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Related Concept Videos

Standard Deviation01:10

Standard Deviation

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The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more variation.
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Variance01:15

Variance

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The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.
The standard deviation measures the spread in the same units as the data....
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Variability: Analysis01:11

Variability: Analysis

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Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...
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Testing a Claim about Standard Deviation01:19

Testing a Claim about Standard Deviation

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A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...
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Regression Toward the Mean01:52

Regression Toward the Mean

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Regression toward the mean (“RTM”) is a phenomenon in which extremely high or low values—for example, and individual’s blood pressure at a particular moment—appear closer to a group’s average upon remeasuring. Although this statistical peculiarity is the result of random error and chance, it has been problematic across various medical, scientific, financial and psychological applications. In particular, RTM, if not taken into account, can interfere when...
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Standard Error of the Mean01:13

Standard Error of the Mean

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The sampling variability of a statistic is defined as how much the statistic varies from one sample to another. The sampling variability of a statistic is typically measured by measuring its standard error.
The standard error of the mean is an example of a standard error. It is a unique standard deviation known as the standard deviation of the sampling distribution of the mean. The standard error of the mean is a statistic that calculates how correctly a sample distribution represents a...
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An R-Based Landscape Validation of a Competing Risk Model
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Market instability and the size-variance relationship.

Sergey V Buldyrev1,2,3, Andrea Flori4, Fabio Pammolli5

  • 1Department of Physics, Yeshiva University, New York, NY, 10033, USA. buldyrev@yu.edu.

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A stochastic model explains mutual fund behavior, showing size-variance relationships can predict financial market instability. This research questions diversification benefits for larger funds.

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Area of Science:

  • Quantitative Finance
  • Financial Market Analysis
  • Systemic Risk Modeling

Background:

  • Mutual fund behavior exhibits complex dynamics not fully captured by traditional models.
  • Understanding the relationship between fund size and growth rate volatility is crucial for financial stability.
  • Periods of market crisis highlight the need for robust risk assessment tools.

Purpose of the Study:

  • To investigate mutual fund behavior using a stochastic proportional growth model.
  • To analyze the size-variance relationship of fund growth rates and its implications during crises.
  • To identify indicators for monitoring financial market instabilities and systemic risk.

Main Methods:

  • Application of a stochastic model of proportional growth to mutual fund data.
  • Statistical analysis of the variance of funds' growth rates in relation to fund size.
  • Examination of volatility changes during crisis periods.

Main Results:

  • The negative dependence of growth rate variance on fund size follows an approximate power law.
  • During crises, the largest funds exhibit increased growth rate volatility compared to mid-sized funds.
  • Growth rate volatility shows a weak dependence on fund size, challenging diversification benefits for large funds.

Conclusions:

  • A lower and flatter slope in the size-variance relationship indicates systemic structure.
  • The slope of the size-variance relationship serves as a synthetic indicator for market instability.
  • Findings question the assumed benefits of diversification for larger mutual funds in volatile markets.