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Related Concept Videos

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.
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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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Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
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Range Rule of Thumb to Interpret Standard Deviation01:13

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The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
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In the field of psychology, there are several ways to organize measurements of a trait, feature, or characteristic (i.e., variables). Qualitative data, such as ethnicity, can be tabulated into a frequency count to provide information about the proportion, as well as the variety of groups in a sample or population. On the other hand, researchers can perform a wider set of calculations on quantitative data. The mean, mode, and median, for instance, are central tendency measures to identify a...
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Range-based volatility, expected stock returns, and the low volatility anomaly.

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  • 1Department of Economics and Finance, Jon M. Huntsman School of Business, Utah State University, Logan, Utah, United States of America.

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This study reveals that higher stock volatility is linked to lower future returns, confirming the low volatility anomaly. This challenges traditional financial economics theories by showing low volatility stocks outperform high volatility stocks.

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Area of Science:

  • Financial Economics
  • Quantitative Finance

Background:

  • Traditional financial economics posits a positive risk-return relationship.
  • Empirical evidence on the risk-return relationship, particularly concerning volatility, remains mixed.

Purpose of the Study:

  • To investigate the relationship between stock risk (volatility) and future returns.
  • To assess the efficacy of a novel range-based volatility measure.

Main Methods:

  • Utilized a range-based measure of volatility, deemed superior to existing methods.
  • Employed time-series multifactor models and cross-sectional tests for robustness checks.

Main Results:

  • Found a significant negative association between range-based volatility and expected stock returns.
  • Confirmed the low volatility anomaly: lower volatility stocks yield higher returns.

Conclusions:

  • The study supports the low volatility anomaly, challenging conventional risk-return paradigms.
  • Identified lottery-like stock characteristics as a driver for lower returns in high volatility stocks.