Factor Models and Return

1

FACTOR MODELS

2

FACTOR MODELS AND RETURN-GENERATING PROCESSES

• FACTOR MODELS– DEFINITION: a model of a return-generating

process that relates returns on securities to the movement of one or more common factors

3

FACTOR MODELS AND RETURN-GENERATING PROCESSES

• FACTOR MODELS– assume returns of two securities are correlated

in some way

4

FACTOR MODELS AND RETURN-GENERATING PROCESSES

• FACTOR MODELS– any unexplained aspects of a return are

assumed to be• unique

• uncorrelated with the unique aspect of other securities

5

THE MARKET MODEL

• THE MARKET MODEL– is a specific example of a factor model– the general form may be written

r i = i, I i, I ri, I

where the factor is the market index (I)

r i is the i th return in the market

6

THE MARKET MODEL

• TWO IMPORTANT FEATURES OF THE ONE-FACTOR MODEL– THE TANGENCY PORTFOLIO– DIVERSIFICATION

7

MULTIPLE-FACTOR MODELS

• MULTIPLE FACTOR MODELS– use more than one explanatory variable in the

return-generating process

8

MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS– some of these factors may include

• THE GROWTH RATE OF GDP

9

MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS– some of these factors may include

• THE LEVEL OF INTEREST RATES

10

MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS– some of these factors may include

• THE YIELD SPREAD BETWEEN CERTAIN VARIABLES

11

MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS– some of these factors may include

• THE INFLATION RATE

12

MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS– some of these factors may include

• THE LEVEL OF OIL PRICES

13

MULTIPLE-FACTOR MODELS

• SECTOR-FACTOR MODELS– Assumption:

• prices may move together for the same industry or economic sector

14

MULTIPLE-FACTOR MODELS

• SECTOR-FACTOR MODELS– sectors possible

• utilities

• transportation

• financial

15

ESTIMATING FACTOR MODELS

• THREE METHODS– TIME-SERIES APPROACH– CROSS-SECTIONAL APPROACH– FACTOR-ANALYTIC APPROACH

16

ESTIMATING FACTOR MODELS

• TIME-SERIES APPROACH– BEGINNING ASSUMPTIONS:

17

ESTIMATING FACTOR MODELS

• TIME-SERIES APPROACH– BEGINNING ASSUMPTIONS:

• investor knows in advance of the factors that influence a security's returns

18

ESTIMATING FACTOR MODELS

• TIME-SERIES APPROACH– BEGINNING ASSUMPTIONS:

• investor knows in advance of the factors that influence a security's returns

• the information may be gained from an economic analysis of the firm

19

ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH– BEGINNING ASSUMPTION

20

ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH– BEGINNING ASSUMPTION

• Identify Attributes: estimates of a security’s sensitivities to certain factors

21

ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH– BEGINNING ASSUMPTION

• Identify Attributes: estimates of a security’s sensitivities to certain factors

• estimate attributes in a particular period of time

22

ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH– BEGINNING ASSUMPTION

• Identify Attributes: estimates of a security’s sensitivities to certain factors

• estimate attributes in a particular period of time

• repeat over multiple time periods to estimate the factor’s standard deviations and correlations

23

ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH– BEGINNING ASSUMPTIONS:

• neither factor values nor securities attributes are known

24

ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH– BEGINNING ASSUMPTIONS

25

ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH– BEGINNING ASSUMPTIONS:

• neither factor values nor security’s attributes are known

• uses factor analysis approach

26

ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH– BEGINNING ASSUMPTIONS:

• neither factor values nor security’s attributes are known

• uses factor analysis approach

• take the returns over many time periods from a sample to identify one or more significant factors generating covariances