Statistical Concepts & Market Returns Flashcards
Master assigned reading #7
Descriptive Statistics
Summarizes the characteristics of a data set
Inferential Statistics
Used to make a probablistic statement about a population based on a sample
Nominal scale
No particular order
Ordinal Scale
Catagories can be ordered
Interval Scale
Differences in data variables are meaningful, but ratios are not meaninful
Ratio Scale
Ratios are meaningful, and zero represents an absence of that characteristic
What is a parameter?
Any measurable characteristic of a population
What is a sample statistic?
A characteristic of a sample
What is an interval?
A range of values
A frequency distribution…
groups observations into classes, or intervals
Relative Frequency
The percentage of total observations falling within an interval
Cumulative Frequency for an Interval
the sum of all relative frequencies for all values less than or equal to that intervals maximum value
Histogram
Bar chart that is grouped into a frequency distribution
Frequency Polygon
- Plots the midpoints of each interval on the horizontal axis and the absolute frequency on the vertical axis
- Then connects the midpoints with straight lines
Advantage of histograms and frequency polygons?
They allow us to quickly see where most observations lie
The arithmetic mean is the…
average (both population and sample means are arithmetic means)
Geometric mean is used to…
Find the compound growth rate
Weighted means does what?
Weights each value according to its influence.
Harmonic Mean is used to..
find an average purchase price, such as dollars per share for periodic investments
The median is the…
midpoint of the data set when data is arranged from largest to smallest
What is the mode?
the value that occurs most frequently
Quartile
distribution divided into quarters
Quintile
distribution divided into fifths
Decile
Distribution divided into tenths
Percentile
Distribution divided into hundreths
Range
Difference between the largest and smallest value in a data set
Exhaustive Events
Include ALL possible outcomes
Example of an exhaustive event
rolling the dice, rolling a number1-6 is exhaustive
Empirical Probabibility
established by analyzing past data
Priori Probability
Determined using a formal reasoning and inspection process
Unconditional Probability
Simply the probablity of an event occuring
Conditional Probablility
- The occurrence of one event affects the probability of another event
- Also called “likelihood”
Multiplication Rule of Probability
P(AB) = P(A given occurrence of B) * P(B)
Addition Rule of Probablility
P(Aor B) = P(A) + P(B) - P(AB)
Total Probability Rule
P(A) = (P(A given occurrance of B1)P(B1)) + (P(A given occurrence of B2) P(B2))…….
-where B1,B2,Bn is a mutually exclusive, exhaustive series of eventsl
Joint Probability Equation (Multiplication Rule)
P(AB)= P(A given that B) * P(B)
Addition rule of probability for Mutually exclusive events
P(A or B) = P(A) + P(B)
With independent events, “and” indicates__ and “or” indicates _____
With independent events, “and” indicates multiplication and “or” indicated addition
Independent Events rule equation
- Independent if P(A given B) = P(A)
- If not they are dependent
Expected Value
Weighted average of all possibe outcomes of a random variable, where weights are the probabilities that the outcomes will occur.
Example of a “Population”
A cross section of returns of all stocks traded on the NYSE
Modal Interval
The interval with the greatest frequency in a frequency distribution
Measures of central tendency
identify the center, or average, of a data set
When there are outliers in data, you should use the_____
Median, because arithmetic means can be affected by outliers
Bimodal
A distribution that has two values that occurs most frequently
The geometric mean is always _________to the arithmetic mean
Geometric mean is always less than or equal to the arithmetic mean
“Dollar Cost Averaging”
purchasing the samme dollar amount of mutual fund share each month or each week
Percentile Calculation
Ly= (n+1) * y/100
“Dispersion” is defined by
variability around the central tendency
Mean Absolute Deviation explanation
the average of the absolute values of the deviations of individual ovservations from the arithmetic mean
Population Variance explanation
-the average of the squared deviations from the mean
Explan the population standard deviation
the population standard deviation is the square root of the population variance
How to find the population standard deviation?
Essentially you take the square root of the population variance equation
What does Covariance measure?
the extent to which two random variables tend to be above and below their respective mean
What is Correlation?
Correlation is the measure of association between two random variables
Equation for Expected returns for a 2-asset portfolio
E(Rp) = w1E(R1) + w2(E(R2)
Correlation Equation
CORR(Ri, Rj) = Cov(Ri, Rj) / (STDVi * STDVj)
Expected Return Equation
P(Xn)Xn + …..
Covariance Equation
E(x) * (Ri - E(Ri)) * (Rj- E(Rj)) +…..
