# on 23-Jul-2017 (Sun)

#### Flashcard 1621391707404

Tags
#tvm
Question
The [...] compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1633823362316

Tags
Question
Periodic bond yields for both straight and zero-coupon bonds are conventionally computed based on [...]
semi-annual periods

status measured difficulty not learned 37% [default] 0

Subject 5. Bond Equivalent Yield
Periodic bond yields for both straight and zero-coupon bonds are conventionally computed based on semi-annual periods, as U.S. bonds typically make two coupon payments per year. For example, a zero-coupon bond with a maturity of five years will mature in 10 6-month periods. The periodic yield for that

#### Flashcard 1636484648204

Tags
Question
In the [...] the midpoint of each class (interval) is shown on the horizontal (x) axis.
Frequency Polygon

status measured difficulty not learned 37% [default] 0

Subject 3. Frequency Distributions
f graphically displaying data. It is similar to a histogram but the bars are replaced by a line joined together. It is constructed in the following manner: Absolute frequency for each interval is plotted on the vertical (y) axis. <span>The midpoint of each class (interval) is shown on the horizontal (x) axis. Neighboring points are connected with a straight line. Unlike a histogram, a frequency polygon adds a degree of continuity to the presentation of the distribution. It

#### Flashcard 1636822027532

Tags
Question
In a frequency distribution If too few intervals are used, [...].
too much data may be summarized and we may lose important characteristics

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
In a frequency distribution It is important to consider the number of intervals to be used. If too few intervals are used, too much data may be summarized and we may lose important characteristics; if too many intervals are used, we may not summarize enough.

#### Original toplevel document

Subject 3. Frequency Distributions
that: Each observation can only lie in one interval. The total number of intervals will incorporate the whole population. The range for an interval is unique. This means a value (observation) can only fall into one interval. <span>It is important to consider the number of intervals to be used. If too few intervals are used, too much data may be summarized and we may lose important characteristics; if too many intervals are used, we may not summarize enough. A frequency distribution is constructed by dividing the scores into intervals and counting the number of scores in each interval. The actual number of scores and the percent

#### Flashcard 1636830416140

Tags
Question
The following steps are required when organizing data into a frequency distribution.
• Identify the highest and lowest values of the observations

• [...]

• Add up the number of observations and assign each observation to its class.

• Count the number of observations in each class.
Setup classes (groups into which data is divided).

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
The following steps are required when organizing data into a frequency distribution together with suggestions on constructing the frequency distribution. Identify the highest and lowest values of the observations. Setup classes (groups into which data is divided). The classes must be mutually exclusive and of equal size. Add up the number of observations and assign

#### Original toplevel document

Subject 3. Frequency Distributions
by the total number of observations. Cumulative absolute frequency and cumulative relative frequency are the results from cumulating the absolute and relative frequencies as we move from the first to the last interval. <span>The following steps are required when organizing data into a frequency distribution together with suggestions on constructing the frequency distribution. Identify the highest and lowest values of the observations. Setup classes (groups into which data is divided). The classes must be mutually exclusive and of equal size. Add up the number of observations and assign each observation to its class. Count the number of observations in each class. This is called the class frequency. Data can be divided into two types: discrete and continuous. Discrete: The values in the data set can be counted. There are distinct spaces between the values, such as

#### Flashcard 1640946339084

Question
RTE Act is applicable to which age group?
The RTE Act, 2009 envisages free and compulsory elementary education to every child in the age group of 6-14 years

status measured difficulty not learned 37% [default] 0
Daily Current Affairs for IAS UPSC Exam Preparation – Civilsdaily
recommendations Better monitoring of funds allocated. Centre and states to finalize an annual work plan and budget for RTE in alignment with the Union budget for better coordination and utilization. Back2basics The RTE Act, 2009 <span>The RTE Act, 2009 envisages free and compulsory elementary education to every child in the age group of 6-14 years . The section 23(2) of the Act specifies that all teachers at elementary level at commencement of this law if did not possess minimum qualifications under it need to acquire these w

#### Annotation 1640983301388

 #fta #un #wto Trade Facilitation Agreement (TFA) The TFA is the WTO’s first-ever multilateral accord that aims to simplify customs regulations for the cross-border movement of goods. It was outcome of WTO’s 9th Bali (Indonesia) ministerial package of 2013The agreement includes provisions for Lowering import tariffs and agricultural subsidies: It will make it easier for developing countries to trade with the developed world in global marketsAbolish hard import quotas: Developed countries would abolish hard import quotas on agricultural products from the developing world and instead would only be allowed to charge tariffs on amount of agricultural imports exceeding specific limitsReduction in red tape at international borders: It aims to reduce red-tapism to facilitate trade by reforming customs bureaucracies and formalities

Daily Current Affairs for IAS UPSC Exam Preparation – Civilsdaily
s reforms and modernization The WCO maintains the international Harmonized System (HS) goods nomenclature, and administers the technical aspects of the World Trade Organization (WTO) Agreements on Customs Valuation and Rules of Origin <span>Trade Facilitation Agreement (TFA) The TFA is the WTO’s first-ever multilateral accord that aims to simplify customs regulations for the cross-border movement of goods. It was outcome of WTO’s 9th Bali (Indonesia) ministerial package of 2013 The agreement includes provisions for Lowering import tariffs and agricultural subsidies: It will make it easier for developing countries to trade with the developed world in global markets Abolish hard import quotas: Developed countries would abolish hard import quotas on agricultural products from the developing world and instead would only be allowed to charge tariffs on amount of agricultural imports exceeding specific limits Reduction in red tape at international borders: It aims to reduce red-tapism to facilitate trade by reforming customs bureaucracies and formalities. The Hindu July 22, 2017 [op-ed snap] The need for lateral entry in civil services [imagelink] Image source Note4studert

