scholarly journals Financial Return Distributions: Past, Present, and COVID-19

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 884
Author(s):  
Marcin Wątorek ◽  
Jarosław Kwapień ◽  
Stanisław Drożdż
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Universal Constant ◽  
Market Dynamics ◽  
Financial Return ◽  
Currency Exchange ◽  
Time Flow ◽  
Two Factors ◽  
Return Distributions ◽  
Real Market

We analyze the price return distributions of currency exchange rates, cryptocurrencies, and contracts for differences (CFDs) representing stock indices, stock shares, and commodities. Based on recent data from the years 2017–2020, we model tails of the return distributions at different time scales by using power-law, stretched exponential, and q-Gaussian functions. We focus on the fitted function parameters and how they change over the years by comparing our results with those from earlier studies and find that, on the time horizons of up to a few minutes, the so-called “inverse-cubic power-law” still constitutes an appropriate global reference. However, we no longer observe the hypothesized universal constant acceleration of the market time flow that was manifested before in an ever faster convergence of empirical return distributions towards the normal distribution. Our results do not exclude such a scenario but, rather, suggest that some other short-term processes related to a current market situation alter market dynamics and may mask this scenario. Real market dynamics is associated with a continuous alternation of different regimes with different statistical properties. An example is the COVID-19 pandemic outburst, which had an enormous yet short-time impact on financial markets. We also point out that two factors—speed of the market time flow and the asset cross-correlation magnitude—while related (the larger the speed, the larger the cross-correlations on a given time scale), act in opposite directions with regard to the return distribution tails, which can affect the expected distribution convergence to the normal distribution.

Influences of Trading Volume on Financial Return Distributions: A Reassessment and a Step Further

2012 ◽  
Author(s):  
Hung Xuan Do ◽  
Robert Darren Brooks ◽  
Sirimon Treepongkaruna ◽  
Eliza Wu
Keyword(s):  
Trading Volume ◽  
Financial Return ◽  
Return Distributions

The two sides of CEO pay injustice

2018 ◽  
Vol 16 (1) ◽  
pp. 3-30 ◽  
Author(s):  
Herman Aguinis ◽  
Geoffrey P. Martin ◽  
Luis R. Gomez-Mejia ◽  
Ernest H. O’Boyle ◽  
Harry Joo
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Chief Executive Officers ◽  
Risk Sharing ◽  
Chief Executive ◽  
Return On Assets ◽  
Content Type ◽  
Ceo Pay ◽  
Executive Officers ◽  
Two Sides

Purpose The purpose of this study was to examine the extent to which chief executive officers (CEOs) deserve the pay they receive both in terms of over and underpayment. Design/methodology/approach Rather than using the traditional normal distribution view in which CEO performance clusters around the mean with relatively little variance, the authors adopt a novel power law approach. They studied 22 industries and N = 4,158 CEO-firm combinations for analyses based on Tobin’s Q and N = 5,091 for analyses based on return on assets. Regarding compensation, they measured the CEO distribution based on total compensation and three components of CEO total pay: salary, bonus, and value of options exercised. Findings In total, 86 percent of CEO performance and 91 percent of CEO pay distributions fit a power law better than a normal distribution, indicating that a minority of CEOs are producing top value for their firms (i.e. CEO performance) and a minority of CEOs are appropriating top value for themselves (i.e. CEO pay). But, the authors also found little overlap between CEOs who are the top performers and CEOs who are the top earners. Implications The findings shed new light on CEO pay deservingness by using a novel conceptual and methodological lens that highlights systematic over and underpayment. Results suggest a violation of distributive justice and offer little support for agency theory’s efficient contracting hypothesis, which have important implications for agency theory, equity theory, justice theory, and agent risk sharing and agent risk bearing theories. Practical implications Results highlight erroneous practices when trying to benchmark CEO pay based on average levels of performance in an industry because the typical approach to CEO compensation based on averages significantly underpays stars and overpays average performers. Originality/value Results offer new insights on the extent of over and underpayment. The findings uncover an extremely large non-overlap between the top earning and top performing CEOs and to an extent far greater in magnitude than previously suggested.

scholarly journals PORTFOLIO RETURN DISTRIBUTIONS: SAMPLE STATISTICS WITH STOCHASTIC CORRELATIONS

2015 ◽  
Vol 18 (02) ◽  
pp. 1550012 ◽  
Author(s):  
DESISLAVA CHETALOVA ◽  
THILO A. SCHMITT ◽  
RUDI SCHÄFER ◽  
THOMAS GUHR
Keyword(s):  
Normal Distribution ◽  
Multivariate Normal Distribution ◽  
Composite Index ◽  
Multivariate Normal ◽  
Correlation Matrices ◽  
Daily Data ◽  
Nasdaq Composite Index ◽  
Return Distributions ◽  
Portfolio Return ◽  
Good Agreement

We consider random vectors drawn from a multivariate normal distribution and compute the sample statistics in the presence of stochastic correlations. For this purpose, we construct an ensemble of random correlation matrices and average the normal distribution over this ensemble. The resulting distribution contains a modified Bessel function of the second kind whose behavior differs significantly from the multivariate normal distribution, in the central part as well as in the tails. This result is then applied to asset returns. We compare with empirical return distributions using daily data from the NASDAQ Composite Index in the period from 1992 to 2012. The comparison reveals good agreement, the average portfolio return distribution describes the data well especially in the central part of the distribution. This in turn confirms our ansatz to model the nonstationarity by an ensemble average.

scholarly journals PEMODELAN DISTRIBUSI TINGKAT IMBAL HASIL INDEKS HARGA DI TUJUH BURSA ASIA

2017 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Brady Rikumahu
Keyword(s):  
Normal Distribution ◽  
Distribution Curve ◽  
Financial Time Series ◽  
Laplace Distribution ◽  
Standard Theory ◽  
Financial Time ◽  
Normal Distribution Curve ◽  
Specific Distribution ◽  
Return Distributions ◽  
Using Data

This paper examines the return distributions of 7 markets in the Asian region, namely Hongkong, Indonesia, Malaysia, Korea, Japan, Shanghai, and Singapore, to find out whether the return distributions in those markets follow a specific distribution. Using data from January 2000 to September 2009, the return distributions of each market were constructed and was first fitted to the normal distribution to find out whether or not each market behaves according to the standard theory of finance and investment – which stated that the financial time series follow a random walk – and thus would fit the normal distribution. The result of fitting the return distributions of the 7 markets to normal distribution shows that none of the return distributions follows the normal distribution as evident from the leptokurtic phenomena marked by the excess kurtosis compared to the normal distribution curve and also from the fatter than normal distribution tails and the existence of returns that lie outside the area predictedby the normal distribution.The return distributions were then fitted to a series of theoretical probability distribution. Each of the distribution was fitted to the theoretical. The results are: the Hongkong and Shanghai markets follow the Laplace distribution while the other five markets: Indonesia, Malaysia, Korea, Japan, and Singapore follow the Johnson SU distribution.

Information spreading on metapopulation networks with heterogeneous contacting

2021 ◽  
Author(s):  
Yanyi Nie ◽  
Liming Pan ◽  
Tao Lin ◽  
Wei Wang
Keyword(s):  
Normal Distribution ◽  
Exponential Distribution ◽  
Power Law ◽  
Social Systems ◽  
Real Data ◽  
Power Law Distribution ◽  
Specific Distribution ◽  
Mean And Variance ◽  
Information Spreading ◽  
Individual Contact

