis in stock return distributions. The method adapts a Gram-Charlier series expansion of the normal density function to provide skewness and kurtosis adjustment terms for the Black-Scholes formula. Using this method, we estimate option-implied coefficients of skewness and kurtosis in S&P 500 stock index returns. We find significant nonnormal skewness and kurtosis implied by option prices.     

Ex Ante Skewness and Expected Stock Returns

We use option prices to estimate ex ante higher moments of the underlying individual securities’ risk‐neutral returns distribution. We find that individual securities’ risk‐neutral volatility, skewness, and kurtosis are strongly related to future returns. Specifically, we find a negative (positive) relation between ex ante volatility (kurtosis) and subsequent returns in the cross‐section, and more ex ante negatively (positively) skewed returns yield subsequent higher (lower) returns. We analyze the extent to which these returns relations represent compensation for risk and find evidence that, even after controlling for differences in co‐moments, individual securities’ skewness matters.     

How does trading volume affect financial return distributions?

We assess investors' reaction to new information arrivals in financial markets by examining the relationships between trading volume and the higher moments of returns in 18 international equity and currency markets. Our volume-volatility results support extant information theories and further contribute new evidence of cross market relations between volume and volatility. We also find that the direct impact of volume on the level of negative skewness is less significant for more diversified regional portfolios. Furthermore, the negative interaction between volume and kurtosis can be explained by the differences of opinion in financial markets. We observe stronger interdependence among higher moments in reaction to significant events, but the strength is dampened by trading volume. This result is consistent with trading volume being a source of heteroskedasticity in asset returns.     

Risk measurement distortion: an improved model of return smoothing

We examine the effects of smoothed hedge fund returns on standard deviation, skewness, and kurtosis of return and on correlation of returns using a MA(2)-GARCH(1,1)-skewed-t representation instead of the traditional MA(2) model employed in the literature. We present evidence that our proposed representation is more consistent with the behavior of hedge fund returns than the traditional MA(2) representation and that the traditional method tends to overstate the degree of smoothing observed in hedge fund returns. We examine methods for correcting the distortive effects of smoothing using our representation.     

Do Sovereign Re‐Ratings Destabilize Equity Markets during Financial Crises? New Evidence from Higher Return Moments

This study investigates the effects of S&P's sovereign re‐ratings on the higher moments of equity market returns over recent financial crises. Using a set of intraday stock market index prices and sovereign credit ratings for a sample of 36 countries that experienced sovereign rating changes over the period from 1996 to 2013, we find that the higher moments of stock market returns are significantly more responsive to sovereign re‐ratings during financial crises, but the effects on stock markets are not the same across different financial crises. The effects during crises are, however, magnified for large downgrades and those that are associated with a loss of investment grade status. We find that there are asymmetric effects during financial crises in that downgrades are consistently more significant than upgrades in increasing realized volatility and realized kurtosis. Both upgrades and downgrades affect realized skewness in times of crises in the expected direction.     

Stock Options as Lotteries

We investigate the relationship between ex ante total skewness and holding returns on individual equity options. Recent theoretical developments predict a negative relationship between total skewness and average returns, in contrast to the traditional view that only coskewness is priced. We find, consistent with recent theory, that total skewness exhibits a strong negative relationship with average option returns. Differences in average returns for option portfolios sorted on ex ante skewness range from 10% to 50% per week, even after controlling for risk. Our findings suggest that these large premiums compensate intermediaries for bearing unhedgeable risk when accommodating investor demand for lottery‐like options.     

Diversification and ownership concentration

If controlling shareholders can divert profits, equity ownership is more concentrated the higher the stock returns correlation. A higher returns correlation reduces the benefits of diversification, giving rise to both a higher investment by the controlling shareholder in the asset that he controls and a lower investment by the non-controlling shareholders. The empirical analysis supports the predictions of the model: equity ownership is more concentrated in countries where the stock returns correlation is higher; moreover the intensity of the relationship between the stock returns correlation and ownership concentration is amplified by poor investor protection.     