#### Flashcard 1641148976396

Tags
Question
The periodic investment of a fixed amount of money.
Cost averaging

status measured difficulty not learned 37% [default] 0

#### Annotation 1641150811404

 #reading-8-statistical-concepts-and-market-returns The harmonic mean is a relatively specialized concept of the mean that is appropriate when averaging ratios (“amount per unit”) when the ratios are repeatedly applied to a fixed quantity to yield a variable number of units.

#### Annotation 1641155005708

 Dollar-cost averaging (DCA) is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. The investor purchases more shares when prices are low and fewer shares when prices are high. The premise is that DCA lowers the average share cost over time, increasing the opportunity to profit. The DCA technique does not guarantee that an investor won't lose money on investments. Rather, it is meant to allow investment over time instead of investment as a lump sum.

Dollar-Cost Averaging (DCA)
What is 'Dollar-Cost Averaging - DCA' <span>Dollar-cost averaging (DCA) is an investment technique of buying a fixed dollar amount of a particular investment on a regular schedule, regardless of the share price. The investor purchases more shares when prices are low and fewer shares when prices are high. The premise is that DCA lowers the average share cost over time, increasing the opportunity to profit. The DCA technique does not guarantee that an investor won't lose money on investments. Rather, it is meant to allow investment over time instead of investment as a lump sum. BREAKING DOWN 'Dollar-Cost Averaging - DCA' Fundamental to the strategy is a commitment to investing a fixed dollar amount each month. Depending

#### Flashcard 1641157102860

Tags
Question
Unless all the observations in a data set have the same value, the [...] is less than the geometric mean
harmonic mean

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641158937868

Tags
Question
What is a good example on when to use the Harmonic Mean?
Cost Averaging (lo que hiciste con Javier)

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641160772876

Tags
#has-images #quantitative-methods-basic-concepts #statistics
Question
For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by:

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
rs x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. <span>For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: <span><body><html>

#### Original toplevel document

Subject 4. Measures of Center Tendency
, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

#### Flashcard 1641163132172

Tags
#has-images #quantitative-methods-basic-concepts #statistics
Question
The special cases of n = 2 Harmonic Mean

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mea

#### Original toplevel document

Subject 4. Measures of Center Tendency
, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

#### Flashcard 1641164705036

Tags
#has-images #quantitative-methods-basic-concepts #statistics
Question
The special cases of n = 3 for the Harmonic Mean are given by:

status measured difficulty not learned 37% [default] 0

#### Parent (intermediate) annotation

Open it
Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mea

#### Original toplevel document

Subject 4. Measures of Center Tendency
, therefore, is not recommended for use as the only measure of central tendency. A further disadvantage of the mode is that many distributions have more than one mode. These distributions are called "multimodal." <span>Harmonic Mean The harmonic mean of n numbers x i (where i = 1, 2, ..., n) is: The special cases of n = 2 and n = 3 are given by: and so on. For n = 2, the harmonic mean is related to arithmetic mean A and geometric mean G by: The mean, median, and mode are equal in symmetric distributions. The mean is higher than the median in positively skewed distributions and lower than the median in negatively skewed dist

#### Flashcard 1641167588620

Tags
Question
If talking about a Survey is it a population or a sample?
Sample

status measured difficulty not learned 37% [default] 0

#### Annotation 1641169423628

 #reading-8-statistical-concepts-and-market-returns What are the reasons for sampling? Sampling is used when: 1. The population is infinite. 2. There is a limited amount of time available. 3. The nature of the test is destructive. 4. The cost of gathering the data is a factor.

#### Flashcard 1641171520780

Tags
Question
When in a histograms there are only midpoints showing how do you find out the interval width?
substract any Midpoint - Midpoint-1 and you have the interval width.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641173355788

Tags
Question
What is class mark in a Frequency distribution?
The average of the values of the class limits

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641175190796

Tags
Question
The class mark is also called [...]
Midvalue or central value

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641179909388

Tags
Question
Quantiles that divide a distribution into four equal parts.
Quartiles

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641181744396

Tags
Question
Quantiles that divide a distribution into five equal parts.
Quintiles

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641183579404

Tags
Question
Quantiles that divide a distribution into 100 equal parts.
Percentiles

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641185414412

Tags
Question
Given a set of observations, how many observations lie below the 33th percentile?
33%

status measured difficulty not learned 37% [default] 0

#### Annotation 1641188035852

 #reading-8-statistical-concepts-and-market-returns When dealing with actual data, we often find that we need to approximate the value of a percentile. For example, if we are interested in the value of the 75th percentile, we may find that no observation divides the sample such that exactly 75 percent of the observations lie at or below that value. The following procedure, however, can help us determine or estimate a percentile. The procedure involves first locating the position of the percentile within the set of observations and then determining (or estimating) the value associated with that position.

