Module 3.2: Skewness, Kurtisis And Correlation

Question 1

What is spurious correlation?

Answer 1

Correlation is either a result of chance, or present due to changes in both variables over time that is caused by their association to a third variable

Question 2

________ is not implied from significant correlation.

Answer 2

Causation

Question 3

What is the range for calculated correlation?

Answer 3

-1 to +1

Question 4

Correlation of +1 means what?
-1? 0?

Answer 4

+1 = perfect correlation between variables

-1 = perfect NEGATIVE correlation between variables

0 = no linear relationship between variables

Question 5

What is the formula to calculate correlation?

Answer 5

Question 6

What is correlation a measure of?

Answer 6

Standardized measure of linear relationships between two variables.

Question 7

What is covariance?

Answer 7

Covariance is a measure of how two variables move together.

Question 8

What is the formula for covariance?

Answer 8

Question 9

What is a scatter plot?

Answer 9

Method to display relationship between two variables.

Question 10

What do scatter plots reveal that correlation coefficient doesn’t?

Answer 10

Non linear relationships

Question 11

What is the formula for sample kurtosis?

Answer 11

Question 12

Greater excess kurtosis and more negative skew means _______.

Answer 12

Higher risk

Question 13

What is excess kurtosis?

Answer 13

When a distribution exhibits either more or less kurtosis than normal distribution.

Question 14

What does a platykurtic distribution mean?

Answer 14

Excess kurtosis less than 0

Question 15

What does a leptokurtic distribution mean?

Answer 15

Excess kurtosis greater than 0.

Question 16

What is the excess kurtosis on a normal distribution?

Answer 16

0

Question 17

What is excess kurtosis?

Answer 17

When a distribution exhibits either more or less kurtosis than normal distribution.

Question 18

What type of of distribution has same kurtosis as normal distribution?

Answer 18

Mesokurtic

Question 19

Describe leptokurtic and platykurtic curves compared to normal distribution.

Answer 19

Leptokurtic curves are MORE peaked than normal distributions.

Platykurtic curves are LESS peaked than normal distributions.

Question 20

What is the equation for sample skewness?

Answer 20

Question 21

What does skew affect the most? Mean, median or mode?

Answer 21

Skew affects mean more than median and mode.

Question 22

Mean is pulled into the direction of the ______.

Answer 22

Skew

Question 23

Describe curve for negatively skewed distribution that’s unimodal?

Answer 23

Mean less than median.
Median less than mode.

Question 24

Describe curve for positively skewed distribution that’s unimodal?

Answer 24

Mode less than median.
Median less than mean.

Question 25

Describe curve with symmetrical skew?

Answer 25

Mean, median and mode are equal.

Question 26

Describe the tails of a positively skewed distribution?

Answer 26

Long right tail that is positively skewed.

Question 27

Describe the tails of a negatively skewed distribution?

Answer 27

Long left tail , that’s skewed left.

Question 28

What is an outlier?

Answer 28

Observations extraordinarily far from mean- above or below.

Question 29

What does skewness refer to?

Answer 29

Refers to extent to which a distribution is not symmetrical.

Question 30

What is a symmetrical distribution?

Answer 30

A distribution shaped identically on both sides of its mean.

Question 31

What does distributional symmetry imply?

Answer 31

Intervals of losses and gains will exhibit the same frequency.

Question 32

What does a symmetrical distribution with a mean return of zero indicate?

Answer 32

Losses in the -6% to -4% interval occur as frequently as gains in the +4% to +6% interval.

Question 33

Why is the extent of symmetry in a returns distribution important?

Answer 33

It indicates if deviations from the mean are more likely to be positive or negative.

Question 34

Define skewness.

Answer 34

The extent to which a distribution is not symmetrical.

Question 35

What are the two types of skewness?

Answer 35

* Positive skewness * Negative skewness

Question 36

What causes nonsymmetrical distributions?

Answer 36

The occurrence of outliers in the dataset.

Question 37

What characterizes a positively skewed distribution?

Answer 37

Outliers greater than the mean in the upper region or right tail.

Question 38

Why is a positively skewed distribution said to be skewed right?

Answer 38

Because of its relatively long upper (right) tail.

Question 39

What characterizes a negatively skewed distribution?

Answer 39

A disproportionately large amount of outliers less than the mean in the lower (left) tail.

