1. CHAPTER ELEVEN
FACTOR MODELS

2. FACTOR MODELS AND RETURN-GENERATING PROCESSES
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
assume returns of two securities are correlated in some way

4. FACTOR MODELS AND RETURN-GENERATING PROCESSES
any unexplained aspects of a return are assumed to be
unique
uncorrelated with the unique aspect of other securities

5. r i,t = a i,I + b i,I r I,t + e i,t THE MARKET MODEL THE MARKET MODEL
is a specific example of a factor model
the general form may be written
r i,t = a i,I + b i,I r I,t + e i,t
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
use more than one explanatory variable in the return-generating process

8. MULTIPLE-FACTOR MODELS
some of these factors may include
THE GROWTH RATE OF GDP

9. MULTIPLE-FACTOR MODELS
some of these factors may include
THE LEVEL OF INTEREST RATES

10. MULTIPLE-FACTOR MODELS
some of these factors may include
THE YIELD SPREAD BETWEEN CERTAIN VARIABLES

11. MULTIPLE-FACTOR MODELS
some of these factors may include
THE INFLATION RATE

12. 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
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
example – sensitivity of GE stock returns to changes in interest rates …

20. Relationship Between Return to General
Electric and Changes in Interest Rates
-25%
-20%
-15%
-10%
-5% 0% 5%
10%
15%
20%
25%
Return to G.E.
Line of Best Fit
April, 1987
-10%
-5% 0% 5%
10%
Percentage Change in Yield on Long-term Govt. Bond

21. ESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
BEGINNING ASSUMPTION

22. ESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
BEGINNING ASSUMPTION
Identify Attributes: estimates of a security’s sensitivities to certain factors

23. 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

24. 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

25. ESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
BEGINNING ASSUMPTIONS:
neither factor values nor securities attributes are known

26. ESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
BEGINNING ASSUMPTIONS

27. ESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
BEGINNING ASSUMPTIONS:
neither factor values nor security’s attributes are known
uses factor analysis approach

28. 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