#### Flashcard 1641189870860

Tags
Question
We know that the median divides a distribution in half. We can define other dividing lines that split the distribution into smaller sizes called [...]
Quantiles

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641191705868

Tags
Question

The formula for the position of a percentile in an array with n entries sorted in ascending order is

Ly = [...]

(n+1) y/100

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641193540876

Tags
Question

The value of Ly may or may not be a [...]

whole number.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641195375884

Tags
Question

In general, as the sample size increases, the percentile location calculation becomes [...]

more accurate;

in small samples it may be quite approximate.​​​​​​​

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641197210892

Tags
Question

When the location, Ly, is a whole number, the location corresponds to [...]

an actual observation.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641199045900

Tags
Question

When Ly is not a whole number or integer, Ly lies [...]

between the two closest integer numbers

(one above and one below)​​​​​​​

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641200880908

Tags
Question

When Ly is not a whole number or integer, Ly lies between the two closest integer numbers (one above and one below), and we use [...] between those two places to determine Py.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641202715916

Tags
Question

The estimation of an unknown value on the basis of two known values that bracket it, using a straight line between the two known values.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641204550924

Tags
Question

Linear interpolation for a value of 12.75 for Py

Py[...]

X12 + (12.75 − 12) (X13X12).

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641206385932

Tags
Question

Using [...] we move the percent of the distance above the integer (e.g 12.75-12= 75%) from X12 to X13 as an estimate of Py.

linear interpolation

status measured difficulty not learned 37% [default] 0

#### Flashcard 1641208220940

Tags
Question

The nearest whole numbers below and above Ly establish the positions of observations that bracket Py and then [...] of those two observations.

interpolate between the values

status measured difficulty not learned 37% [default] 0

#### Annotation 1644271111436

 He was committed to the scientific study of society, empirical research, and the search for causes of social phenomena. He devoted considerable attention to various social institu- tions (for example, politics, economy) and their interrelationships. He was inter- ested in comparing primitive and modern societies

#### pdf

cannot see any pdfs

#### Annotation 1644272684300

 Ibn-Khaldun stressed the importance of linking socio- logical thought and historical observation

#### pdf

cannot see any pdfs

#### Annotation 1644274257164

 he served a variety of sultans in Tunis, Morocco, Spain, and Algeria as ambassador, chamberlain, and member of the scholars’ council. He also spent two years in prison in Morocco for his belief that state rulers were not divine leaders

#### pdf

cannot see any pdfs

#### Annotation 1644295752972

 Investment styles #reading-8-statistical-concepts-and-market-returns (1) firm size (buying stocks of small firms and selling stocks of large firms), (2) value/growth (buying stocks of value firms, defined as firms for which the stock price is relatively low in relation to earnings per share, book value per share, or dividends per share, and selling stocks of growth firms, defined as firms for which the stock price is relatively high in relation to those same measures)

#### Annotation 1644297587980

 Investment styles #reading-8-statistical-concepts-and-market-returns As the well-known researcher Fischer Black has written, “[t]he key issue in investments is estimating expected return.”

#### Flashcard 1644299422988

Tags
Question
The mean tells us where returns are centered but, to completely understand an investment, we also need to know how returns are [...]
dispersed around the mean.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644301257996

Tags
Question
[...] is the variability around the central tendency.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644303093004

Tags
Question
The most common measures of dispersion: [...] , [...] , variance, and standard deviation.
mean absolute deviation

range

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644304928012

Tags
Question
The most common measures of dispersion: mean absolute deviation, [...], range and [...]
variance

standard deviation.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644306763020

Tags
Question
The amount of variability present without comparison to any reference point or benchmark.
Absolute Dispersion

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644308598028

Tags
Question
The [...] or [...] of return is often used as a measure of risk pioneered by Nobel laureate Harry Markowitz.
variance

standard deviation

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644310695180

Tags
Question
The simplest of all the measures of dispersion is [...]
range

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644312005900

Tags
Question
Range can be computed with [...] or [...] data.
interval

ratio

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644315413772

Tags
Question
The difference between the maximum and minimum values in a dataset.
Range

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644317248780

Tags
Question
• Range = [...]

Maximum value – Minimum value

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644319083788

Tags
Question

how the data are distributed is called the [...]

shape of the distribution

status measured difficulty not learned 37% [default] 0

#### Annotation 1644320918796

 Interquartile Range #reading-8-statistical-concepts-and-market-returns Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q3 − Q1. The IQR represents the length of the interval containing the middle 50 percent of the data, with a larger interquartile range indicating greater dispersion, all else equal.

#### Flashcard 1644322753804

Tags
Question
The interquartile range is a [...]
distance measure of dispersion

status measured difficulty not learned 37% [default] 0

Interquartile Range
Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles o

#### Flashcard 1644325113100

Tags
Question
The interquartile range, focuses on [...] rather than [...] .
The middle

the extremes

status measured difficulty not learned 37% [default] 0

Interquartile Range
Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q 3 − Q 1 . The IQR represents the length of the interval containing the mi

#### Flashcard 1644327472396

Tags
Question
The interquartile range (IQR) is the difference between [...]
the third and first quartiles of a data set

status measured difficulty not learned 37% [default] 0

Interquartile Range
Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q 3 − Q 1 . The IQR represents the length of the interval containing the middle 50 percent of the data, with a larger interquartile range indicating greater dispersion, all else

#### Flashcard 1644329831692

Tags
Question
IQR = [...]
Q3Q1

status measured difficulty not learned 37% [default] 0

Interquartile Range
span>Another distance measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: <span>IQR = Q 3 − Q 1 . The IQR represents the length of the interval containing the middle 50 percent of the data, with a larger interquartile range indicating greater dispersion, all else equal.</sp

#### Flashcard 1644332190988

Tags
Question
The IQR represents the length of the interval containing [...] of the data,
the middle 50 percent

status measured difficulty not learned 37% [default] 0

Interquartile Range
ce measure of dispersion that we may encounter, the interquartile range, focuses on the middle rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q 3 − Q 1 . <span>The IQR represents the length of the interval containing the middle 50 percent of the data, with a larger interquartile range indicating greater dispersion, all else equal.<span><body><html>

#### Flashcard 1644334550284

Tags
Question
All else equal, a larger interquartile range indicaties [...]
greater dispersion.

status measured difficulty not learned 37% [default] 0

Interquartile Range
le rather than the extremes. The interquartile range (IQR) is the difference between the third and first quartiles of a data set: IQR = Q 3 − Q 1 . The IQR represents the length of the interval containing the middle 50 percent of the data, <span>with a larger interquartile range indicating greater dispersion, all else equal.<span><body><html>

#### Flashcard 1644336909580

Tags
Question

The difference between the third and first quartiles of a dataset.

Interquatile range

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644338744588

Tags
Question

Why don't we compute measures of dispersion as the arithmetic average of the deviations around the mean?

The deviations around the mean always sum to 0.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644340579596

Tags
Question

With reference to a sample, the mean of the absolute values of deviations from the sample mean.

Mean Absolute Deviation

status measured difficulty not learned 37% [default] 0

Article 1644342676748

Subject 6. Measures of Dispersion

Dispersion is defined as "variability around the central tendency." Investment is all about reward versus variability (risk). A central tendency is a measure of the reward of an investment and dispersion is a measure of investment risk. There are two types of dispersions: Absolute dispersion is the amount of variability without comparison to any benchmark. Measures of absolute dispersion include range, mean absolute deviation, variance, and standard deviation. Relative dispersion is the amount of variability in comparison to a benchmark. Measures of relative dispersion include the coefficient of variance. The range is the simplest measure of spread or dispersion. It is equal to the difference between the largest and the smallest values. The range can be a useful measure of spread because it is so easily understood. However, it is very sensitive to extreme scores because it is based on only two values. It also cannot reveal the shape of the distribution. The range should almost never be u

#### Flashcard 1644351851788

Tags
Question

The mean absolute deviation formula

status measured difficulty not learned 37% [default] 0
Subject 6. Measures of Dispersion
artile range. Example The range of the numbers 1, 2, 4, 6,12,15,19, 26 = 26 - 1 = 25 Recall that the deviation from the arithmetic mean is the distance between the mean and an observation in the data set. <span>The mean absolute deviation (MAD) is the arithmetic average of the absolute deviations around the mean. In calculating the MAD, we ignore the signs of deviations around the mean. Remember that the sum of all the deviations from the mean is equal to

#### Flashcard 1644353424652

Tags
Question

The mean absolute deviation (MAD) is the [...] of [...]

arithmetic average

the absolute deviations around the mean.

status measured difficulty not learned 37% [default] 0
Subject 6. Measures of Dispersion
artile range. Example The range of the numbers 1, 2, 4, 6,12,15,19, 26 = 26 - 1 = 25 Recall that the deviation from the arithmetic mean is the distance between the mean and an observation in the data set. <span>The mean absolute deviation (MAD) is the arithmetic average of the absolute deviations around the mean. In calculating the MAD, we ignore the signs of deviations around the mean. Remember that the sum of all the deviations from the mean is equal to

#### Flashcard 1644356046092

Tags
Question

In calculating MAD, we ignore [...] of the deviations around the mean.

the signs

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644357881100

Tags
Question

One technical drawback of MAD is that it is difficult to manipulate mathematically compared with the [...] .

variance

status measured difficulty not learned 37% [default] 0

#### Annotation 1644359716108

 In some analytic work such as optimization, the calculus operation of differentiation is important. Variance as a function can be differentiated, but absolute value cannot.

#### Flashcard 1644362075404

Tags
Question

A second approach to the treatment of deviations adding up to 0 is to [...]

square them.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644363910412

Tags
Question

The expected value of squared deviations from a random variable’s expected value.

Variance

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644366007564

Tags
Question

[...] is defined as the average of the squared deviations around the mean

Variance

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644367842572

Tags
Question

[...] is the positive square root of the variance.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644369677580

Tags
Question

The positive square root of the variance; a measure of dispersion in the same units as the original data.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644371512588

Tags
Question

The formula for the variance in a population is

status measured difficulty not learned 37% [default] 0
Subject 6. Measures of Dispersion
ons in the sample. However, the absolute value is difficult to work with mathematically. The variance is a measure of how spread out a distribution is. It is computed as the average squared deviation of each number from its mean. <span>The formula for the variance in a population is where: μ = the mean N = the number of scores When the variance is computed in a sample, the statistic(m = the mean of the sample) can be used

#### Flashcard 1644373871884

Tags
Question

Because the variance is measured in squared units, we need a way to return to the original units thus the [...]

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644375706892

Tags
Question

Standard deviation is the [...]

square root of the variance.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644377541900

Tags
Question
When the variance is computed in a sample, the formula is [...]

status measured difficulty not learned 37% [default] 0
Subject 6. Measures of Dispersion
read out a distribution is. It is computed as the average squared deviation of each number from its mean. The formula for the variance in a population is where: μ = the mean N = the number of scores <span>When the variance is computed in a sample, the statistic(m = the mean of the sample) can be used. However, s 2 is a biased estimate of σ 2 . By far the most common formula for computing variance in a sample is: &#13

#### Annotation 1644380163340

 Forbes magazine annually selects US equity mutual funds meeting certain criteria for its Honor Roll. The criteria relate to capital preservation (performance in bear markets), continuity of management (the fund must have a manager with at least six years’ tenure), diversification, accessibility (disqualifying funds that are closed to new investors), and after-tax long-term performance.

#### Annotation 1644381998348

 We could not properly use the Honor Roll funds to estimate the population variance of portfolio turnover (for example) of any other differently defined population, because the Honor Roll funds are not a random sample from any larger population of US equity mutual funds.

#### Flashcard 1644383833356

Tags
Question

We use [...] to symbolize sample quantities.

Roman letters

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644386454796

Tags
Question
The formula for computing variance in a sample is:

s2 = [...]

status measured difficulty not learned 37% [default] 0
Subject 6. Measures of Dispersion
n is where: μ = the mean N = the number of scores When the variance is computed in a sample, the statistic(m = the mean of the sample) can be used. However, s 2 is a biased estimate of σ 2 . By far <span>the most common formula for computing variance in a sample is: This gives an unbiased estimate of σ 2 . Since samples are usually used to estimate parameters, s 2 is the most commonly used measure of variance

#### Annotation 1644388814092

 #reading-8-statistical-concepts-and-market-returns In the math of statistics, using only N in the denominator when using a sample to represent its population will result in underestimating the population variance, especially for small sample sizes. This systematic understatement causes the sample variance to be a biased estimator of the population variance. By using (N - 1) instead of N in the denominator, we compensate for this underestimation. Thus, using N - 1, the sample variance (s2) will be an unbiased estimator of the population variance (σ2).

Subject 6. Measures of Dispersion
tion variance except for the use of the sample mean, X, and the denominator. In the case of the population variance, we divide by the size of the population, N. For the sample variance, however, we divide by the sample size minus 1, or N - 1. <span>In the math of statistics, using only N in the denominator when using a sample to represent its population will result in underestimating the population variance, especially for small sample sizes. This systematic understatement causes the sample variance to be a biased estimator of the population variance. By using (N - 1) instead of N in the denominator, we compensate for this underestimation. Thus, using N - 1, the sample variance (s 2 ) will be an unbiased estimator of the population variance (σ 2 ). The major problem with using the variance is the difficulty interpreting it. Why? The variance, unlike the mean, is in terms of units squared. How does one interpret square

#### Flashcard 1644390386956

Tags
Question

By using [...] , we improve the statistical properties of the sample variance.

n − 1 (rather than n) as the divisor

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644392221964

Tags
Question

The quantity n − 1 is also known as the number of [...] in estimating the population variance.

degrees of freedom

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644394056972

Tags
Question

Once we have computed the sample mean, there are only [...] independent deviations from it.

n − 1

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644395891980

Tags
Question

The sample standard deviation is [...]

The positive square root of the sample variance.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644397726988

Tags
Question

The mean absolute deviation will always be less than or equal to the standard deviation because [...]

standard deviation gives more weight to large deviations than to small ones

(remember, the deviations are squared).

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644399037708

Tags
Question

The mean absolute deviation will always be [...] to the standard deviation

less than or equal

status measured difficulty not learned 37% [default] 0

#### Annotation 1644402183436

 Because the standard deviation is a measure of dispersion about the arithmetic mean, we usually present the arithmetic mean and standard deviation together when summarizing data. When we are dealing with data that represent a time series of percent changes, presenting the geometric mean—representing the compound rate of growth—is also very helpful.

#### Annotation 1644404804876

 Variance and standard deviation of returns take account of returns above and below the mean, but investors are concerned only with downside risk, for example, returns below the mean. As a result, analysts have developed semivariance, semideviation, and related dispersion measures that focus on downside risk.

#### Flashcard 1644406639884

Tags
Question

[...] is defined as the average squared deviation below the mean.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644408474892

Tags
Question

[...] is the positive square root of semivariance.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644410309900

Tags
Question

Semideviation is sometimes called [...]

Semistandard deviation

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644412144908

Tags
Question

To compute the sample semivariance, for example, we take the following steps:

1. Calculate the sample mean.

2. [...] .

3. Compute the sum of the squared negative deviations from the mean.

4. Divide the sum from Step iii by [...] .

Identify the observations that are smaller than or equal to the mean (discarding observations greater than the mean)

the total sample size minus 1: n − 1

status measured difficulty not learned 37% [default] 0

#### Annotation 1644413979916

 #reading-8-statistical-concepts-and-market-returns An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score.

Subject 6. Measures of Dispersion
variance indicates the adequacy of the mean as representative of the population by measuring the deviation from expectation. Basically, the variance and the standard deviation are measures of the average deviation from the mean. <span>An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score. In a normal distribution, about 68% of the scores are within one standard deviation of the mean and about 95% of the scores are within two standards deviations of the mean.