Question 40

Fill in the blank: A positively skewed distribution has outliers that are _______ the mean.

Answer 40

greater than

Question 41

Fill in the blank: A negatively skewed distribution has outliers that are _______ the mean.

Answer 41

less than

Question 42

What is a scatter plot?

Answer 42

A method for displaying the relationship between two variables

Question 43

On which axes are the two variables plotted in a scatter plot?

Answer 43

One variable on the vertical axis and the other on the horizontal axis

Question 44

What does each paired observation in a scatter plot represent?

Answer 44

Each paired observation can be plotted as a single point

Question 45

What is a key advantage of creating scatter plots?

Answer 45

They can reveal nonlinear relationships not described by the correlation coefficient

Question 46

What is a standardized measure of the linear relationship between two variables called?

Answer 46

Correlation coefficient ## Footnote Often referred to simply as correlation.

Question 47

What does correlation measure?

Answer 47

The strength of the linear relationship between two random variables ## Footnote It indicates how closely the variables move in relation to each other.

Question 48

What is the range of correlation values?

Answer 48

-1 to +1 ## Footnote This indicates the possible strength and direction of the relationship.

Question 49

What does a correlation of pxy = 1.0 indicate?

Answer 49

Perfect positive correlation ## Footnote Movement in one variable results in a proportional positive movement in the other.

Question 50

What does a correlation of pxy = -1.0 indicate?

Answer 50

Perfect negative correlation ## Footnote Movement in one variable results in an exact opposite proportional movement in the other.

Question 51

What does a correlation of pxy = 0 indicate?

Answer 51

No linear relationship between the variables ## Footnote This means that prediction of Y cannot be made based on X using linear methods.

Question 52

What are the three measures of central tendency?

Answer 52

Mean, median, mode ## Footnote These measures summarize a set of data points.

Question 53

How does skewed data affect the mean compared to the median and mode?

Answer 53

Skew affects the mean more than the median and mode ## Footnote The mean is sensitive to extreme values, while the median and mode are more robust.

Question 54

In which direction is the mean pulled in a skewed distribution?

Answer 54

In the direction of the skew ## Footnote A positively skewed distribution pulls the mean to the right, while a negatively skewed distribution pulls it to the left.

Question 55

Where is the median located in relation to the mean and mode in skewed distributions?

Answer 55

Between the mean and mode ## Footnote This holds true for both positively and negatively skewed distributions.

Question 56

True or False: The mode is affected by skewness more than the mean.

Answer 56

False ## Footnote The mean is more affected by skewness than the mode.

Question 57

Fill in the blank: The mean is pulled in the direction of the _______.

Answer 57

skew ## Footnote This indicates how the mean reacts to the distribution of data.

Question 58

What is excess kurtosis?

Answer 58

A measure of kurtosis that indicates whether a distribution has more or less kurtosis than the normal distribution ## Footnote Excess kurtosis is calculated as kurtosis minus three.

Question 59

What is the computed kurtosis for all normal distributions?

Answer 59

Three

Question 60

What excess kurtosis value does a normal distribution have?

Answer 60

Zero

Question 61

What does a leptokurtic distribution indicate in terms of excess kurtosis?

Answer 61

Excess kurtosis greater than zero

Question 62

What does a platykurtic distribution indicate in terms of excess kurtosis?

Answer 62

Excess kurtosis less than zero

Question 63

Why is kurtosis critical in risk management?

Answer 63

It helps understand the distribution of securities returns which are often not normally distributed

Question 64

How do actual securities returns typically behave in terms of distribution?

Answer 64

They tend to exhibit both skewness and kurtosis

Question 65

Why are skewness and kurtosis important for risk management?

Answer 65

They provide insights into potential for extremely large, negative outcomes which normal distribution models do not account for

Question 66

What do most risk managers focus on instead of the mean and standard deviation?

Answer 66

The distribution of returns in the tails of the distribution

Question 67

What does greater excess kurtosis and more negative skew in return distributions indicate?

Answer 67

Increased risk

Question 68

Fill in the blank: A normal distribution has an excess kurtosis of _______.

Answer 68

Zero

Question 69

True or False: A leptokurtic distribution has excess kurtosis less than zero.

Answer 69

False

Question 70

What is the relationship between excess kurtosis and risk?

Answer 70

Greater excess kurtosis indicates increased risk