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Comparison of the Tails of Market Return Distributions

100%
Koronkiewicz G., Jamróz P.
Optimum. Studia Ekonomiczne
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2014
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vol. 5(71)
EN
The aim of this study is to analyze the tails of the distributions of stock market returns and to compare the differences between them. It is a well-established fact that the vast majority of stock market return distributions exhibit fat tails (a bigger probability of extreme outcomes then in the case of the normal probability). Apart from that, there seems to be a popular opinion that most market returns are negatively skewed with a fatter left tail. The study utilizes two methods for comparing the tails of a distribution. A simple approached based on the sample kurtosis, with a modification that allows for the calculation of kurtosis separately for the right and the left tail of a single distribution and a more complex approach based on the maximum likelihood fitting of the Generalized Pareto Distribution to both tales of standardized return distributions. The second approach is based on the assumptions of the Extreme Value Theory (EVT) and the Pickands-Balkema-de Haan theorem. Both approaches provide similar conclusions. Results suggest that whether the left or the right tail of the return distribution is bigger varies from market to market. All four major equity indices of the Polish Warsaw Stock Exchange exhibited a fatter left tale. However, in the whole sample it was actually more common for the right tail to be heavier, with 12 indices out of 20 exhibiting a fatter right tail then the left. The sample kurtosis indicated that all stock market return’s distributions were heavy tailed, whereas the estimates of Generalized Pareto Distribution parameters did indicate standard or thin tails in two cases. Statistical tests indicate that the differences between the tails of stock market distributions are not statistically significant
2

A Comparison of Tail Behaviour of Stock Market Returns

100%
Echaust K.
Folia Oeconomica Stetinensia
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2014
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vol. 14
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issue 1
22-34
EN
Most investors believe that left tails of the stock returns distribution are heavier than the right ones. It is a natural consequence of crashes perception as much more turbulent than the booms. Crashes develop in shorter time intervals than booms and changes of prices are significantly bigger. This paper focuses on the extreme behavior of stock market returns. The differences in the tails thickness of distribution are negligible. Its main result is that the differences between tails have been found in the clustering of extremes, especially during the crash of 2007-2009.
3

A Comparative Analysis of Value at Risk Measurement on Emerging Stock Markets: Case of Montenegro

75%
Cerović J., Lipovina-Božović M., Vujošević S.
Business Systems Research Journal
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2015
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vol. 6
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issue 1
36-55
EN
Background: The concept of value at risk gives estimation of the maximum loss of financial position at a given time for a given probability. The motivation for this analysis lies in the desire to devote necessary attention to risks in Montenegro, and to approach to quantifying and managing risk more thoroughly. Objectives: This paper considers adequacy of the most recent approaches for quantifying market risk, especially of methods that are in the basis of extreme value theory, in Montenegrin emerging market before and during the global financial crisis. In particular, the purpose of the paper is to investigate whether extreme value theory outperforms econometric and quantile evaluation of VaR in emerging stock markets such as Montenegrin market. Methods/Approach: Daily return of Montenegrin stock market index MONEX20 is analyzed for the period January, 2004 - February, 2014. Value at Risk results based on GARCH models, quantile estimation and extreme value theory are compared. Results: Results of the empirical analysis show that the assessments of Value at Risk based on extreme value theory outperform econometric and quantile evaluations. Conclusions: It is obvious that econometric evaluations (ARMA(2,0)- GARCH(1,1) and RiskMetrics) proved to be on the lower bound of possible Value at Risk movements. Risk estimation on emerging markets can be focused on methodology using extreme value theory that is more sophisticated as it has been proven to be the most cautious model when dealing with turbulent times and financial turmoil.
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An approach to measuring the relation between risk and return. Bayesian analysis for WIG data

63%
Pipień M.
Folia Oeconomica Cracoviensia
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2007
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vol. 48
95-117
EN
The main goal of this paper is an application of Bayesian inference in testing the relation between risk and return of the financial time series. On the basis of the Intertemporal CAl’M model, proposed by Merton (1973), we built a general sampling model suitable in analysing such relationship. The most important feature of our model assumptions is that the possible skewness of conditional distribution of returns is used as an alternative source of relation between risk and return. Thus, pure statistical feature of the sampling model is equipped with economic interpretation. This general specification relates to GARCH-In-Mean model proposed by Osiewalski and Pipień (2000). In order to make conditional distribution of financial returns skewed we considered a constructive approach based on the inverse probability integral transformation. In particular, we apply the hidden truncation mechanism, two approaches based on the inverse scale factors in the positive and the negative orthant, order statistics concept, Beta distribution transformation, Bernstein density transformation and the method recently proposed by Ferreira and Steel (2006). Based on the daily excess returns of WIG index we checked the total impact of conditional skewness assumption on the relation between return and risk on the Warsaw Stock Market. Posterior inference about skewness mechanisms confirmed positive and decisively significant relationship between expected return and risk. The greatest data support, as measured by the posterior probability value, receives model with conditional skewness based on the Beta distribution transform ation with two free parameters.
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