#### Annotation 1644415552780

 #reading-8-statistical-concepts-and-market-returns In a normal distribution, about 68% of the scores are within one standard deviation of the mean and about 95% of the scores are within two standards deviations of the mean.

Subject 6. Measures of Dispersion
An important attribute of the standard deviation as a measure of spread is that if the mean and standard deviation of a normal distribution are known, it is possible to compute the percentile rank associated with any given score. <span>In a normal distribution, about 68% of the scores are within one standard deviation of the mean and about 95% of the scores are within two standards deviations of the mean. The standard deviation has proven to be an extremely useful measure of spread in part because it is mathematically tractable. Many formulas in inferential statistics use th

#### Flashcard 1644417125644

Tags
Question

A formula for semivariance approximating the unbiased estimator is:

$$\sum (X_i-\bar {X}) \over n-1$$

for all [...]

Xi ≤ ¯X

status measured difficulty not learned 37% [default] 0

#### Annotation 1644419747084

 For a group of of Selected American Shares with returns (in percent) the semideviation is 21.3% which is less than the standard deviation of 26.7%. From this downside risk perspective, therefore, standard deviation overstates risk.

#### Annotation 1644421582092

 In practice, we may be concerned with values of return (or another variable) below some level other than the mean. For example, if our return objective is 12.75 percent annually, we may be concerned particularly with returns below 12.75 percent a year. We can call 12.75 percent the target. The name target semivariance has been given to average squared deviation below a stated target, and target semideviation is its positive square root.

#### Flashcard 1644423417100

Tags
Question

The average squared deviation below a target value.

Target Semivariance

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644425252108

Tags
Question

The positive square root of target semivariance.

Target Semideviation

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644427087116

Tags
Question

To calculate a sample target semivariance, what is the first step?

we specify the target as a first step.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644428922124

Tags
Question

A formula for target semivariance is

∑(Xi−B)2 / (n−1)

for all [...]

Xi ≤ B

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644430757132

Tags
Question

When return distributions are symmetric, semivariance and variance are [...]

effectively equivalent.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644432592140

Tags
Question

For asymmetric distributions, variance and semivariance rank [...]

prospects’ risk differently

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644434427148

Tags
Question

Semivariance (or semideviation) and target semivariance (or target semideviation) have intuitive appeal, but [...]

they are harder to work with mathematically than variance

status measured difficulty not learned 37% [default] 0

#### Annotation 1644436262156

 We can find a portfolio’s variance as a straightforward function of the variances and correlations of the component securities. We cannot do it for semivariance and target semivariance. We also cannot take the derivative of semivariance or target semivariance. Will be disscussed in probability.

#### Flashcard 1644438097164

Tags
Question

Variance or standard deviation enters into the definition of many of the most commonly used finance risk concepts, such as the [...] and [...] .

Sharpe ratio

beta

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644439932172

Tags
Question

The Chebyshev inequality gives the proportion of values within [...] .

k standard deviations of the mean

status measured difficulty not learned 37% [default] 0

#### Annotation 1644441767180

 According to Chebyshev’s inequality, for any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 − 1/k2 for all k > 1.

#### Flashcard 1644444388620

Tags
Question

According Chebyshev’s inequality a two-standard-deviation interval around the mean must contain at least [...] of the observations, and a three-standard-deviation interval around the mean must contain at least [...] of the observations, no matter how the data are distributed.

75 percent

89 percent

status measured difficulty not learned 37% [default] 0

#### Annotation 1644446223628

 Chebyshev’s inequality holds for samples and populations and for discrete and continuous data regardless of the shape of the distribution.

#### Flashcard 1644448058636

Tags
Question

Does Chebyshev’s inequality give the minimum of observations that must fall within a given interval around the mean?

yes

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644449893644

Tags
Question

Does Chebyshev’s inequality give the maximum of observations that must fall within a given interval around the mean?

no

status measured difficulty not learned 37% [default] 0

#### Annotation 1644451728652

 We may sometimes find it difficult to interpret what standard deviation means in terms of the relative degree of variability of different sets of data, however, either because the data sets have markedly different means or because the data sets have different units of measurement.

#### Flashcard 1644453563660

Tags
Question

[...] is the amount of dispersion relative to a reference value or benchmark.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644455398668

Tags
Question

Standard deviation (and variance) has the property of remaining unchanged if [...]

we add a constant amount to each observation.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644457233676

Tags
Question

The [...] is the ratio of the standard deviation of a set of observations to their mean value

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644459068684

Tags
Question

Coefficient of Variation Formula.

CV= [...]

s/¯X

standard-deviation / Mean

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644460903692

Tags
Question

When the observations are returns the coefficient of variation measures the amount of [...]

risk (standard deviation) per unit of mean return.

status measured difficulty not learned 37% [default] 0

#### Annotation 1644462738700

 Expressing the magnitude of variation among observations relative to their average size, the coefficient of variation permits direct comparisons of dispersion across different data sets.

