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 beuniqueuncorrelated with the unique aspect of

other securities

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

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 includeTHE GROWTH RATE OF GDP

MULTIPLE-FACTOR MODELS MULTIPLE-FACTOR MODELS

•some of these factors may includeTHE LEVEL OF INTEREST RATES

MULTIPLE-FACTOR MODELS MULTIPLE-FACTOR MODELS

•some of these factors may includeTHE YIELD SPREAD BETWEEN CERTAIN

VARIABLES

MULTIPLE-FACTOR MODELS MULTIPLE-FACTOR MODELS

•some of these factors may includeTHE INFLATION RATE

MULTIPLE-FACTOR MODELS MULTIPLE-FACTOR MODELS

•some of these factors may includeTHE LEVEL OF OIL PRICES

MULTIPLE-FACTOR MODELS SECTOR-FACTOR MODELS

•Assumption:prices may move together for the same

industry or economic sector

MULTIPLE-FACTOR MODELS SECTOR-FACTOR MODELS

•sectors possibleutilitiestransportationfinancial

ESTIMATING 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 returns

ESTIMATING FACTOR MODELS TIME-SERIES APPROACH

•BEGINNING ASSUMPTIONS: investor knows in advance of the factors

that influence a security's returnsthe information may be gained from an

economic analysis of the firm

ESTIMATING FACTOR MODELS CROSS-SECTIONAL APPROACH

•BEGINNING ASSUMPTION

ESTIMATING FACTOR MODELS CROSS-SECTIONAL APPROACH

•BEGINNING ASSUMPTIONIdentify Attributes: estimates of a

securities sensitivities to certain factors

ESTIMATING FACTOR MODELS CROSS-SECTIONAL APPROACH

•BEGINNING ASSUMPTIONIdentify Attributes: estimates of a

securities sensitivities to certain factorsestimate attributes in a particular period

of time

ESTIMATING FACTOR MODELS CROSS-SECTIONAL APPROACH

•BEGINNING ASSUMPTIONIdentify Attributes: estimates of a

securities sensitivities to certain factorsestimate attributes in a particular period

of timerepeat over multiple time periods to

estimate the factor’s standard deviations and correlations

ESTIMATING FACTOR MODELS FACTOR-ANALYTIC APPROACH

•BEGINNING ASSUMPTIONS:neither factor values nor securities

attributes are know

ESTIMATING FACTOR MODELS FACTOR-ANALYTIC APPROACH

•BEGINNING ASSUMPTIONS

ESTIMATING FACTOR MODELS FACTOR-ANALYTIC APPROACH

•BEGINNING ASSUMPTIONS:neither factor values nor securities

attributes are knowuses factor analysis approach

ESTIMATING FACTOR MODELS FACTOR-ANALYTIC APPROACH

•BEGINNING ASSUMPTIONS:neither factor values nor securities

attributes are knowuses factor analysis approachtake the returns over many time periods

from a sample to identify one or more significant factors generating covariances

END OF CHAPTER 10