RiskandReturn(投资分析与投资组合管理)

Arbitrage Pricing Theory (APT)
Rt Et bi1 i bi2 i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period
Arbitrage Pricing Theory (APT)
• How do you test the APT by examining anomalies found with the CAPM?
ቤተ መጻሕፍቲ ባይዱ
Chapter 9 - Multifactor Models of Risk and Return
• What are the empirical test results related to the APT?
• Why do some authors contend that the APT model is untestable?
• What are the concerns related to the multiple factors of the APT model?
Chapter 9 - Multifactor Models of Risk and Return
Arbitrage Pricing Theory (APT)
Bik determine how each asset reacts to this common factor
Each asset may be affected by growth in GNP, but the effects will differ
Arbitrage Pricing Theory (APT)
Rt Et bi1 i bi2 i ... bik k i For i = 1 to N where: Ri = return on asset i during a specified time period Ei = expected return for asset i
Rt Et bi1 i bi2 i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
bik = reaction in asset i’s returns to movements in a common factor
Arbitrage Pricing Theory (APT)
Rt Et bi1 i bi2 i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
Arbitrage Pricing Theory (APT)
• APT assumes that, in equilibrium, the return on a zero-investment, zero-systematic-risk portfolio is zero when the unique effects are diversified away
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero
• An alternative pricing theory with fewer assumptions was developed:
• Arbitrage Pricing Theory
Arbitrage Pricing Theory - APT
Three major assumptions: 1. Capital markets are perfectly competitive 2. Investors always prefer more wealth to less wealth with certainty 3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes
= reaction in asset i’s returns to movements in a common bik factor
= a common factor with a zero mean that influences the k returns on all assets
= a unique effect on asset i’s return that, by assumption, is i completely diversifiable in large portfolios and has a mean of zero = number of assets N
Questions to be answered:
• What is the arbitrage pricing theory (APT) and what are its similarities and differences relative to the CAPM?
• What are the major assumptions not required by the APT model compared to the CAPM?
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
• How is risk estimated in a multifactor setting?
Arbitrage Pricing Theory (APT)
• CAPM is criticized because of the difficulties in selecting a proxy for the market portfolio as a benchmark
In application of the theory, the factors are not identified
Similar to the CAPM, the unique effects are independent and will be diversified away in a large portfolio
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP – Major political upheavals
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates – And many more….
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets:
– Inflation – Growth in GNP
Arbitrage Pricing Theory (APT)
bik = reaction in asset i’s returns to movements in a common factor
= a common factor with a zero mean that influences the k returns on all assets
Arbitrage Pricing Theory (APT)
Rt Et bi1 i bi2 i ... bik k i
For i = 1 to N where: Ri = return on asset i during a specified time period
Ei = expected return for asset i
Arbitrage Pricing Theory (APT)
• What are multifactor models and how are related to the APT?
• What are the steps necessary in developing a usable multifactor model?
• What are the multifactor models in practice?
Rt Et bi1 i bi2 i ... bik k i For i = 1 to N where: Ri = return on asset i during a specified time period Ei = expected return for asset i
= reaction in asset i’s returns to movements in a common bik factor
– Inflation – Growth in GNP – Major political upheavals – Changes in interest rates – And many more….
Contrast with CAPM insistence that only beta is relevant
Assumptions of CAPM That Were Not Required by APT
APT does not assume • A market portfolio that contains all risky
assets, and is mean-variance efficient • Normally distributed security returns • Quadratic utility function
Lecture Presentation Software
to accompany
Investment Analysis and Portfolio Management
Seventh Edition by
Frank K. Reilly & Keith C. Brown
Chapter 9
Chapter 9 – Multifactor Models of Risk and Return
Arbitrage Pricing Theory (APT)
k Multiple factors expected to have an
impact on all assets:
Arbitrage Pricing Theory (APT)
Multiple factors expected to have an impact on all assets: