CHAPTER ELEVEN

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CHAPTER ELEVEN

• FACTOR MODELS

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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

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FACTOR MODELS AND RETURN-GENERATING PROCESSES

• FACTOR MODELS
• assume returns of two securities are correlated
  in some way

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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

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THE MARKET MODEL

• THE MARKET MODEL
• is a specific example of a factor model
• the general form may be written
• r i ai, I b i, I r e i, I
• where the factor is the market index (I)
• r i is the i th return in the market

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THE MARKET MODEL

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

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MULTIPLE-FACTOR MODELS

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

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MULTIPLE-FACTOR MODELS

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

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MULTIPLE-FACTOR MODELS

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

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MULTIPLE-FACTOR MODELS

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

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MULTIPLE-FACTOR MODELS

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

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MULTIPLE-FACTOR MODELS

• MULTIPLE-FACTOR MODELS
• some of these factors may include
• THE LEVEL OF OIL PRICES

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MULTIPLE-FACTOR MODELS

• SECTOR-FACTOR MODELS
• Assumption
• prices may move together for the same industry or
  economic sector

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MULTIPLE-FACTOR MODELS

• SECTOR-FACTOR MODELS
• sectors possible
• utilities
• transportation
• financial

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ESTIMATING FACTOR MODELS

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

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ESTIMATING FACTOR MODELS

• TIME-SERIES APPROACH
• BEGINNING ASSUMPTIONS

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ESTIMATING FACTOR MODELS

• TIME-SERIES APPROACH
• BEGINNING ASSUMPTIONS
• investor knows in advance of the factors that
  influence a security's returns

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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

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ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION

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ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
• Identify Attributes estimates of a securitys
  sensitivities to certain factors

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ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
• Identify Attributes estimates of a securitys
  sensitivities to certain factors
• estimate attributes in a particular period of
  time

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ESTIMATING FACTOR MODELS

• CROSS-SECTIONAL APPROACH
• BEGINNING ASSUMPTION
• Identify Attributes estimates of a securitys
  sensitivities to certain factors
• estimate attributes in a particular period of
  time
• repeat over multiple time periods to estimate the
  factors standard deviations and correlations

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ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS
• neither factor values nor securities attributes
  are known

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ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS

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ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS
• neither factor values nor securitys attributes
  are known
• uses factor analysis approach

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ESTIMATING FACTOR MODELS

• FACTOR-ANALYTIC APPROACH
• BEGINNING ASSUMPTIONS
• neither factor values nor securitys 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