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This paper aims to investigate the effect of non-normality in returns and market capitalization of stock portfolios and stock indices on value at risk and conditional VaR estimation. It is a well-documented fact that returns of stocks and stock indices are not normally distributed, as Indian financial markets are more prone to shocks caused by regulatory changes, exchange rate fluctuations, financial instability, political uncertainty and inadequate economic reforms. Further, the relationship of liquidity represented by volume traded of stocks and the market risk calculated by VaR of the firms is studied.

In this paper, VaR is estimated by fitting empirical distribution of returns, parametric method and by using GARCH(1,1) with Student’s t innovation method.

It is observed that both the stocks, stock indices and their residuals exhibit non-normality; therefore, conventional methods of VaR calculation are not accurate in real word situation. It is observed that parametric method of VaR calculation is underestimating VaR and CVaR but, VaR estimated by fitting empirical distribution of return and finding out 1-a percentile is giving better results as non-normality in returns is considered. The distributions fitted by the return series are following Logistic, Weibull and Laplace. It is also observed that VaR violations are increasing with decreasing market capitalization. Therefore, we can say that market capitalization also affects accurate VaR calculation. Further, the relationship of liquidity represented by volume traded of stocks and the market risk calculated by VaR of the firms is studied. It is observed that the decrease in liquidity increases the value at risk of the firms.

This methodology can further be extended to other assets’ VaR calculation like foreign exchange rates, commodities and bank loan portfolios, etc.

This finding can help risk managers and mutual fund managers (as they have portfolios of different assets size) in estimating VaR of portfolios with non-normal returns and different market capitalization with precision. VaR is used as tool in setting trading limits at trading desks. Therefore, if VaR is calculated which takes into account non-normality of underlying distribution of return then trading limits can be set with precision. Hence, both risk management and risk measurement through VaR can be enhanced if VaR is calculated with accuracy.

This paper is considering the joint issue of non-normality in returns and effect of market capitalization in VaR estimation.

The purpose of this study is to assess the extent to which the Ghana stock market performance has been impacted by the novel COVID-19 pandemic.

The study used the exponential generalized autoregressive conditional heteroscedasticity (EGARCH) model, by using daily time series data from 2 January 2015 to 13 October 2020. Both pre-estimation (Augmented Dickey-Fuller and Phillips-Perron) and post-estimation tests (Jarque-Bera) were conducted to validate the results.

While the study shows a statistically insignificant negative relationship between the COVID-19 pandemic and the Ghana stock returns, the results confirm that the COVID-19 pandemic has occasioned an increase in the Ghana stock returns volatility by 8.23%. Furthermore, the study confirmed the presence of volatility clustering and asymmetric effect, with the latter implying that worthy news tends to affect volatility more than unwelcome news of equal size.

To dampen uncertainties that trigger stock market volatility, the government should surgically target worse affected COVID-19 pandemic businesses and households to check the drop in profits and demand. Rigidities associated with stock market operations must be addressed to make it attractive to investors even in the midst of a pandemic.

This paper is a pioneer attempt at assessing the extent to which a developing economy stock market has been impacted by the novel COVID-19 pandemic using the EGARCH model.

Control chart pattern recognition is a critical issue in statistical process control, as unnatural patterns on control charts are often associated with specific assignable causes adversely affecting the process. Several researchers have recently applied neural networks to pattern recognition for control charts. However, nearly all studies in this area assume that the in‐control process data in the control charts follow a normal distribution. This assumption contradicts the facts of practical manufacturing situations. This paper investigates how non‐normality affects the performance of neural network based control chart pattern recognition models. Extensive performance evaluation was carried out using simulated data with various non‐normalities. The non‐normality was measured in skewness and kurtosis. Numerical results indicate that the neural network based control chart pattern recognition models still perform well in a non‐normal distribution environment in terms of recognition accuracy and speed.

The purpose of this paper is to find and describe some stylized facts for foreign exchange and stock market returns, which are explored using statistical methods.