Extensive real-data reveals that individuals exhibit heterogeneous contacting frequency in social systems. We propose a mathematical model to investigate the effects of heterogeneous contacting for information spreading in metapopulation networks. In the proposed model, we assume the number of contacting (NOC) distribution follows a specific distribution, including the normal, exponential, and power-law distributions. We utilize the Markov chain method to study the information spreading dynamics and find that mean and variance display no significant effect on the outbreak threshold for all the considered distributions. Under the same values of NOC distribution’s mean and variance, the information prevalence is largest when the distribution of NOC follows the normal distribution and second-largest for the exponential distribution, the smallest for the power-law distribution. When the distribution of NOC obeys the normal distribution, experimental results show that the information prevalence will decrease with individual contact ability heterogeneity. We observe similar phenomena when the distribution of NOC follows a power-law and exponential distribution. Furthermore, a larger mean of individual contact capacity distribution will result in higher information prevalence.

distribution of the ratio of jointly normal variables

2004 ◽  
Vol 1 (1) ◽  
pp. 99-108
Author(s):  
Anton Cedilnik ◽  
Katarina Košmelj ◽  
Andrej Blejec
Keyword(s):  
Linear Regression ◽  
Normal Distribution ◽  
Inflection Point ◽  
Shape Parameter ◽  
Polynomial Regression ◽  
Bivariate Normal Distribution ◽  
Quadratic Regression ◽  
Bivariate Normal ◽  
Two Factors ◽  
Ratio Of Components

We derive the probability density of the ratio of components of the bivariate normal distribution with arbitrary parameters. The density is a product of two factors, the first is a Cauchy density, the second a very complicated function. We show that the distribution under study does not possess an expected value or other moments of higher order. Our particular interest is focused on the shape of the density. We introduce a shape parameter and show that according to its sign the densities are classified into three main groups. As an example, we derive the distribution of the ratio Z = − Bm−1 /(mBm ) for a polynomial regression of order m. For m=1, Z is the estimator for the zero of a linear regression, for m = 2 , an estimator for the abscissa of the extreme of a quadratic regression, and for m = 3 , an estimator for the abscissa of the inflection point of a cubic regression.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

Diminishing Cognitive Capacities in an Ever Hotter World: Evidence From an Applicable Power-Law Description

2019 ◽  
Vol 61 (6) ◽  
pp. 906-919 ◽  
Author(s):  
José Ignacio López-Sánchez ◽  
P. A. Hancock
Keyword(s):  
Thermal Stress ◽  
Power Law ◽  
Human Performance ◽  
Core Body Temperature ◽  
Universal Constant ◽  
Cognitive Capacities ◽  
Thermal Range ◽  
Scaling Parameters ◽  
Core Body ◽  
Power Law Distributions

Objective: Modeling and evaluating a series of power law descriptions for boundary conditions of undiminished cognitive capacities under thermal stress. Background: Thermal stress degrades cognition, but precisely which components are affected, and to what degree, has yet to be fully determined. With increasing global temperatures, this need is becoming urgent. Power-law distributions have proven their utility in describing differing natural mechanisms, including certain orders of human performance, but never as a rationalization of stress-altered states of attention. Method: From a survey of extant empirical data, absolute thresholds for thermal tolerance for varying forms of cognition were identified. These thresholds were then modeled using a rational power-law description. The implications of the veracity of that description were then identified and analyzed. Results: Cognitive performance thresholds under thermal stress are advanced as power-law relationships, t = f(T) = c[(T – Tref)/Tref]-α. Coherent scaling parameters for diverse cognitive functionalities are specified that are consistent with increases in deep (core) body temperature. Therefore, scale invariance provides a “universal constant,” viz, 20% detriment in mental performance per 10% increase in T deviation, from a comfortable reference temperature Tref. Conclusion: We know the thermal range within which humans can survive is quite narrow. The presented power-law descriptions imply that if making correct decisions is critical for our future existence, then our functional thermal limits could be much more restricted than previously thought. Application: We provide our present findings, such that others can both assess and mitigate the effects of adverse thermal loads on cognition, in whatever human scenario they occur.

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