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CAPMandAPT1.pptxCAPM and APT
Bodie, Kane, and Marcus
Essentials of Investments Eleventh Edition
7
Chapter
7.1 The Capital Asset Pricing Model
Capital Asset Pricing Model (CAPM)
Security’s required rate of return relates to systematic risk measured by beta
Market Portfolio (M)
Each security held in proportion to market value
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7.1 The Capital Asset Pricing Model: Assumptions
| Market Assumptions | Investor Assumptions |
| All investors are price takers | Investors plan for the same (single-period) horizon |
| All information relevant to security analysis is free and publicly available. | Investors are efficient users of analytical methods investors have homogeneous expectations. |
| All securities are publicly owned and traded. | Investors are rational, mean-variance optimizers. |
| No taxes on investment returns. | |
| No transaction costs. | |
| Lending and borrowing at the same risk-free rate are unlimited. |
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7.1 The Capital Asset Pricing Model
Hypothetical Equilibrium
All investors choose to hold market portfolio
Market portfolio is on efficient frontier, optimal risky portfolio
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7.1 The Capital Asset Pricing Model
Hypothetical Equilibrium
Risk premium on market portfolio is proportional to variance of market portfolio and investor’s risk aversion
Risk premium on individual assets
Proportional to risk premium on market portfolio
Proportional to beta coefficient of security on market portfolio
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Figure 7.1 Efficient Frontier and Capital Market Line
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7.1 The Capital Asset Pricing Model
Passive Strategy is Efficient
Mutual fund theorem: All investors desire same portfolio of risky assets, can be satisfied by single mutual fund composed of that portfolio
If passive strategy is costless and efficient, why follow active strategy?
If no one does security analysis, what brings about efficiency of market portfolio?
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7.1 The Capital Asset Pricing Model
Risk Premium of Market Portfolio
Demand drives prices, lowers expected rate of return/risk premiums
When premiums fall, investors move funds into risk-free asset
Equilibrium risk premium of market portfolio proportional to
Risk of market
Risk aversion of average investor
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7.1 The Capital Asset Pricing Model
Expected Returns on Individual Securities
Expected return-beta relationship
Implication of CAPM that security risk premiums (expected excess returns) will be proportional to beta
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7.1 The Capital Asset Pricing Model
The Security Market Line (SML)
Represents expected return-beta relationship of CAPM
Graphs individual asset risk premiums as function of asset risk
Alpha
Abnormal rate of return on security in excess of that predicted by equilibrium model (CAPM)
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Figure 7.2 The SML and a Positive-Alpha Stock
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7.1 The Capital Asset Pricing Model
Applications of CAPM
Use SML as benchmark for fair return on risky asset
SML provides “hurdle rate” for internal projects
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7.2 CAPM and Index Models
Index Model, Realized Returns, Mean-Beta Equation
: HPR
i: Asset
t: Period
: Intercept of security characteristic line
: Slope of security characteristic line
: Index return
: Firm-specific effects
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7.2 CAPM and Index Models
Estimating Index Model
, excess return
Residual = Actual return Predicted return for Google
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7.2 CAPM and Index Models: SCL
Security Characteristic Line (SCL)
Plot of security’s expected excess return over risk-free rate as function of excess return on market
Required rate = Risk-free rate + β x Expected excess return of index
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7.2 CAPM and Index Models
Predicting Betas
Mean reversion
Betas move towards mean over time
To predict future betas, adjust estimates from historical data to account for regression towards 1.0
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7.3 CAPM and the Real World
CAPM is false based on validity of its assumptions
Useful predictor of expected returns
Untestable as a theory
Principles still valid
Investors should diversify
Systematic risk is the risk that matters
Well-diversified risky portfolio can be suitable for wide range of investors
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7.4 Multifactor Models and CAPM
Multifactor models
Models of security returns that respond to several systematic factors
Two-index portfolio in realized returns
Two-factor SML
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7.4 Multifactor Models and CAPM
Fama-French Three-Factor Model
Estimation results
Three aspects of successful specification
Higher adjusted R-square
Lower residual SD
Smaller value of alpha
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Table 7.2 Multifactor Models and CAPM
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7.5 Arbitrage Pricing Theory
Arbitrage
Relative mispricing creates riskless profit
Arbitrage Pricing Theory (APT)
Risk-return relationships from no-arbitrage considerations in large capital markets
Well-diversified portfolio
Nonsystematic risk is negligible
Arbitrage portfolio
Positive return, zero-net-investment, risk-free portfolio
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7.5 Arbitrage Pricing Theory
Calculating APT
Returns on well-diversified portfolio
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Table 7.5 Portfolio Conversion
*When alpha is negative, you would reverse the signs of each portfolio weight to achieve a portfolio A with positive alpha and no net investment.
Steps to convert a well-diversified portfolio into an arbitrage portfolio:
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Figure 7.5 Security Characteristic Lines
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7.5 Arbitrage Pricing Theory
Multifactor Generalization of APT and CAPM
Factor portfolio
Well-diversified portfolio constructed to have beta of 1.0 on one factor and beta of zero on any other factor
Two-Factor Model for APT
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Table 7.9 Constructing an Arbitrage Portfolio
Constructing an arbitrage portfolio with two systemic factors
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