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# The Nature and Purpose of Econometric

## 1. Chapter 1

IntroductionIntroductory Econometrics for Finance © Chris Brooks 2014 1

## 2. The Nature and Purpose of Econometrics

• What is Econometrics?• Literal meaning is “measurement in economics”.

• Definition of financial econometrics:

The application of statistical and mathematical techniques to problems in

finance.

Introductory Econometrics for Finance © Chris Brooks 2014 2

## 3. Examples of the kind of problems that may be solved by an Econometrician

1. Testing whether financial markets are weak-form informationallyefficient.

2. Testing whether the CAPM or APT represent superior models for the

determination of returns on risky assets.

3. Measuring and forecasting the volatility of bond returns.

4. Explaining the determinants of bond credit ratings used by the ratings

agencies.

5. Modelling long-term relationships between prices and exchange rates

Introductory Econometrics for Finance © Chris Brooks 2014 3

## 4. Examples of the kind of problems that may be solved by an Econometrician (cont’d)

6. Determining the optimal hedge ratio for a spot position in oil.7. Testing technical trading rules to determine which makes the most

money.

8. Testing the hypothesis that earnings or dividend announcements have

no effect on stock prices.

9. Testing whether spot or futures markets react more rapidly to news.

10.Forecasting the correlation between the returns to the stock indices of

two countries.

Introductory Econometrics for Finance © Chris Brooks 2014 4

## 5. What are the Special Characteristics of Financial Data?

• Frequency & quantity of dataStock market prices are measured every time there is a trade or

somebody posts a new quote.

• Quality

Recorded asset prices are usually those at which the transaction took place.

No possibility for measurement error but financial data are “noisy”.

Introductory Econometrics for Finance © Chris Brooks 2014 5

## 6. Types of Data and Notation

There are 3 types of data which econometricians might use for analysis:

1. Time series data

2. Cross-sectional data

3. Panel data, a combination of 1. & 2.

The data may be quantitative (e.g. exchange rates, stock prices, number of

shares outstanding), or qualitative (e.g. day of the week).

Examples of time series data

Series

GNP or unemployment

government budget deficit

money supply

value of a stock market index

Frequency

monthly, or quarterly

annually

weekly

as transactions occur

Introductory Econometrics for Finance © Chris Brooks 2014 6

## 7. Time Series versus Cross-sectional Data

• Examples of Problems that Could be Tackled Using a Time Series Regression- How the value of a country’s stock index has varied with that country’s

macroeconomic fundamentals.

- How the value of a company’s stock price has varied when it announced the

value of its dividend payment.

- The effect on a country’s currency of an increase in its interest rate

• Cross-sectional data are data on one or more variables collected at a single

point in time, e.g.

- A poll of usage of internet stock broking services

- Cross-section of stock returns on the New York Stock Exchange

- A sample of bond credit ratings for UK banks

Introductory Econometrics for Finance © Chris Brooks 2014 7

## 8. Cross-sectional and Panel Data

• Examples of Problems that Could be Tackled Using a Cross-Sectional Regression- The relationship between company size and the return to investing in its shares

- The relationship between a country’s GDP level and the probability that the

government will default on its sovereign debt.

• Panel Data has the dimensions of both time series and cross-sections, e.g. the

daily prices of a number of blue chip stocks over two years.

• It is common to denote each observation by the letter t and the total number of

observations by T for time series data, and to to denote each observation by the

letter i and the total number of observations by N for cross-sectional data.

Introductory Econometrics for Finance © Chris Brooks 2014 8

## 9. Continuous and Discrete Data

• Continuous data can take on any value and are not confined to take specificnumbers.

• Their values are limited only by precision.

o For example, the rental yield on a property could be 6.2%, 6.24%, or 6.238%.

• On the other hand, discrete data can only take on certain values, which are usually

integers

o For instance, the number of people in a particular underground carriage or the number

of shares traded during a day.

• They do not necessarily have to be integers (whole numbers) though, and are

often defined to be count numbers.

o For example, until recently when they became ‘decimalised’, many financial asset

prices were quoted to the nearest 1/16 or 1/32 of a dollar.

Introductory Econometrics for Finance © Chris Brooks 2014 9

## 10. Cardinal, Ordinal and Nominal Numbers

• Another way in which we could classify numbers is according to whether they arecardinal, ordinal, or nominal.

• Cardinal numbers are those where the actual numerical values that a particular

variable takes have meaning, and where there is an equal distance between the

numerical values.

o Examples of cardinal numbers would be the price of a share or of a building, and the

number of houses in a street.

• Ordinal numbers can only be interpreted as providing a position or an ordering.

o Thus, for cardinal numbers, a figure of 12 implies a measure that is `twice as good' as a

figure of 6. On the other hand, for an ordinal scale, a figure of 12 may be viewed as

`better' than a figure of 6, but could not be considered twice as good. Examples of

ordinal numbers would be the position of a runner in a race.

Introductory Econometrics for Finance © Chris Brooks 2014 10

## 11. Cardinal, Ordinal and Nominal Numbers (Cont’d)

• Nominal numbers occur where there is no natural ordering of the values at all.o Such data often arise when numerical values are arbitrarily assigned, such as telephone

numbers or when codings are assigned to qualitative data (e.g. when describing the

exchange that a US stock is traded on.

