The Role of the Normal Distribution in Financial Markets

Costa, Michele; Cavaliere, Giuseppe; Iezzi, Stefano

doi:10.1007/3-540-27373-5_41

Cited by 7 publications

(3 citation statements)

References 11 publications

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“…We know that the hypothesis that financial variables are normally distributed is often rejected in theoretical studies and particular cases. However, Costa et al [ 38 ] argue that in the “real” world of financial investors, where risk-averse agents mainly hold government bonds and a few equities and do not hold derivatives, the normal distribution still plays a lead role. Hence, the normal distribution assumption outperforming the skewed-Student t distribution assumption in this study should not be surprising.…”

Section: Discussionmentioning

confidence: 99%

A K-Means Classification and Entropy Pooling Portfolio Strategy for Small and Large Capitalization Cryptocurrencies

Clément

Angaman

2023

Entropy

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In this study, we propose three portfolio strategies: allocation based on the normality assumption, the skewed-Student t distribution, and the entropy pooling (EP) method for 14 small- and large-capitalization (cap) cryptocurrencies. We categorize our portfolios into three groups: portfolio 1, consisting of three large-cap cryptocurrencies and four small-cap cryptocurrencies from various K-means classification clusters; and portfolios 2 and 3, consisting of seven small-cap and seven large-cap cryptocurrencies, respectively. Then, we investigate the performance of the proposed strategies on these portfolios by performing a backtest during a crypto market crash. Our backtesting covers April 2022 to October 2022, when many cryptocurrencies experienced significant losses. Our results indicate that the wealth progression under the normality assumption exceeds that of the other two strategies, though they all exhibit losses in terms of final wealth. In addition, we found that portfolio 3 is the best-performing portfolio in terms of wealth progression and performance measures, followed by portfolios 1 and 2, respectively. Hence, our results suggest that investors will benefit from investing in a portfolio consisting of large-cap cryptocurrencies. In other words, it may be safer to invest in large-cap cryptocurrencies than in small-cap cryptocurrencies. Moreover, our results indicate that adding large- and small-cap cryptocurrencies to a portfolio could improve the diversification benefit and risk-adjusted returns. Therefore, while cryptocurrencies may offer potentially high returns and diversification benefits in a portfolio, investors should be aware of the risks and carefully consider their investment objectives and risk tolerance before investing in them.

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Section: Discussionmentioning

confidence: 99%

A K-Means Classification and Entropy Pooling Portfolio Strategy for Small and Large Capitalization Cryptocurrencies

Clément

Angaman

2023

Entropy

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“…The quenched random numbers are chosen from normal distribution because of its ubiquitous nature, such as velocity distribution of an ideal gas [31], in optics, the Gaussian beam [32] is a monochromatic electromagnetic radiation and its amplitude evolves as a Gaussian function, the width of spectral lines, and the distribution of noise in radio receivers are normally distributed [33]. There numerous other examples from the field of finance [34], biology [35] and astronomy [36] where normal distributions are used. Moreover, the central limit theorem guarantees that any distribution for large sample size, and for finite values of variance will converge to a normal distribution.…”

Section: Introductionmentioning

confidence: 99%

Entanglement and avoided crossing dynamics in the disordered Majumdar-Ghosh model

Barkataki

Ramkarthik

2021

Phys. Scr.

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We study the ground and first excited state of the finite one dimensional Majumdar-Ghosh model with quenched disorder about the avoided crossings. We find a relation between the shift of the first avoided crossing and average value of random numbers. For low disorder regime, the two-qubit, odd and even partition entanglement gets exchanged at avoided crossings for low spin, and former two for any value of spin. This effect has a deep relation with the dimerization nature of these states. We develop an expression sans entanglement measures to detect and study these crossings.

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“…Normality of the data is the underlying distributional assumption of multitude of statistical procedures and estimation techniques. In both cross-sectional and time series data, assuming the data normality without testing may affect the accuracy of the econometric inference [ 1 ]. Statistical inference from regression models applied to time series [ 2 ], categorical [ 3 ] and count data [ 4 ] depends crucially on the assumption of normal errors.…”

Section: Introductionmentioning

confidence: 99%

Min-max approach for comparison of univariate normality tests

Islam

2021

PLoS ONE

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Comparison of normality tests based on absolute or average powers are bound to give ambiguous results, since these statistics critically depend upon the alternative distribution which cannot be specified. A test which is optimal against a certain type of alternatives may perform poorly against other alternative distributions. Thus, an invariant benchmark is proposed in the recent normality literature by computing Neyman-Pearson tests against each alternative distribution. However, the computational cost of this benchmark is significantly high, therefore, this study proposes an alternative approach for computing the benchmark. The proposed min-max approach reduces the calculation cost in terms of computing and estimating the Neyman-Pearson tests against each alternative distribution. An extensive simulation study is conducted to evaluate the selected normality tests using the proposed methodology. The proposed min-max method produces similar results in comparison with the benchmark based on Neyman-Pearson tests but at a low computational cost.

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The Role of the Normal Distribution in Financial Markets

Cited by 7 publications

References 11 publications

A K-Means Classification and Entropy Pooling Portfolio Strategy for Small and Large Capitalization Cryptocurrencies

A K-Means Classification and Entropy Pooling Portfolio Strategy for Small and Large Capitalization Cryptocurrencies

Entanglement and avoided crossing dynamics in the disordered Majumdar-Ghosh model

Min-max approach for comparison of univariate normality tests

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