Formal statistics for testing presence of autocorrelation, asymmetry, and other deviations from normality are applied. Dynamic correlations and different kernel estimations and approximations to the empirical distributions are also under scrutiny. Furthermore, dynamic analysis of mean, standard deviation, skewness and kurtosis are also performed to evaluate time‐varying properties in return distributions.

The findings include: different types of non‐normality in both markets, fat tails, excess furtosis, return clustering and unconditional time‐varying moments. Identifiable volatility cycles in both forex and stock markets are associated to common macro financial uncertainty events.

The paper is the first work of this type in Peru.

As the normality concept for frictional dilatant material has a serious drawback, the key feature in this numerical study is that the material here is characterized by elastic-viscoplastic constitutive relation with plastic non-normality effect for two different hardness functions. The paper aims to discuss this issue.

Quasi-static, mode I plane strain crack tip fields have been investigated for a plastically compressible isotropic hardening–softening–hardening material under small-scale yielding conditions. Finite deformation, finite element calculations are carried out in front of the crack with a blunt notch. For comparison purpose a few results of a hardening material are also provided.

The present numerical calculations show that crack tip deformation and the field quantities near the tip significantly depend on the combination of plastic compressibility and slope of the hardness function. Furthermore, the consideration of plastic non-normality flow rule makes the crack tip deformation as well as the field quantities significantly different as compared to those results when the constitutive equation exhibits plastic normality.

To the best of the authors’ knowledge, analyses, related to the constitutive relation exhibiting plastic non-normality in the context of plastic compressibility and softening (or softening hardening) on the near tip fields, are not explored in the literature.

The purpose of this paper is to develop an yield-based process capability index (PCI), C _py , to overcome the shortcomings of existing PCIs that limit their use and lead to inaccurate measures of quality conformance under a variety of common conditions.

–C _py is developed conceptually to flexibly and accurately reflect conformance and then used to numerically measure inaccuracies of C _pk .

–C _py overcomes many of the problems associated with existing PCIs, including C _pk . The degree of process distribution non-normality, level of quality (the sigma level), and whether the process is centered or shifted left or right affect the direction and size of process capability error produced by C _pk . The accuracy of C _pk can be greatly affected by process data that deviate even slightly from normality.

–C _py offers numerous advantages compared to existing PCIs. It accurately reflects process conformance regardless of the process distribution. It is applicable even if the process has multiple characteristics and with both variable and attribute data. Its calculation is relatively simple and the necessary data for it are likely already captured by most organizations.

The main contributions are the development of a new PCI, C _py ; a conceptual analysis of its advantages; and a numerical analysis of the improved accuracy of C _py as compared to C _pk for shifted and non-shifted process means for normal, nearly normal, and highly non-normal distributions over a range of process variability levels.

Purpose – The purpose of this chapter is to estimate non-Gaussian distributions by means of Johnson distributions. An empirical illustration on hedge fund returns is detailed.

Methodology/approach – To fit non-Gaussian distributions, the chapter introduces the family of Johnson distributions and its general extensions. We use both parametric and non-parametric approaches. In a first step, we analyze the serial correlation of our sample of hedge fund returns and unsmooth the series to correct the correlations. Then, we estimate the distribution by the standard Johnson system of laws. Finally, we search for a more general distribution of Johnson type, using a non-parametric approach.

Findings – We use data from the indexes Credit Suisse/Tremont Hedge Fund (CSFB/Tremont) provided by Credit Suisse. For the parametric approach, we find that the SU Johnson distribution is the most appropriate, except for the Managed Futures. For the non-parametric approach, we determine the best polynomial approximation of the function characterizing the transformation from the initial Gaussian law to the generalized Johnson distribution.

Originality/value of chapter – These findings are novel since we use an extension of the Johnson distributions to better fit non-Gaussian distributions, in particular in the case of hedge fund returns. We illustrate the power of this methodology that can be further developed in the multidimensional case.

