Quant: Stats & Market Returns

Question 1

Descriptive vs Inferential Statistics =

Answer 1

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.

Question 2

Population =

Answer 2

= set of all possible members of a stated group

Question 3

Nominal scales =

NOIR

Answer 3

• Contains least amount of info
• Observations classified/counted in no particular order
• ie assigning numbers to different types of mutual funds and counting them

Question 4

Ordinal Scales =

NOIR

Answer 4

• 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

Question 5

Interval Scale (intervals may be known as classes) =

NOIR

Answer 5

• 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°)

Question 6

Ratio Scales =

NOIR

Answer 6

• Most refined level of measurement
• Order, intervals and ratios are consistent/make sense across the scale
• Bank account balance/height

Question 7

Parameter =

Answer 7

= 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

Question 8

Sample Statistic =

Answer 8

= a parameter for sample, describes a characteristic of the sample

Question 9

Frequency Distribution =

Answer 9

= table for statistical data, shows data assigned to a group or interval.

Data in a FD may be measured in ANY type of scale

Question 10

Constructing a frequency distribution =

Answer 10

• 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

Question 11

Relative (cumulative) Frequency =

Answer 11

= percentage of total observations in each interval

ALSO: the cumulative relative frequency, which includes observations from lower intervals

Question 12

Absolute (cumulative) frequency =

Answer 12

= the number of observations in the interval. DUH. Cumulative includes those from lower intervals as well.

Question 13

Histogram =

Answer 13

= graphical presentation of the absolute frequency distribution. Bar chart of continuous data classified into a FD. Gratuitous picture.

Question 14

Frequency Polygon =

Answer 14

= same purpose as histogram. Midpoint of each interval is plotted on the X axis.

Question 15

Measures of central tendency =

Answer 15

= identifies the center/average of a data set.

Can serve as the typical/expected value of the set.

Question 16

Population mean =

Answer 16

= sum of values in the population divided by the number of observations.

Question 17

Sample Mean =

Answer 17

= sum of all values in the sample population divided by the number of observations. Used to make inferences about the population mean.

Question 18

Arithmetic Means =

Answer 18

= 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

Question 19

Weighted mean =

Answer 19

Portfolio return is a weighted average of returns.

Question 20

Median =

Answer 20

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

Question 21

Mode =

Answer 21

Most frequently occuring value. One value = unimodal. Also bi/tri modal. Data set can have no mode.

Question 22

Geometric Mean =

Answer 22

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 n^th rooting, then subtract 1 to get mean return value.

Question 23

Harmonic Mean =

Answer 23

Used for calculations such as avg cost of shares over time.

Question 24

Means and Dollar Cost Averaging =

Answer 24

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.”

Question 25

Quantile (measures of location) =

Answer 25

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.

Question 26

Mean average deviation =

Answer 26

average of the absolute values of the deviations of observations from the arithmetic mean. NB SD\>MAD

Question 27

Population variance =

Answer 27

average of the squared devations of observations from the mean.

Question 28

Population standard deviation =

Answer 28

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

Question 29

Sample Variance =

Answer 29

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)

Question 30

Sample Standard Deviation =

Answer 30

square root of sample variance.

Question 31

Estimating proportion of observations falling in *k* standard deviations of the mean = AKA Chebyshev's inequality

Answer 31

for any set of observations % of observations within k SDs of the mean is **at least** 1-1/k² for all k\>1.

Question 32

Co-efficient of variation =

Answer 32

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

Question 33

Sharpe Ratio =

Answer 33

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.

Question 34

Skewness: positive and negative =

Answer 34

Asymmetry of a distritbution Positive: more outliers on the right tail, making it longer. Negative: more outliers on the left tail, making it longer.

Question 35

Measures of Central Tendency for skewed unimodal distributions =

Answer 35

Positively skewed: Mean \> median \> mode Mean is 'pulled' up by outliers. Reverse for negative skew

Question 36

Kurtosis: Lepto, Platy, Meso =

Answer 36

Degrees of kurtosis (peakedness) Lepto is more peaked, fatter tails. Platy, opposite of lepto. Meso: normal distr.

Question 37

Sample Skewness =

Answer 37

S_K \> 0 = right skewed (positive), deviations above the mean are larger on average. Values greater than 0.5 indicate significant skew.

Question 38

Sample Kurtosis =

Answer 38

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.

Question 39

Use of Geometric Mean when analyzing investment returns =

Answer 39

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%

Question 40

Use of Arithmetic Mean when analyzing investment returns =

Answer 40

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