On the robustness of higher-moment factors in explaining average expected returns: Evidence from Australia

This study tests the importance of systematic skewness and systematic kurtosis of Australian stock returns in the spirit of the higher-moment asset pricing model. We apply the Dagenais and Dagenais (1997) higher-moment estimators to correct for the errors-in-variables (EIVs) problems commonly found in the Fama and MacBeth (1973) two-pass regression methodology. After correcting for the EIVs problems, the two higher-moment factors, especially systematic skewness, are important in pricing Australian stocks. Systematic kurtosis appears to replace beta which plays a diminished role in the heavy-tailed return distribution.     

Modeling Conditional Skewness in Stock Returns

Abstract

In this paper, we propose a new GARCH-in-Mean (GARCH-M) model allowing for conditional skewness. The model is based on the so-called z distribution capable of modeling skewness and kurtosis of the size typically encountered in stock return series. The need to allow for skewness can also be readily tested. The model is consistent with the volatility feedback effect in that conditional skewness is dependent on conditional variance. Compared to previously presented GARCH models allowing for conditional skewness, the model is analytically tractable, parsimonious and facilitates straightforward interpretation.Our empirical results indicate the presence of conditional skewness in the monthly postwar US stock returns. Small positive news is also found to have a smaller impact on conditional variance than no news at all. Moreover, the symmetric GARCH-M model not allowing for conditional skewness is found to systematically overpredict conditional variance and average excess returns.     

International asset allocation under regime switching, skew, and kurtosis preferences

This paper investigates the international asset allocation effectsof time-variations in higher-order moments of stock returnssuch as skewness and kurtosis. In the context of a four-momentInternational Capital Asset Pricing Model (ICAPM) specificationthat relates stock returns in five regions to returns on a globalmarket portfolio and allows for time-varying prices of covariance,co-skewness, and co-kurtosis risk, we find evidence of distinctbull and bear regimes. Ignoring such regimes, an unhedged USinvestor's optimal portfolio is strongly diversified internationally.The presence of regimes in the return distribution leads toa substantial increase in the investor's optimal holdings ofUS stocks, as does the introduction of skewness and kurtosispreferences.     

Monthly Pattern and Portfolio Effect on Higher Moments of Stock Returns: Empirical Evidence from Hong Kong

Using a direct test, this paper studies the month-of-the-year effect on the higher moments of six industrial stock indices of the Hong Kong market. We also examine the portfolio effect on skewness and kurtosis across month of the year to see if such an anomaly exists. The empirical results support a weak month-of-the-year effect in higher moments of stock returns. Using a complete sample of all possible combinations for each portfolio size, we show that portfolio effect varies across month of the year for both skewness and kurtosis. In particular, our results show that diversification does not necessarily provide benefits to rational investors when the stock return distribution is non-normal, even though portfolio formation can reduce standard deviation. In June, August and October, diversification across industrial sectors results in a more negatively skewed and leptokurtic return distribution, which is not preferred by investors with risk-aversion. Two (one) possible explanations for the portfolio effect on skewness (kurtosis) are also provided. Our empirical results add new evidence to the existence of anomalies in the Hong Kong stock market. This revised version was published online in August 2006 with corrections to the Cover Date.     

On the distribution of government bond returns: evidence from the EMU

This paper assesses the statistical distribution of daily EMU bond returns for the period 1999–2012. The normality assumption is tested and clearly rejected for all European countries and maturities. Although skewness plays a minor role in this departure from normality, it is mainly due to the excess kurtosis of bond returns. Therefore, we test the Student’s t, skewed Student’s t, and stable distribution that exhibit this feature. The financial crisis leads to a structural break in the time series. We account for this and retest the alternative distributions. A value-at-risk application underlines the importance of our findings for investors. In sum, excess kurtosis in bond returns is essential for risk management, and the stable distribution captures this feature best.     

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.     

Robust estimation with flexible parametric distributions: estimation of utility stock betas

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.