1. Descriptive Statistics

Question 1

Return of an Asset (Formula)

Question 2

Covariance matrix (Formula)

Question 3

Variance (Formula) and what is it’s relationship to the covariance matrix?

Question 4

Covariance (formula)

Question 5

Empirical mean (formula)

Question 6

Empirical covariance (formula)

Question 7

Skewness (formula) and how do you interpret the results?

Answer 7

> 0 gives positive (right) asymmetry

= 0 gives symmetry

< 0 gives negative (left) symmetry

Question 8

Kurtosis (formula) and how do you interpret it?

Answer 8

> 3 fat tails
= 3 normal
< 3 thin tails

With fat tails you would have a higher probability of getting larger outcomes

Question 9

What’s kurtosis vs excess kurtosism + how do you calculate them?

Answer 9

Excess kurtosis subtracts 3 from the answer which allows you to compare the results to 0 instead of 3

Question 10

How do you make an estimator unbiased?

Answer 10

You divide by the number of observations minus 1 (T - 1)

Question 11

What does it mean to fit a normal distribution?

Answer 11

Find the mean and standard deviation

Question 12

What is the skewness and kurtosis of a normal distribution?

Answer 12

Skewness = 0
Kurtosis = 3

Question 13

Does it make sense to expect a non-normal distribution of financial returns?

Answer 13

Yes it does because financial returns are not typically normally distributed. Rather you would see skewness and kurtosis, the presence of extreme events, volatility clustering and non-stationarity