Reading 7: Statistical Concepts

Front 1

Definition of Statistics

Back 1

Used to refer to data and the methods we use to analyze data

Front 2

Descriptive statistics

Back 2

used to summarize the important characterists of large data sets

Front 3

Inferential Statistics

Back 3

procedures used to make forecassts, estimates, or jedgements about a large set of data on the basis of characteristics of a smaller set (sample)

Front 4

Population

Back 4

All members of a stated group

Front 5

Sample

Back 5

a subset of a teh population of interest

Front 6

4 Types of Measurement Scales

Back 6

1. Nominal
2. Ordinal
3. Interval
4. Ratio

Front 7

Nominal Scale

Back 7

Numbers used to classify objects in no particular order. LEAST ACCURATE LEVEL.
i.e. All Large Cap Funds=1
all small cap funds =2

Front 8

Ordinal Scale

Back 8

Observations are assigned to a category and these are arranged according to characteristics
i.e. Morning Star ratings
SECOND LEAST ACCURATE LEVEL

Front 9

Interval Scale

Back 9

Provide relative ranking, and assurance that difference between scale volumes are equal. Main problem is that a measurement of 0 does not mean "Absence of"
i.e. farenheight measurements

Front 10

Ration Scales

Back 10

Most refined/accurate level of measurement. Provided ranking, equal difference between scale values and 0 is the absence of.
MOST ACCURATE LEVEL

Front 11

Parameter

Back 11

measure used to describe a characteristic

Front 12

Sample Statistic

Back 12

used to measure a characteristic of a sample

Front 13

Frequency distribution

Back 13

Tabular presentation that aids in data analysis. Summarizes statistical data by assigning it to specified groups. May be measured using any measurement scale

Front 14

Construct Frequency Distribution

Back 14

1. Define intervals
2. Tally information and assign to group
3. Count the observations

Front 15

Modal Interval

Back 15

The interval with the greatest frequency in a frequency distribution

Front 16

Relative Frequency

Back 16

Percentage of total observations falling in each category.

Front 17

Cumulative Absolute Frequency

Back 17

Summing the Absolute Frequency by starting at the lowest interval and working towards the higher frequency

Front 18

Cumulative Relative frequency

Back 18

Dividing the Cumulative Absolute frequency the same way as the relative frequency

Front 19

Histogram

Back 19

graphical presentation of the absolute frequency distribution A bar chart of continuous data that has been classified into a frequency distribution
INTERVALS ARE SCALED ON HORIZONTAL AXIS

Front 20

Weighted Mean
Example: Portfolio with 50% stocks that return 12%, 40% bonds that return 7% and 10% cash that return 3%

Back 20

.5(12)+.4(7)+.1(3)=9.1%

Front 21

Median

Back 21

Midpoint of a set of data when it is arranged in ascending or descending order

Front 22

Mode

Back 22

Value that occurs most frequently in a data set. Data set can have more than one Mode

Front 23

Unimodal vs. Bimodal

Back 23

One mode in a data set vs. numerous modes in a data set

Front 24

Geometric Return Process

Back 24

1. Add each percent return to 1
2. Multiply all together
3. Raise that number to 1/n
n=number of periods

Front 25

Harmonic Mean

Back 25

most common application is average pricing shares

Front 26

Harmonic Mean example: an investor purchased 3 lots of $1000 of stock at 8, 9 and 10 dollars. Avg price of stock

Back 26

3/ (1/8) + (1/9) + (1/10)=8.926

Front 27

Quantile

Back 27

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

Front 28

4 types of Quantiles

Back 28

1. Quartiles
2. Quintile
3. Decile
4. Percentile

Front 29

Quartiles: What is the third quartile for the following distribution of returns?
8,10,12,13,15,17,18,19,23,24

Back 29

(11+1)*1/4=9. Therefore 75% of the data points lie below 19%

Front 30

Quartiles when number is not odd:
8,10,12,13,15,17,18,19,23,24, 26

Back 30

(12+1)*3/4=9.75.
(19+(.75)*(23-19)=22%
Therefore 75% of all observations fall below 22%

Front 31

Mean Absolute Deviation

Back 31

The average of the absolute values of the deviations of individual observations from the arithmetic mean

Front 32

MAD Example: What is the MAD of the following investment returns 30, 12, 25, 20, 23?

Back 32

1. Find the arithmetic mean which equals 22
2. Find absolute value of each number minus 22, i.e. 30-22, 12-22 etc.
3. Add all numbers and divide by total amount of numbers.
Answer should be 4.8

Front 33

Interpretation of MAD of 4.8%

Back 33

On average an individual will deviate 4.8% from the mean return of X

Front 34

Population Variance

Back 34

The average of squared deviations from the mean

Front 35

Solve population variance with the following values: 30, 12, 25, 20, 23

Back 35

1. First find arithmetic mean
2. subtract arithmetic mean from each value and square the result
3. Divide by number of values
4. Final number will be squared. Very illogical

Front 36

Population Standard Deviation

Back 36

the square root of the population variance

Front 37

Sample Variance

Back 37

Same as population variance but the denominator is n-1

Front 38

Sample standard deviation

Back 38

square root of the sample variance

Front 39

Chebyshev's Inequality

Back 39

For any set of observations the percentage of the observations that lie within K standard deviations of the mean is at least 1-1/k^2 for all k>1

Front 40

Relative dispersion

Back 40

the amount of variability in a distribution relative to a reference point or benchmark. Commonly measured with the coefficient of variation

Front 41

Coefficient of variation (CV)

Back 41

Standard Deviation of x / average value of x

Front 42

CV example: Compute CV for Tbill with mean monthly return of .25% and Standard Deviation of .36% vs. SP500 1.09% monthly mean and 7.30% Standard Deviatin

Back 42

Tbills: .36 / .25 = 1.44
SP: 7.3 / 1.09 = 6.70
less risk per unit of monthly return for tbills than for sp500

Front 43

Sharpe Ratio

Back 43

Excess return / standard deviation

Front 44

Excess Return

Back 44

Portfolio Return - Risk free return; named because it is the return you get for exposing yourself to excess risk

Front 45

Compute Sharpe Ratio:
Tbill: .25%
Mean Montly SP500: 1.3%
Standard Deviation: 7.30

Back 45

(1.3-.25) / 7.3 = 0.144
This means that the sp500 earned .144% of excess return per unit of risk taken

Front 46

Symmetrical Distribution

Back 46

a distribution that is shaped symmetically on both sides of ITS MEAN

Front 47

Will a symmetrical distribution with a mean return of 0 have more points on at -6, -4 or 6, 4?

Back 47

It should have them equally

Front 48

Skewness

Back 48

Refers to the extent to which a distribution is not symmetrical

Front 49

How does a distribution get skewed?

Back 49

Outliers -- observations with extraordinary large values on either side of the mean

Front 50

Positively skewed

Back 50

1. Longer right tail
2. More outliers in positive
3. Mode Median Mean

Front 51

Negatively Skewed

Back 51

1. Longer left tail
2. More outliers in negative
3. Mean Median Mode

Front 52

Kutrosis

Back 52

The degree to which a distribution is more or less peaked than a normal distribution

Front 53

Leptokurtic Kurtosis

Back 53

More peaked than a normal distribution. It will have more points near the mean, and more points with large deviations from the mean (fatter tails)

Front 54

Platykurtic Kurtosis

Back 54

distribution that is less peaked than a normal distributions. Will have a greater percentage of distributions that are equidistant from the mean.

Front 55

Mesokurtic

Back 55

Reflects a normal distribution