Statistical Concepts and Market Returns

Question 1

Nominal Scale

Answer 1

Data is put into categories that have no particular order

Question 2

Ordinal Scale

Answer 2

Data is put into categories that can be ordered with respect to some characteristic

Question 3

Interval Scale

Answer 3

Differences in data values are meaningful, but ratios, such as twice as much or twice as large, are not meaningful

Question 4

Ratio Scale

Answer 4

Ratios of values, such as twice as much or half as large, are meaningful and zero represents the complete absence of the characteristic being measured

Question 5

Parameter

Answer 5

Any measurable characteristic of a population

Question 6

Sample Statistic

Answer 6

Can describe characteristic of a sample

Question 7

Relative Frequency

Answer 7

Percentage of total observations falling within a frequency

Question 8

Cumulative Relative Frequency

Answer 8

for an interval is the sum of the relative frequencies for all values less than or equal to that interval’s maximum value

Question 9

Histogram

Answer 9

Bar chart of data the has been grouped into a frequency distribution

Question 10

Frequency Polygon

Answer 10

Plots the midpoint of each interval on the horizontal axis and the absolute frequency for that interval on the vertical axis and connects midpoints with straight lines

Question 11

Quantile

Answer 11

general term for a value at or below which a stated proportion of the data in a distribution lies

Question 12

Range

Answer 12

Difference between the largest and smallest values in a data set

Question 13

Variance

Answer 13

Mean of squared deviations form the arithmetic mean or from the expected value of a distribution

Question 14

Standard Deviation

Answer 14

Positive square root of the variance and is frequently used as a quantitative measure of risk

Question 15

Chebyshev’s Inequality

Answer 15

States that the proportion of observations within k standard deviations of the mean is 1 - 1/(k^2) for all k > 1. It states that:
36% of observations lie within +/- 1.25 std. dev. of mean
56% of observations lie within +/- 1.5 std. dev. of mean
75% of observations lie within +/- 2 std. dev. of mean
89% of observations lie within +/- 3 std. dev. of mean
94% of observations lie within +/- 4 std. dev. of mean

Question 16

Skewness

Answer 16

Describes the degree to which a distribution is not symmetric about its mean. Right-skewed distribution had positive skewness. Left-skewed distribution has negative skewness. Sample skew with absolute value greater than 0.5 is considered significantly different from zero

Question 17

Positive Skew, Unimodal Distribution

Answer 17

Mean > Median > Mode

Question 18

Negative Skew, Unimodal Distribution

Answer 18

Mean < Median < Mode

Question 19

Kurtosis

Answer 19

Measures the peakedness of a distribution and the probability of extreme outcomes

Question 20

Excess Kurtosis

Answer 20

Measured relative to a normal distribution, which has a kurtosis of 3. With an absolute value greater than 1 is considered to be significant

Question 21

Leptokurtosis

Answer 21

Positive values of excess kurtosis (fat tails, more peaked). Probability of extreme outcomes are greater than for a normal distribution

Question 22

Platykurtic Distribution

Answer 22

Negative values of excess kurtosis. Thin tails, less peaked

Question 23

Arithmetic Mean Return

Answer 23

Appropriate for forecasting single period returns in future periods

Question 24

Geometric Mean Return

Answer 24

Appropriate for forecasting future compound returns over multiple periods