Empirical Methods of Finance
Exam: 11-12-2017
Resit:
Part 1: Pavanini
Week 1: Introduction
Financial econometrics
What are problems in finance?
1. Suppose you learn two different theories of asset pricing (CAPM & APT) and you collect data
on returns on risky assets over time
a. With econometrics you can apply the theory to the data, testing which of the
theories better determines the returns
2. Suppose you work for a central bank and you are asked to forecast how interest rates,
inflation rates, or GDP will evolve in the next quarter or year
a. Collecting past data on these variables, econometrics gives you the statistical tools
necessary to forecast them
3. Suppose you are the owner of a firm and you need to decide on whether to adjust the salary
of your CEO, given the past performance
a. You want make sure you don’t pay your CEO too much or too little compared to rival
companies
b. If collect data on other companies’ performance and CEOs’ salaries, you can use
econometrics to determine the relationship between these variables.
In these examples, the main uses of financial econometrics are depicted:
Testing theories in finance
Forecasting future values of financial variables
Determining the relationship between financial variables
Here are the steps to follow when using financial econometrics:
1. Formulate a clear question of interest
2. Construct an economic/financial model to
guide your understanding of the problem
3. Find the data
4. Turn the economic/financial model into an
econometric model, this means specifying the
form of the function F(x)
All statistical techniques differ depending on the types of data that is uses
1. Cross-sectional data: these are data on one or more variables collected at a single point in
time
a. CEO salaries and past performance for different companies about fiscal year 2004
2. Time series data: these are data on one or more variables collected at many points in time
a. Weekly returns from 1976-1989
3. Panel data: this is a time series for each cross-sectional member of the dataset
a. Housing rental prices and town population for 1980-1990
b. This is a time series for each cross-sectional member of the dataset
,Week 1: Maths & Stats Review
Statistics
Random variables
A random variable is one that can take on any value from a given set, and where this value is at least
in part determined by chance. There are three types of random variables:
Bernoulli: that can take on only value 0 or 1
o Tossing a coin
Discrete: takes on only for finite numbers
o Rolling a dice
Continuous: infinitely many values
o Change in stock price
The diagram showing the probability of each possible score is called
the Probability distribution function.
The probabilities of each score can be defined as:
o Pj = P(X=j) where j = 2,…,12
▪ With 0 ≤ pj ≤ 1 and sum of all prob = 1
If we increase the number of dice towards infinity -> X converges
towards a continuous random variable and the diagram showing the
probability of each possible score converges to a Probability Density
Function (PDF).
The PDF summarizes the information on the possible outcomes of X and
corresponding probabilities.
Often however is it more interesting to know the probability that a certain
variable is below/above a certain value.
This probability is given by the Cumulative Distribution Function (CDF):
Joint distributions and Independence
Joint distribution:
Independence: Two random variables X, Y are independent if knowing the
outcome of X does not change the probabilities of The possible outcomes of Y and vice versa.
Conditional distributions and Dependence
Conditional:
Independent :
Dependent:
Distributions
Measures of Central tendency
o E(x) = the expected value, the mean of
random variable X
o The median of a random variable X: the
middle nummer of the ordered values.
▪ Difference between mean and median: the median is less sensitive to
changes in extreme values
, Measures of dispersion
o Var(X): the variance that is a measure of
how far a random variable X is from it’s
mean
o Sd(x): the standard deviation, that is the
positive square root of the variance
Measures of association
o Covariance (x,y)
o Correlation (x,y)
.correlate
Descriptive statistics
Stata: .tabstat variable, stat(………..) col (stat)
Normal (Gaussian) distribution
This is the most commonly used distribution in statistics and econometrics since it is easy to work
with, it’s symmetric, and has useful mathematical properties.
Other distributions
1. Chi-Square Distribution:
The slope / shape of the distribution depends on the degrees of
freedom (df).
2. T distribution:
3. F distribution:
Exam: 11-12-2017
Resit:
Part 1: Pavanini
Week 1: Introduction
Financial econometrics
What are problems in finance?
1. Suppose you learn two different theories of asset pricing (CAPM & APT) and you collect data
on returns on risky assets over time
a. With econometrics you can apply the theory to the data, testing which of the
theories better determines the returns
2. Suppose you work for a central bank and you are asked to forecast how interest rates,
inflation rates, or GDP will evolve in the next quarter or year
a. Collecting past data on these variables, econometrics gives you the statistical tools
necessary to forecast them
3. Suppose you are the owner of a firm and you need to decide on whether to adjust the salary
of your CEO, given the past performance
a. You want make sure you don’t pay your CEO too much or too little compared to rival
companies
b. If collect data on other companies’ performance and CEOs’ salaries, you can use
econometrics to determine the relationship between these variables.
In these examples, the main uses of financial econometrics are depicted:
Testing theories in finance
Forecasting future values of financial variables
Determining the relationship between financial variables
Here are the steps to follow when using financial econometrics:
1. Formulate a clear question of interest
2. Construct an economic/financial model to
guide your understanding of the problem
3. Find the data
4. Turn the economic/financial model into an
econometric model, this means specifying the
form of the function F(x)
All statistical techniques differ depending on the types of data that is uses
1. Cross-sectional data: these are data on one or more variables collected at a single point in
time
a. CEO salaries and past performance for different companies about fiscal year 2004
2. Time series data: these are data on one or more variables collected at many points in time
a. Weekly returns from 1976-1989
3. Panel data: this is a time series for each cross-sectional member of the dataset
a. Housing rental prices and town population for 1980-1990
b. This is a time series for each cross-sectional member of the dataset
,Week 1: Maths & Stats Review
Statistics
Random variables
A random variable is one that can take on any value from a given set, and where this value is at least
in part determined by chance. There are three types of random variables:
Bernoulli: that can take on only value 0 or 1
o Tossing a coin
Discrete: takes on only for finite numbers
o Rolling a dice
Continuous: infinitely many values
o Change in stock price
The diagram showing the probability of each possible score is called
the Probability distribution function.
The probabilities of each score can be defined as:
o Pj = P(X=j) where j = 2,…,12
▪ With 0 ≤ pj ≤ 1 and sum of all prob = 1
If we increase the number of dice towards infinity -> X converges
towards a continuous random variable and the diagram showing the
probability of each possible score converges to a Probability Density
Function (PDF).
The PDF summarizes the information on the possible outcomes of X and
corresponding probabilities.
Often however is it more interesting to know the probability that a certain
variable is below/above a certain value.
This probability is given by the Cumulative Distribution Function (CDF):
Joint distributions and Independence
Joint distribution:
Independence: Two random variables X, Y are independent if knowing the
outcome of X does not change the probabilities of The possible outcomes of Y and vice versa.
Conditional distributions and Dependence
Conditional:
Independent :
Dependent:
Distributions
Measures of Central tendency
o E(x) = the expected value, the mean of
random variable X
o The median of a random variable X: the
middle nummer of the ordered values.
▪ Difference between mean and median: the median is less sensitive to
changes in extreme values
, Measures of dispersion
o Var(X): the variance that is a measure of
how far a random variable X is from it’s
mean
o Sd(x): the standard deviation, that is the
positive square root of the variance
Measures of association
o Covariance (x,y)
o Correlation (x,y)
.correlate
Descriptive statistics
Stata: .tabstat variable, stat(………..) col (stat)
Normal (Gaussian) distribution
This is the most commonly used distribution in statistics and econometrics since it is easy to work
with, it’s symmetric, and has useful mathematical properties.
Other distributions
1. Chi-Square Distribution:
The slope / shape of the distribution depends on the degrees of
freedom (df).
2. T distribution:
3. F distribution:
