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The purpose of this paper is to introduce a non‐normality premium (NNP) to identify the extra return that will compensate an investor for a non‐normal return distribution. The NNP quantifies the economic significance of non‐normality to complement a statistical significance test of non‐normality, such as the Jarque‐Bera test.

The NNP is patterned after the risk premium, the amount that compensates an investor for the risk of an investment. The theoretical NNP is examined on the margins with Taylor series approximation and applied to hedge fund data.

An increase of 1 in the skewness has the same effect on an investor as an increase in the mean of 2.5 basis points per month. An increase of 1 in the kurtosis has the same effect on an investor as a decrease in the mean of 0.15 basis points per month. A sample of 716 hedge funds revealed that while 72 per cent statistically reject normality, only 29 per cent require more than a single basis point per month difference in the mean to compenscate an investor for the non‐normality.

The NNP allows for a valuation on the higher moments (skewness and kurtosis) of an investor's return distribution. The evaluation is tailored to the individual through use of a utility function. Once applied to an alternative investment vehicle, it is learned that rejecting normality is not sufficient grounds to suspect that the non‐normality is important to investors.

The purpose of this paper is to develop a loan insurance pricing model allowing for the skewness and kurtosis existing in underlying asset returns.

Using the theory of Gram-Charlier option, the authors first derive a closed-form solution of the Gram-Charlier pricing model. To address the difficulties in implementing the pricing model, the authors subsequently propose an iterative method to estimate skewness and kurtosis in practical application, which shows a relatively fast convergence rate in the empirical test.

Not only the theoretical analysis but also the empirical evidence shows that the effects of skewness and kurtosis on loan insurance premium tend to be negative and positive, respectively. Furthermore, the actual values of skewness and kurtosis are usually negative and positive, respectively, which leads to the empirical result that the pricing model ignoring skewness and kurtosis substantially underestimates loan insurance premium.

This paper proposes a loan insurance pricing model considering the skewness and kurtosis of asset returns, in which the authors use the theory of Gram-Charlier option. More importantly, the authors further propose a novel iterative method to estimate skewness and kurtosis in practical application. The empirical evidence suggests that the Gram-Charlier pricing model captures the information content of skewness and kurtosis.

The purpose of this study is to investigate the influence of texture on hydrodynamic lubrication performance of slide surface from the perspective of skewness and kurtosis.

Hydrodynamic lubrication theoretical model of textured surface was established based on two-dimensional Reynolds equation, and finite difference algorithm was used as the numerical approach in the paper. Skewness and kurtosis of surface were obtained by discrete calculation.

Numerical analysis results show that the influence law of texture types on skewness, kurtosis and hydrodynamic lubrication was the more negative skewness and higher kurtosis, the better hydrodynamic lubrication performance when texture cross section contour and geometric parameters were the same. Similarly, the same influence law of skewness, kurtosis and hydrodynamic lubrication performance by texture cross-section contour was observed. However, it was unable to evaluate the effect of texture angle on hydrodynamic lubrication performance of textured surface from the perspective of skewness and kurtosis.

This paper confirms the feasibility of evaluating influence of texture types and texture cross-section contour on hydrodynamic lubrication performance from the perspective of skewness and kurtosis and provides a way to optimize texture type and texture cross section.

For the KOSPI 200 index options market. we examine the power of influence on pricing options of the skewness and the kurtosis of the risk neutral distribution. We compare the Black and Scholes (1973) model which does not consider the skewness or the kurtosis of the risk neutral distribution with Corrado and sue 1996)’s model which consider both the skewness and the kurtosis and the models which consider only the skewness or the kurtosis.

It is found that Corrado and sue 1996)‘s model which consider both skewness and kurtosis shows the best performance closely followed by the model which consider only the skewness for tile in-sample pricing and the out-of-sample pricing. As a result. it contributes to pricing options to consider both skewness and kurtosis and the skewness is more important factor for pricing options than the kurtosis.

The study investigates the impact of higher moments on cross-sectional returns in the Indian equity market.

Using the daily data of 3,085 Bombay Stock Exchange-listed stocks spanning over 20 years from January 2000 to December 2019, the study evaluates the relationship between higher moments (skewness and kurtosis) and stock returns at individual stock and portfolio levels. The variations in the returns of the equal-weighted and the value-weighted portfolios are analysed, where the portfolios are constructed by sorting the stocks on skewness and kurtosis. The returns are adjusted for five common factors – market excess-returns, size, value, momentum and illiquidity, to controls other cross-sectional effects. Besides, the study employs Fama-MacBeth cross-sectional regression and time-series tests of higher moments as robustness measures.

The study presents higher moments anomaly in the Indian equity market. Contrary to what is expected based on a risk-averse rational agent model, a robust positive relationship is observed between the skewness and stock returns. The relationship between the kurtosis and stock returns is negative, albeit statistically weak. These results are robust for the Fama-MacBeth cross-sectional regression and time-series tests.

It is among the earlier attempts to investigate the pricing impact of higher moments at different levels of asset prices in an emerging market. Besides the standard portfolio methodology for explaining cross-sectional variations, the study also employs the time-series tests for higher moment factors, hence provides more robust results. Results have wider implications for asset pricing in emerging markets and highlight many issues for further research.

The purpose of this paper is to examine the relationships between the higher moments of returns (realized skewness and kurtosis) and subsequent returns at the industry level, with a focus on both empirical predictability and practical application via trading strategies.

