CHAPTER TEN
FACTOR MODELS
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
FACTOR MODELS AND RETURN- GENERATING PROCESSES
FACTOR MODELS
• assume returns of two securities are
correlated in some way
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 securitiesTHE MARKET MODEL
THE MARKET MODEL
• is a specific example of a factor model
• the general form may be written
r
i=
i, I
i, Ir
i, Iwhere the factor is the market index (I) r i is the i th return in the market
THE MARKET MODEL
TWO IMPORTANT FEATURES OF THE ONE-FACTOR MODEL
• THE TANGENCY PORTFOLIO
• DIVERSIFICATION
MULTIPLE-FACTOR MODELS
MULTIPLE FACTOR MODELS
• use more than one explanatory variable in
the return-generating process
MULTIPLE-FACTOR MODELS
MULTIPLE-FACTOR MODELS
• some of these factors may include
THE GROWTH RATE OF GDPMULTIPLE-FACTOR MODELS
MULTIPLE-FACTOR MODELS
• some of these factors may include
THE LEVEL OF INTEREST RATESMULTIPLE-FACTOR MODELS
MULTIPLE-FACTOR MODELS
• some of these factors may include
THE YIELD SPREAD BETWEEN CERTAIN VARIABLESMULTIPLE-FACTOR MODELS
MULTIPLE-FACTOR MODELS
• some of these factors may include
THE INFLATION RATEMULTIPLE-FACTOR MODELS
MULTIPLE-FACTOR MODELS
• some of these factors may include
THE LEVEL OF OIL PRICESMULTIPLE-FACTOR MODELS
SECTOR-FACTOR MODELS
• Assumption:
prices may move together for the same industry or economic sectorMULTIPLE-FACTOR MODELS
SECTOR-FACTOR MODELS
• sectors possible
utilities
transportation
financialESTIMATING FACTOR MODELS
THREE METHODS
• TIME-SERIES APPROACH
• CROSS-SECTIONAL APPROACH
• FACTOR-ANALYTIC APPROACH
ESTIMATING FACTOR MODELS
TIME-SERIES APPROACH
• BEGINNING ASSUMPTIONS:
ESTIMATING FACTOR MODELS
TIME-SERIES APPROACH
• BEGINNING ASSUMPTIONS:
investor knows in advance of the factors that influence a security's returnsESTIMATING 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 firmESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
ESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
Identify Attributes: estimates of a securities sensitivities to certain factorsESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
Identify Attributes: estimates of a securities sensitivities to certain factors
estimate attributes in a particular period of timeESTIMATING FACTOR MODELS
CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
Identify Attributes: estimates of a securities sensitivities to certain factors
estimate attributes in a particular period of time
repeat over multiple time periods to estimate the factor’s standard deviations andcorrelations
ESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS:
neither factor values nor securities attributes are knowESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS
ESTIMATING FACTOR MODELS
FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS:
neither factor values nor securities attributes are know
uses factor analysis approachESTIMATING FACTOR MODELS