#### Flashcard 1644464573708

Tags
Question

the coefficient of variation is a [...] measure

scale-free

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644466408716

Tags
Question

A higher coefficient of variation means that sample has [...] than the other sample.

greater variability (dispersion) in whatever is being measured

status measured difficulty not learned 37% [default] 0

#### Annotation 1644468243724

 CV vs Standard Deviation Hong Kong s=22.24, CV = 2.383 Singapoure s=19.2, CV = 2.065 As measured both by standard deviation and CV, Hong Kong market was riskier than the Singapore market. The standard deviation of Hong Kong returns was (22.4 − 19.2)/19.2 = 0.167 or about 17 percent larger than Singapore returns, compared with a difference in the CV of (2.383 − 2.065)/2.065 = 0.154 or about 15 percent. Thus, the CVs reveal slightly less difference between Hong Kong and Singapore return variability than that suggested by the standard deviations alone.

#### Annotation 1644471651596

 #reading-8-statistical-concepts-and-market-returns Although CV was designed as a measure of relative dispersion, its inverse reveals something about return per unit of risk. For example, a portfolio with a mean monthly return of 1.19 percent and a standard deviation of 4.42 percent has an inverse CV of 1.19%/4.42% = 0.27. This result indicates that each unit of standard deviation represents a 0.27 percent return.

#### Flashcard 1644474273036

Tags
Question

A more precise return–risk measure than the CV recognizes the existence of [...]

a risk-free return, a return for virtually zero standard deviation.

status measured difficulty not learned 37% [default] 0

#### Annotation 1644476108044

 #reading-8-statistical-concepts-and-market-returns With a risk-free asset, an investor can choose a risky portfolio, p, and then combine that portfolio with the risk-free asset to achieve any desired level of absolute risk as measured by standard deviation of return, sp.

#### Annotation 1644477943052

 #reading-8-statistical-concepts-and-market-returns Consider a graph with mean return on the vertical axis and standard deviation of return on the horizontal axis. Any combination of portfolio p and the risk-free asset lies on a ray (line) with slope equal to the quantity (Mean return − Risk-free return) divided by sp. The ray giving investors choices offering the most reward (return in excess of the risk-free rate) per unit of risk is the one with the highest slope. The ratio of excess return to standard deviation of return for a portfolio p—the slope of the ray passing through p—is a single-number measure of a portfolio’s performance known as the Sharpe ratio, after its developer, William F. Sharpe.

#### Flashcard 1644479778060

Tags
Question

spread from or as if from a central point.

ray

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644482399500

Tags
Question

a measure of the average excess return earned per unit of standard deviation of return.

Sharpe Ratio

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644484234508

Tags
Question

Sharpe Ratio Formula.

Sh = Rp − RF / sp

Rp = [...]

RF = [...]

sp = [...]

Sp = standard deviation of return on the portfolio

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644486069516

Tags
Question

Sharpe Ratio Formula.

Sh = [...]

Rp − RF / sp

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644487904524

Tags
Question

The average rate of return in excess of the risk-free rate.

Mean excess return

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644489739532

Tags
Question

the Sharpe ratio measures the reward in terms of [...] per [...]

unit of risk

mean excess return

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644491574540

Tags
Question

We often find that portfolios exhibit negative Sharpe ratios when it is calculated over periods in which [...]

bear markets for equities dominate.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644493409548

Tags
Question

What happens to a portfolio's positive Sharpe ratio if we increase risk

Sharpe ratio decreases if we increase risk, all else equal

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644495244556

Tags
Question

With negative Sharpe ratios, increasing risk results in a [...]

numerically larger Sharpe ratio

( doubling risk may increase the Sharpe ratio from −1 to −0.5).

status measured difficulty not learned 37% [default] 0

#### Annotation 1644497079564

 #reading-8-statistical-concepts-and-market-returns To make an interpretable comparison in cases with negative Sharpe ratio, we may need to increase the evaluation period such that one or more of the Sharpe ratios becomes positive; we might also consider using a different performance evaluation metric.

#### Flashcard 1644498914572

Tags
Question

The conceptual limitation of the Sharpe ratio is that it [...]

considers only one aspect of risk, standard deviation of return.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644500749580

Tags
Question

[...] is most appropriate as a risk measure for portfolio strategies with approximately symmetric return distributions.

Standard deviation

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644502584588

Tags
Question

Strategies with option elements have [...] returns.

asymmetric returns

status measured difficulty not learned 37% [default] 0

#### Annotation 1644504419596

 #reading-8-statistical-concepts-and-market-returns Relatedly, an investment strategy may produce frequent small gains but have the potential for infrequent but extremely large losses. Such a strategy is sometimes described as picking up coins in front of a bulldozer; for example, some hedge fund strategies tend to produce that return pattern. Calculated over a period in which the strategy is working (a large loss has not occurred), this type of strategy would have a high Sharpe ratio. In this case, the Sharpe ratio would give an overly optimistic picture of risk-adjusted performance because standard deviation would incompletely measure the risk assumed. Therefore, before applying the Sharpe ratio to evaluate a manager, we should judge whether standard deviation adequately describes the risk of the manager’s investment strategy.