Daily returns for 48 US industries over the period 1970–2019 from Kenneth French’s data library are used to calculate the higher moments and to construct short- and medium-term single-sort trading strategies. The analysis adjusts returns for common risk factors (market, size, value, investment, profitability and illiquidity) to confirm whether conventional asset pricing models can capture these relationships.

Past skewness positively relates to subsequent industry returns and this relationship is unexplained by common risk factors. There is also a time-varying effect in which the predictive role of skewness is much stronger over business cycle expansions than recessions, a result consistent with varying investor optimism. However, there is no significant relationship between kurtosis and subsequent industry returns. The analysis confirms robustness using both value- and equal-weighted returns.

The calculation of realized moments conventionally uses high-frequency intra-day data, regrettably unavailable for industries. In addition, the chosen portfolio-sorting method may omit some information, as it compares only average group returns. Nonetheless, the close relationship between skewness and future returns at the industry level suggests variations in returns unexplained by common risk factors. This enriches knowledge of market anomalies and questions yet again weak-form market efficiency and the validity of conventional asset pricing models. One suggestion is that it is possible to significantly improve the existing multi-factor asset pricing models by including industry skewness as a risk factor.

Given the relationship between skewness and future returns at the industry level, investors may predict subsequent industry returns to select better-performing funds. They may even construct trading strategies based on return distributions that would generate abnormal returns. Further, as the evaluation of individual stocks also contains industry information, and stocks in industries with better performance earn higher returns, risks related to industry return distributions can also shed light on individual stock picking.

While there is abundant evidence of the relationships between higher moments and future returns at the firm level, there is little at the industry level. Further, by testing whether there is time variation in the relationship between industry higher moments and future returns, the paper yields novel evidence concerning the asymmetric effect of stock return predictability over business cycles. Finally, the analysis supplements firm-level results focusing only on the decomposed components of higher moments.

It has been demonstrated in the US market that expected market excess returns can be predicted using the average higher-order moments of all firms. This study aims to empirically test this theory in emerging markets.

Two measures of average higher moments have been used (equal-weighted and value-weighted) along with the market moments to predict subsequent aggregate excess returns using the linear as well as the quantile regression model.

The authors report that both equal-weighted skewness and kurtosis significantly predict subsequent market returns in two countries, while value-weighted average skewness and kurtosis are significant in predicting returns in four out of nine sample markets. The results for quantile regression show that the relationship between the risk variable and aggregate returns varies along the spectrum of conditional quantiles.

This is the first study that investigates the impact of third and fourth higher-order average realized moments on the predictability of subsequent aggregate excess returns in the MSCI Asian emerging stock markets. This study is also the first to analyze the sensitivity of future market returns over various quantiles.

The purpose of this paper is to discuss how numerous tests that are available in statistical literature to assess normality of a given set of observations perform in normal and near-normal situations. Not all these tests are suitable for all situations but each test has an exclusive area of application.

These tests are assessed for their power at varying degrees of skewness, kurtosis and sample size on the basis of simulated experiments.

It is observed that almost all these tests are indifferent for smaller values of skewness and kurtosis. Further, the power of accepting normality reduces with increasing sample size.

The article gives guidelines to researchers to apply normality assessing tests in different situations.

The purpose of this paper is to develop an option pricing model applicable to US options. The lognormality assumption that has typically been imposed with past binomial and trinomial option pricing models is relaxed. The relaxed lattice model is then used to determine skewness and kurtosis of distributions of futures prices implied from option prices.

The relaxed lattice is based on Gaussian quadrature. The markets studied include corn, soybeans, and wheat. Skewness and kurtosis are implied by minimizing the squared deviations of actual option premia from predicted premia.

Positive skewness is the major source of nonnormality, but both skewness and kurtosis are important as the trinomial model that considers kurtosis has greater accuracy than the binomial model. The out‐of‐sample forecasting accuracy of the relaxed lattice models is better than the Black‐Scholes model in most, but not all cases.

The model might benefit from using option prices from more than one day. The implied skewness and kurtosis were quite variable and using more data might reduce this variability.

Empirical results mostly show positive implied skewness, which suggests extreme price rises were more likely than extreme price decreases.

The relaxed lattice is a new model and the results about implied higher moments are new for these commodities. There are competing models available that should be able to get similar accuracy, so one key advantage of the new approach is its simplicity and ease of use.

This study aims to include the diagnosis of an old concrete deck steel truss rural road bridge in the damaged and retrofitted state through vibration response signals.

The analysis of the vibration response signals is performed in time and time-frequency domains using statistical features-root mean square, impulse factor, crest factor, kurtosis, peak2peak and Stockwell transform. The proposed methodology uses the Hilbert transform in combination with spectral kurtosis and bandpass filtering technique for obtaining robust outcomes of modal frequencies.

The absence or low amplitude of considered mode shape frequencies is observed both before and after retrofitting of bridge indicates the deficient nodes. The kurtosis feature among all statistical approaches is able to reflect significant variation in the amplitude of different nodes of the bridge. The Stockwell transform showed better resolution of present modal frequencies but due to the yield of additional frequency peaks in the vicinity of the first three analytical modal frequencies no decisive conclusions are achieved. The methodology shows promising outcomes in eliminating noise and visualizing distinct modal frequencies of a steel truss bridge.

The findings of the present study help in analyzing noisy vibration signals obtained from various structures (civil or mechanical) and determine vulnerable locations of the structure using mode shape frequencies.

The literature review gave an insight into few experimental investigations related to the combined application of Hilbert transform with spectral kurtosis and bandpass filtering technique in determining mode frequencies of a steel truss bridge.