This study investigates the effect of volatility scaling on valuing financial assets by examining the long-term return properties of the spot USD/AUD. Tests are conducted for evidence of a scaling law in USD/AUD returns. The economic implications of dependence and non-normality of the distribution of returns are explored using the Garman and Kohlhagen modified Black–Scholes model for valuing foreign currency options. The results suggest that the USD/AUD does not conform to a stable distribution and that as a result of differential scaling laws, Garman and Kohlhagen option values using implied annual volatility will be consistently too high or too low.

The purpose of this paper is to analyze the mean-variance capital asset pricing model (CAPM) and downside risk-based CAPM (DR-CAPM) developed by Bawa and Lindenberg (1977), Harlow and Rao (1989), and Estrada (2002) to assess which downside beta better explains expected stock returns. The paper also explores whether investors respond differently to stocks that co-vary with declining market than to those of co-vary with rising market.

The paper uses monthly data of closing prices of stocks listed at the Karachi Stock Exchange (KSE). The data cover the period from January 2000 to December 2012. The standard, downside, and upside betas are estimated for different sub-periods,and then,their validity to quantify the risk premium is tested for subsequent sub-periods in a cross sectional regression framework. Though our empirical methodology is similar to that of Fama and MacBeth (1973) for testing the CAPM and the DR-CAPM, our approach to estimate the downside beta is different from earlier studies. In particular, we follow Estrada ' s (2002) suggestions and obtain the correct and unbiased estimation of the downside beta by running the time series regression through origin. The authors carry out the two-pass regression analysis using the generalized method of moment (GMM) in the first pass and the generalized least squares (GLS) estimation method in the second pass.

The results indicate that the mean-variance CAPM shows a negative risk premium for monthly returns of selected stocks. However, the results for the DR-CAPM of Bawa and Lindenberg (1977) and Harlow and Rao (1989) provide evidence of a positive risk premium for the downside beta. In contrast, the DR-CAPM of Estrada (2002) shows a negative risk premium in some sub-periods while the positive premium in the others. By comparing the risk premium for both downside and upside risks in a single-equation framework, the authors show that the stocks that co-vary with a declining market are compensated with a positive premium for bearing the downside risk. Yet, the risk premium for stocks that are negatively correlated with declining market returns is negative for all the three-downside betas in all the examined sub-periods.

The empirical findings of the paper are of great significance for investors for designing effective investment strategies. Specifically, the results help investors to identify an appropriate measure of risk and to construct well-diversified portfolio. The results are also useful for firm managers in capital budgeting decision-making process as they enable them to cost equities appropriately. The results also suggest that the risk-return relationship implied by mean-variance CAPM is negative and therefore this model is not suitable for gauging the risk associated with stocks traded in KSE. Yet, the authors show that DR-CAPM out performs in quantifying the risk premium.

Unlike prior empirical studies, the authors follow Estrada’s (2002) suggestions where downside beta is calculated using regression through origin to find correct and unbiased beta. Departing from the existing literature the authors estimate three different versions of DR-CAPM along with the standard CAPM for comparison purpose. Finally, the authors apply sophisticated econometrics methods that help in lessening the problem of non-synchronous trading and the issue of non-normality of returns distribution.

This article investigates the determinants of cross-section variation of initial public offerings' (IPOs) first-day returns in a sample of 710 issues across seven emerging markets between 2013 and 2017.

Ordinary least squares regression (OLS) and the semi-parametric quantile regression (QR) technique are employed. QR enables to analyse beyond the explanatory variables' relative mean effect at various points in the endogenous variable distribution. Furthermore, parameter estimates under QR are robust to the existence of outliers and long tails in the data distribution.

Underpricing varies across countries with an average of 78%. According to the OLS results, independent variables explain 26% of the variation of IPOs' first-day returns. Findings show that employing QR is important, given the non-normality of the data and because each quantile is associated with a different effect of explanatory variables.

In addition to firm-specific, market-specific and issue-specific factors, the paper extends IPOs' underpricing literature through studying the impact of country-specific characteristics, largely neglected by literature, on IPO underpricing.