Question

### One frequently used rule of thumb is to round a mean (or a standard deviation) to [...].

one additional decimal than the data

status measured difficulty not learned 37% [default] 0

Question

### 5-2 = [...] = [...]

1/(52) = 1/25

status measured difficulty not learned 37% [default] 0

Question

### An exponent of 1/2 is equivalent to [...]

The square root

status measured difficulty not learned 37% [default] 0

Tags
#exponents
Question

### Any number raised to 0 (y0) = [...]

1

status measured difficulty not learned 37% [default] 0

Tags
#exponents
Question

### ym * yn = [...]

y(n+m)

status measured difficulty not learned 37% [default] 0

Tags
#exponents
Question

### (yn)m = [...]

y(n*m)

status measured difficulty not learned 37% [default] 0

Tags
#exponents
Question

### (y * x)n = [...]

yn * xn

status measured difficulty not learned 37% [default] 0

Tags
#exponents
Question

### A logarithm (of the base b) is the [...]

power to which the base needs to be raised to yield a given number.​​​​​​​

status measured difficulty not learned 37% [default] 0

Tags
#math
Question

### How many of one number do we multiply to get another number? This question is answered by [...]

Logarithms

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644524866828

Tags
#logarithms
Question
How many 2s do we multiply to get 8?

2 × 2 × 2 = 8

write this mathematically
log2 (8) = 3

status measured difficulty not learned 37% [default] 0

#### Annotation 1644544003340

 #reading-8-statistical-concepts-and-market-returns In calculations of variance since the deviations around the mean are squared, we do not know whether large deviations are likely to be positive or negative.

#### Flashcard 1644545838348

Tags
Question

One important characteristic of interest to analysts is the degree of [...] in return distributions.

symmetry

status measured difficulty not learned 37% [default] 0

#### Annotation 1644547935500

 #reading-8-statistical-concepts-and-market-returns If a return distribution is symmetrical about its mean, then each side of the distribution is a mirror image of the other. Thus equal loss and gain intervals exhibit the same frequencies. Losses from −5 percent to −3 percent, for example, occur with about the same frequency as gains from 3 percent to 5 percent.

#### Flashcard 1644550032652

Tags
Question

As a mnemonic, in the case of skewness and distribution the mean, median, and mode occur [...]

in the same order as they would be listed in a dictionary.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644551867660

Tags
Question

[...] means not symmetrical.

Skewed

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644553702668

Tags
Question

A return distribution with [...] has frequent small losses and a few extreme gains.

positive skew

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644555799820

Tags
Question

Which type of distribution is completely described by its mean and variance.

Normal distribution

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644557896972

Tags
Question

A return distribution with [...] has frequent small gains and a few extreme losses.

negative skew

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644560518412

Tags
Question

skewness is computed using [...]

each observation’s deviation from its mean

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644562353420

Tags
Question

A quantitative measure of lack of symmetry

Skewness

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644564450572

Tags
Question

Skewness is computed as the [...] standardized by [...] to make the measure free of scale

average cubed deviation from the mean

dividing by the standard deviation cubed

status measured difficulty not learned 37% [default] 0

#### Annotation 1644566547724

 #reading-8-statistical-concepts-and-market-returns We are discussing a moment coefficient of skewness. Some textbooks present the Pearson coefficient of skewness, equal to 3(Mean − Median)/Standard deviation, which has the drawback of involving the calculation of the median.

#### Flashcard 1644568382732

Tags
Question

A symmetric distribution has skewness of [...]

0

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644570217740

Tags
Question

In Skewness formula we use cube because cubing, unlike squaring, [...]

preserves the sign of the deviations from the mean.

status measured difficulty not learned 37% [default] 0

#### Annotation 1644572052748

 #reading-8-statistical-concepts-and-market-returns If a distribution is positively skewed with a mean greater than its median, then more than half of the deviations from the mean are negative and less than half are positive. In order for the sum to be positive, the losses must be small and likely, and the gains less likely but more extreme. Therefore, if skewness is positive, the average magnitude of positive deviations is larger than the average magnitude of negative deviations.

#### Flashcard 1644574149900

Tags
Question

The term n / [(n − 1)(n − 2)] in Skewness formula corrects for a [...]

downward bias in small samples.

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644576247052

Tags
Question

Sample Skewness Formula.

$$Sk = {n \over (n-1)(n-2)}$$ [...]

$${\Sigma(Xi-\bar{X})^3 \over s^3}$$

status measured difficulty not learned 37% [default] 0

#### Flashcard 1644577033484

Tags
Question
What indicates the direction of skew?

status measured difficulty not learned 37% [default] 0

#### Annotation 1644580703500

 #reading-8-statistical-concepts-and-market-returns Note that as n becomes large, the expression reduces to the mean cubed deviation, SK ≈ (1/n) n∑i=1(Xi−X)3 / s3 . As a frame of reference, for a sample size of 100 or larger taken from a normal distribution, a skewness coefficient of ±0.5 would be considered unusually large.

#### Flashcard 1644583324940

Tags
Question
As a reference, for a sample size of 100 or larger taken from a normal distribution, a skewness coefficient of [...] would be considered unusually large.
±0.5

status measured difficulty not learned 37% [default] 0

Open it
Note that as n becomes large, the expression reduces to the mean cubed deviation, SK ≈ (1/n) n∑ i=1 (Xi−X) 3 / s 3 . As a frame of reference, for a sample size of 100 or larger taken from a normal distribution, a skewness coefficient of ±0.5 would be considered unusually large.

#### Annotation 1644585946380

 #reading-8-statistical-concepts-and-market-returns Some researchers believe that investors should prefer positive skewness, all else equal—that is, they should prefer portfolios with distributions offering a relatively large frequency of unusually large payoffs.