Reading 8: Statistical Concepts & Market Returns Flashcards
LOS 8.A-
a.) Distinguish between descriptive statistics & inferential statistics
There are 2 different types of statistics:
Differential Statistics- statistics that refers to population statistics which gives important details about the population to interpret data sets. (parameters)
Inferential Statistics- inferential statistics uses measurements from a sample to draw estimates for the population via extrapolation.
LOS 8.A-
b.) distinguish between a population & a sample
Population- the whole population is being evaluated
Sample- the sample is selected w/o bias for representation of the population.
LOS 8.A-
c.) among the types of measurement scales
Nominal- (1- boy 2-girl) basic values but no definition for the values
Ordinal- order and definition to the values. (5=high pain, 4= pain, 3= average, 2= normal, 1= below pain)
Interval- like salaries that is based on an interval but it has no set zero.
Scalar- has an absolute zero; also has infinite values in between data points.
LOS 8.B-
Define a parameter, a sample statistic, & a frequency distribution.
Parameter- a parameter is based on the population
Sample Statistic- based on a sample like ‘sample mean’
Frequency Distribution- a tabular distribution that gives absolute frequencies, relative frequencies, etc.
LOS 8.C-
Calculate & interpret relative frequencies and cumulative relative frequencies, given a frequency distributions.
relative frequency- its a percentage of ‘wanted values’/ ‘total value’
cumulative relative frequency- its a percentage of ‘wanted values’/ ‘total values’ sum of all values below as well.
LOS 8.D-
Describe the properties of a data set presented as a histogram or a frequency polygon.
Histogram- it is the sum of all the absolute frequencies.
Frequency Polygon- a.) take the average between both ends of the class interval
b.) then take the absolute frequency as the value for the y-axis.
LOS 8.E-
a.) Calculate and interpret measures of central tendency
What are the measures of central tendency?
- population mean
- sample mean
- arithmetic mean (Sum of mean derivatives (SUM(x- x bar =0))
LOS 8.E-
b.) how to calculate weighted average mean
WEIGHTED AVERAGE MEAN= Sum of ALL (WiXi)
LOS 8.E-
c.) calculate Geometric Mean
G mean = (x1 * x2 * x3* x4…….) (1/n)
n= the number of items in the list x= the number itself
Used for forecasting the rate of return in the future for the FUTURE vs. arithmetic mean which is for current year
LOS 8.E-
d.) calculate the Harmonic mean
Harmonic mean = N/ (SUM OF 1/Xi)
LOS 8.F-
Calculate and interpret quartiles, quintiles, deciles, and percentiles.
1.) To find quantiles, you will need to calculate:
Ly= (n+1)(y/100)
n= total numbers
y= the percentile
2.) Then count towards that number to see where that range will begin for the quantile.
LOS 8.G-
a.) Calculate and interpret a range & a mean absolute deviation
Range- a measure of variability; gives understanding of distance
Mean Absolute Deviation-
MAD = SUM [(x- x bar)] / n
LOS 8.G-
b. & c.) Calculate and interpret a variance & SD of a population/SAMPLE
VARIANCE OF POPULATION
S^2= [(X-U)^2/N]
SD OF POPULATION
S^2= [(X-U)^2/(N-1)]
SD= SQUARE ROOT OF S^2
LOS 8.H- Calculate and interpret the coefficient of variation and the Sharpe Ratio.
CV= Standard Deviation/ Mean
*** measures the relative distance BETWEEN STATISTIC AND the mean
Sharpe Ratio- the rate of return after risk free rate is taken out
SR= (IR- RFR)/(SD)
** Excess Return per unit of Risk **
LOS 8.K: Describe the relative locations of the mean, median, and mode for a unimodal, non-symmetrical distribution for skewness
Positive Skew- (mode < median < mean)
Negative Skew- (mode> median> mean)
LOS 8.1: Explains measures of sample skewness and kurtosis
Kurtosis- Leptokurtotic, Mesokurtotic, Platykurtotic
Skewness- positively, negatively skewed
LOS 8.1: Explains measures of sample skewness and kurtosis
a.) How do you calculate and interpret skewness?
1.) Find sample skewness via calculation
2.) compare to the guidelines below.
———————————————————————————–
Skewness Calculation:
Sample Skewness = (1/n) [ [(x-xbar)^3]/SD^3]
SS> 0 POSITIVELY SKEWED
SS<0 NEGATIVELY SKEWED
SS=0 NO SKEW
LOS 8.1: Explains measures of sample skewness and kurtosis
a.) How do you calculate and interpret kurtosis?
1.) Find Sample Kurtosis
2.) Find Ke value
3.) Compare to the guidelines
———————————————————————————–
Sample Kurtosis = (1/n) * [(x-x bar)^4/ (sd)^4]
[Sample Kurtosis- 3= Ke Value]
Ke > 0 leptokurtotic
Ke < 0 platykurtotic
Ke = 0 mesokurtotic
LOS 8.M: Compare the use of arithmetic and geometric means when analyzing investment returns
Arithmetic Means are used to determine the current investment return from extrapolation based on past data.
Geometric means are used to determine the future investment return 5 years into the future to find 1 time value to multiply when compounded annually.
