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.
Arithmetic Means =
= are unique ie a data set has only one
Consider all pieces of information/data points
The sum of deviations from the mean is always 0
Weighted mean =
Portfolio return is a weighted average of returns.
Median =
Middle value of data set.
- Half of the observations lie above/below
- Not affected by extreme values
- For an even number of observations take the mean of the two middle observations
Mode =
Most frequently occuring value. One value = unimodal. Also bi/tri modal. Data set can have no mode.
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.
Means and Dollar Cost Averaging =
For values that are not all equal:
harmonic mean < geometric mean < arithmetic mean.
This mathematical fact is the basis for the claimed benefit of purchasing the same dollar amount of mutual fund shares each month or each week. Some refer to this practice as “dollar cost averaging.”
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.
Skewness: positive and negative =
Asymmetry of a distritbution
Positive: more outliers on the right tail, making it longer.
Negative: more outliers on the left tail, making it longer.
Measures of Central Tendency for skewed unimodal distributions =
Positively skewed: Mean > median > mode
Mean is ‘pulled’ up by outliers.
Reverse for negative skew
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.
Use of Geometric Mean when analyzing investment returns =
Appropriate when considering future/predicted returns over multiple years
returns of 5%, 12%, 9%: (1.05 x 1.12 x 1.09)1/3-1 = 8.63%
Use of Arithmetic Mean when analyzing investment returns =
Use for future/predicted returns for a single year
ie returns of 5%, 12%, 9%: (5+12+9)/3 = 8.67% to predict return for the following year
