3. Statistics

Question 1

Population vs. sample

Answer 1

Population = summation of all the elements of interest to a researcher
Sample = set of elements that represent the population

Question 2

Parameter vs sample statistic

Answer 2

Parameter = measure used to describe a characteristic of population
Statistic = measure that describes a characteristic of the sample

Question 3

Expected value

Answer 3

anticipated value for an investment at some point in the future

Question 4

Key characteristics of normal distrbution (5)

Answer 4

Mean = mode = median
Skewness = 0
Kurtosis = 3 –> excess kurtosis = 0
50% of values above mean, 50% below
68% of obs within 1 sd, 95% within 2 sd, 99.7% within 3 sd

Question 5

Any normal distribution can be standardised by converting into

Answer 5

z-scores –> tell you how many standard deviations from the mean each value lies

Question 6

What is the distribution of stock prices, market capitalisation, income, etc?

Answer 6

Lognormal –> unable to get stocks for less than $0
* right skewed instead of bell curve
* if you can get a normal distribution by applying log function then original distribution = lognormal

Question 7

Characteristics of lognormal distribution (3)

Answer 7

Becomes normal by taking log of all values, positively skewed (right skew), extreme values on positive side of dist.

Question 8

Chi-squared test

Answer 8

Compare sample variance with population variance

Formula = ((n-1) x variance^2)/(sample var^2)

Question 9

Possible hypothesis pairs for Chi-Squared Test

Answer 9

• Two Tailed H0: S^2 = variance^2
• Right Tailed H0: S^2 <= Variance^2
• Left Tailed H): S^2 >= Variance^2

Question 10

F-Test

Answer 10

Only one difference between F-Test and Chi-Squared
* check whether two population or sample variances are equal or not
*variance 1/variance 2

Question 11

What are the critical values

Answer 11

> = 1.96 - statistically significant
-1.96 < x < 1.96 - statistically insignificant

Question 12

t-distribution (6)

Answer 12

similar to normal (Z) distribution
* symmetric
* mean of 0
* no assumption that the population std dev is known
* defined by df
* most useful for small sample sizes when the population standard deviation is not known
* as sample size increases, becomes more similar to normal distribution

Question 13

What are the 4 moments in finance?

Answer 13

Mean - average
Variance - degree to which returns vary over time
Skewness - lack of symmetry
Kurtosis - extreme values in either tail

Question 14

+ve skewness (2)

Answer 14

Mean > median > mode
right skew (income)

Question 15

-ve skew

Answer 15

mean < median < mode
left skewed (retired)

Question 16

Why is skewness important for investors?

Answer 16

Shows extreme values not only average

Question 17

Kurtosis (3)

Answer 17

Measures extreme values in either tail
High kurtosis = fat tails (differs from 3)
Normal = 3

Question 18

Name for high kurtosis

Answer 18

Leptokurtic - experiences occasional extreme returns (positive or negative)

Question 19

Name for low kurtosis

Answer 19

Platykurtic - flat tails (less kurtosis than normal distribution)

Question 20

You can not reach a conclusion about the skew of a distrbution if the skewness test (Zskew) falls within what values? –> kurtosis follows the same rules

Answer 20

+1.96 and -1.96
above +1.96 = +ve
Below - 1.96 = -ve

Question 21

How often do we experience a 2.5% drop in stock prices?

Answer 21

less than 5% probability (2.427 s.d. away from the mean)

Question 22

Distribution of daily returns is more

Answer 22

peaked (more obs. close to mean) than normal distribution
actual data has fat tails (higher number of extreme observations)

Question 23

Covariance

Answer 23

Determines the relationship between the movement of two asset prices, indicating the direction of the linear relationship
-1.0 to +1.0 scale

Question 24

Autocorrelation

Answer 24

correlation between a series and the lagged version of itself

Question 25

Does the classic 60/40 (stocks/bonds) portfolio offer true diversification?

Answer 25

No - true diversification is when both assets are risky and have low or negative correlation

Question 26

Is there diversification benefits of adding junk bonds to equity portfolio?

Answer 26

Yes - junk bonds = bond of very risky companies, risky asset hence, if there is low/negative correlation there is diversification`

Question 27

Any diversification of adding gold to equity portfolio?

Answer 27

No - gold = safe asset

Question 28

Any diversification benefits of adding treasury bonds to equity portfolio?

Answer 28

No - treasury bonds = risk-free

Question 29

Z and t-tests (2)

Answer 29

both hypothesis tests for establishing if there is a significant difference between two groups
* t-test for small sample or when population standard deviation is unknown

Question 30

Paired t-test (2)

Answer 30

Estimated using difference between paired observations
same sample sizes

Question 31

Other two t-tests

Answer 31

independent samples, unpaired, equal variances
independent samples, unpaired, unequal variances

Question 32

Spearman Rank Ordered Correlation (SROCC) (3)

Answer 32

Use when the relationship between two variables is not linear
* rank via a characteristic
* rank converts into linear relationship

Question 33

Pearsons Product Moment Correlation Coefficient (PPMCC)

Answer 33

Use when unsure whether the relationship is linear or non linear
* estimates a measure of linear relationship between X and Y
* plot empirical observations in a scatter plot and use OLS to fit a line of best fit