Quant: Stats & Market Returns Flashcards
Descriptive vs Inferential Statistics =
Descr: summarizes important characteristics, turning a mass of numerical data into useful info.
Infer: uses statistical characteristics of a sample to make forecasts/estimates/judgments about a set of data.
Population =
= set of all possible members of a stated group
Nominal scales =
NOIR
- Contains least amount of info
- Observations classified/counted in no particular order
- ie assigning numbers to different types of mutual funds and counting them
Ordinal Scales =
NOIR
- Higher level of measurement than nominal
- Categories are ordered in relation to a specific characteristic
- All observations are assigned to a category
- We can use this to compare observations across categories WRT the characteristic, but not those within the same category
Interval Scale (intervals may be known as classes) =
NOIR
- Provides relative ranking between scales (like ordinal)
- Differences between scale values are equal (10° to 20° is the same as 20° to 30°)
- 0 does not does not necessarily mean the absence of what we are measuring
- Interval-scale-base ratios are meaningless (30° is not 3x hotter than 10°)
Ratio Scales =
NOIR
- Most refined level of measurement
- Order, intervals and ratios are consistent/make sense across the scale
- Bank account balance/height
Parameter =
= measure used to describe a characteristic of a population
- Inv analysis tends to use only a few, incl. mean return and standard deviation of returns
Sample Statistic =
= a parameter for sample, describes a characteristic of the sample
Frequency Distribution =
= table for statistical data, shows data assigned to a group or interval.
Data in a FD may be measured in ANY type of scale
Constructing a frequency distribution =
- intervals must be mutually exclusive and cover the range of the entire population
- Intervals - few = broad summary, many = detailed summary
- TALLY OBSERVATIONS
- COUNT OBSERVATIONS
- IT’S FUCKING ROCKET SCIENCE
Relative (cumulative) Frequency =
= percentage of total observations in each interval
ALSO: the cumulative relative frequency, which includes observations from lower intervals
Absolute (cumulative) frequency =
= the number of observations in the interval. DUH. Cumulative includes those from lower intervals as well.
Histogram =
= graphical presentation of the absolute frequency distribution. Bar chart of continuous data classified into a FD. Gratuitous picture.
Frequency Polygon =
= same purpose as histogram. Midpoint of each interval is plotted on the X axis.
Measures of central tendency =
= identifies the center/average of a data set.
Can serve as the typical/expected value of the set.
Population mean =
= sum of values in the population divided by the number of observations.
Sample Mean =
= sum of all values in the sample population divided by the number of observations. Used to make inferences about the population mean.
Weighted mean =
Portfolio return is a weighted average of returns.
Geometric Mean =
Used for calculating investment returns over multiple periods (average growth rate/return)
Will not work if value under radical is < 0
For returns, add 1 before nth rooting, then subtract 1 to get mean return value.
Harmonic Mean =
Used for calculations such as avg cost of shares over time.
Quantile (measures of location) =
a value at or below which a particular proportion of data lies.
Quartile, quintile, percentile.
3rd quartile, 75th percentile, 3 quarters of observations fall below that value.
Mean average deviation =
average of the absolute values of the deviations of observations from the arithmetic mean. NB SD>MAD
Population variance =
average of the squared devations of observations from the mean.
Population standard deviation =
square root of the population variance. This allows us to avoid dealing with units ‘2’, which applies in the case of the variance. NB SD>MAD
Sample Variance =
Similar to population variance except the sum of squared differences is divided by ‘n-1’ to avoid systematic underestimation of σ2 (and use of sample mean X BAR)
Sample Standard Deviation =
square root of sample variance.
Estimating proportion of observations falling in k standard deviations of the mean =
AKA Chebyshev’s inequality
for any set of observations % of observations within k SDs of the mean is at least 1-1/k2 for all k>1.
Co-efficient of variation =
CV measures the amount of dispersion in a distribution relative to its mean.
Allows us to compare relative dispersion between two sets of data -
VARIATION PER UNIT OF RETURN
Sharpe Ratio =
EXCESS RETURN PER UNIT OF RISK
Negative SR - increasing risk will move the ratio closer to zero, ie characteristics of SR are diff when (-)
SD is not an appropriate measure of risk for certain options strategies.
Kurtosis: Lepto, Platy, Meso =
Degrees of kurtosis (peakedness)
Lepto is more peaked, fatter tails.
Platy, opposite of lepto. Meso: normal distr.
Sample Skewness =
SK > 0 = right skewed (positive), deviations above the mean are larger on average. Values greater than 0.5 indicate significant skew.
Sample Kurtosis =
Measured relative to a kurtosis of a normal distribution (3).
Positive excess kurtosis = platykurtic (more peaked, fat tails)
Excess kurtosis (sample kurtosis - 3) greater than 1 are considered large.