• Cardinal, ordinal and nominal variables may require different modelling

approaches or at least different treatments, as should become evident in the

subsequent chapters.

Introductory Econometrics for Finance © Chris Brooks 2014 11

## 12. Returns in Financial Modelling

It is preferable not to work directly with asset prices, so we usually convert the raw prices into a series of

returns. There are two ways to do this:

Simple returns

p pt 1

Rt t

100%

pt 1

or

log returns

pt

100%

Rt ln

pt 1

where, Rt denotes the return at time t

pt denotes the asset price at time t

ln denotes the natural logarithm

We also ignore any dividend payments, or alternatively assume that the price series have been already

adjusted to account for them.

Introductory Econometrics for Finance © Chris Brooks 2014 12

## 13. Log Returns

The returns are also known as log price relatives, which will be used throughout this

book. There are a number of reasons for this:

1. They have the nice property that they can be interpreted as continuously

compounded returns.

2. Can add them up, e.g. if we want a weekly return and we have calculated

daily log returns:

r1 = ln p1/p0 = ln p1 - ln p0

r2 = ln p2/p1 = ln p2 - ln p1

r3 = ln p3/p2 = ln p3 - ln p2

r4 = ln p4/p3 = ln p4 - ln p3

r5 = ln p5/p4 = ln p5 - ln p4

ln p5 - ln p0 = ln p5/p0

Introductory Econometrics for Finance © Chris Brooks 2014 13

## 14. A Disadvantage of using Log Returns

• There is a disadvantage of using the log-returns. The simple return on aportfolio of assets is a weighted average of the simple returns on the

individual assets:

N

Rpt wip Rit

i 1

• But this does not work for the continuously compounded returns.

Introductory Econometrics for Finance © Chris Brooks 2014 14

## 15. Real Versus Nominal Series

The general level of prices has a tendency to rise most of the time because of

inflation

We may wish to transform nominal series into real ones to adjust them for

inflation

This is called deflating a series or displaying a series at constant prices

We do this by taking the nominal series and dividing it by a price deflator:

real seriest = nominal seriest 100 / deflatort

(assuming that the base figure is 100)

We only deflate series that are in nominal price terms, not quantity terms.

Introductory Econometrics for Finance © Chris Brooks 2014 15

## 16. Deflating a Series

• If we wanted to convert a series into a particular year’s figures (e.g. houseprices in 2010 figures), we would use:

real seriest = nominal seriest deflatorreference year / deflatort

• This is the same equation as the previous slide except with the deflator for

the reference year replacing the assumed deflator base figure of 100

• Often the consumer price index, CPI, is used as the deflator series.

Introductory Econometrics for Finance © Chris Brooks 2014 16

## 17. Steps involved in the formulation of econometric models

Economic or Financial Theory (Previous Studies)Formulation of an Estimable Theoretical Model

Collection of Data

Model Estimation

Is the Model Statistically Adequate?

No

Yes

Reformulate Model

Interpret Model

Use for Analysis

Introductory Econometrics for Finance © Chris Brooks 2014

17

## 18. Some Points to Consider when reading papers in the academic finance literature

1. Does the paper involve the development of a theoretical model or is itmerely a technique looking for an application, or an exercise in data

mining?

2. Is the data of “good quality”? Is it from a reliable source? Is the size of

the sample sufficiently large for asymptotic theory to be invoked?

3. Have the techniques been validly applied? Have diagnostic tests been

conducted for violations of any assumptions made in the estimation

of the model?

Introductory Econometrics for Finance © Chris Brooks 2014 18

## 19. Some Points to Consider when reading papers in the academic finance literature (cont’d)

4. Have the results been interpreted sensibly? Is the strength of the resultsexaggerated? Do the results actually address the questions posed by the

authors?

5. Are the conclusions drawn appropriate given the results, or has the

importance of the results of the paper been overstated?

Introductory Econometrics for Finance © Chris Brooks 2014 19

## 20. Bayesian versus Classical Statistics

• The philosophical approach to model-building used here throughout isbased on ‘classical statistics’

• This involves postulating a theory and then setting up a model and

collecting data to test that theory

• Based on the results from the model, the theory is supported or refuted

• There is, however, an entirely different approach known as Bayesian

statistics

• Here, the theory and model are developed together

• The researcher starts with an assessment of existing knowledge or beliefs

formulated as probabilities, known as priors

• The priors are combined with the data into a model

Introductory Econometrics for Finance © Chris Brooks 2014 20

## 21. Bayesian versus Classical Statistics (Cont’d)

• The beliefs are then updated after estimating the model to form a set ofposterior probabilities

• Bayesian statistics is a well established and popular approach, although

less so than the classical one

• Some classical researchers are uncomfortable with the Bayesian use of

prior probabilities based on judgement

• If the priors are very strong, a great deal of evidence from the data would

be required to overturn them

• So the researcher would end up with the conclusions that he/she wanted in

the first place!

• In the classical case by contrast, judgement is not supposed to enter the

process and thus it is argued to be more objective.

Introductory Econometrics for Finance © Chris Brooks 2014 21