CHAPTER ELEVEN FACTOR MODELS

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

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

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

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

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

MULTIPLE-FACTOR MODELS use more than one explanatory variable in the return-generating process

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

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

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

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

MULTIPLE-FACTOR MODELS some of these factors may include THE 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 possible utilities transportation financial

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

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 …

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

ESTIMATING FACTOR MODELS CROSS-SECTIONAL APPROACH BEGINNING ASSUMPTION

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

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

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

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

ESTIMATING FACTOR MODELS FACTOR-ANALYTIC APPROACH BEGINNING ASSUMPTIONS

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

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