1. The Capital Asset Pricing Model
CHAPTER 9

2. Capital Asset Pricing Model (CAPM)
It is the equilibrium model that underlies all modern financial theory
Derived using principles of diversification with simplified assumptions
Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development
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3. Assumptions: Investors
Individual investors are price takers
Single-period investment horizon
Investments are limited to traded financial assets
There are homogeneous expectations
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4. Assumptions: Assets
Information is costless and available to all investors
No taxes and transaction costs
Risk-free rate available to all
Investors are rational mean-variance optimizers
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5. Resulting Equilibrium Conditions
All investors will hold the same portfolio for risky assets – market portfolio, which contains all securities and the proportion of each security is its market value as a percentage of total market value
held by all investors
includes all traded assets
suppose not: then price… -> included
is on the efficient frontier
asset weights: for each $ in risky assets, how much is in IBM?
for stock i: market cap of stock i / market cap of all stocks
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6. Resulting Equilibrium Conditions Continued
Risk premium on the market depends on the average risk aversion of all market participants
Risk premium on an individual security is a function of its covariance with the market
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7. Figure 9.1 The Efficient Frontier and the Capital Market Line
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8. Market Risk Premium
The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor:
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9. Return and Risk For Individual Securities
The risk premium on individual securities is a function of the individual security’s contribution to the risk of the market portfolio
An individual security’s risk premium is a function of the covariance of returns with the assets that make up the market portfolio
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10. Using GE Text Example
Covariance of GE return with the market portfolio:
Therefore, the reward-to-risk ratio for investments in GE would be:
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11. Using GE Text Example Continued
Reward-to-risk ratio for investment in market portfolio:
Reward-to-risk ratios of GE and the market portfolio:
And the risk premium for GE:
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12. Expected Return-Beta Relationship
CAPM holds for the overall portfolio because:
This also holds for the market portfolio:
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13. Figure 9.2 The Security Market Line
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14. Figure 9.3 The SML and a Positive-Alpha Stock
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15. The Index Model and Realized Returns
To move from expected to realized returns—use the index model in excess return form:
The index model beta coefficient turns out to be the same beta as that of the CAPM expected return-beta relationship
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16. Figure 9.4 Estimates of Individual Mutual Fund Alphas, 1972-1991
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17. The CAPM and Reality
Is the condition of zero alphas for all stocks as implied by the CAPM met
Not perfect but one of the best available
Is the CAPM testable
Proxies must be used for the market portfolio
CAPM is still considered the best available description of security pricing and is widely accepted
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18. Econometrics and the Expected Return-Beta Relationship
It is important to consider the econometric technique used for the model estimated
Statistical bias is easily introduced
Miller and Scholes paper demonstrated how econometric problems could lead one to reject the CAPM even if it were perfectly valid
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19. Extensions of the CAPM Zero-Beta Model
Helps to explain positive alphas on low beta stocks and negative alphas on high beta stocks
Consideration of labor income and non-traded assets
Merton’s Multiperiod Model and hedge portfolios
Incorporation of the effects of changes in the real rate of interest and inflation
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20. Extensions of the CAPM Continued
A consumption-based CAPM
Models by Rubinstein, Lucas, and Breeden
Investor must allocate current wealth between today’s consumption and investment for the future
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21. Liquidity and the CAPM Liquidity Illiquidity Premium
Research supports a premium for illiquidity.
Amihud and Mendelson
Acharya and Pedersen
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22. Figure 9.5 The Relationship Between Illiquidity and Average Returns
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23. Three Elements of Liquidity
Sensitivity of security’s illiquidity to market illiquidity:
Sensitivity of stock’s return to market illiquidity:
Sensitivity of the security illiquidity to the market rate of return:
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24. CAPM: Examples of Practical Problems 1
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25. CAPM: Examples of Practical Problems 2
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26. CAPM: Examples of Practical Problems 3
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27. CAPM: Examples of Practical Problems 4
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28. CAPM: Examples of Practical Problems 5
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29. CAPM: Examples of Practical Problems 6
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30. CAPM: Examples of Practical Problems 7
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31. CAPM: Examples of Practical Problems 8
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32. Index model vs. CAPM Risk CAPM (theoretical, unobservable portfolio)
Index model (observable, “proxy” portfolio)
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33. Index model vs. CAPM 2 Beta Relationship
CAPM (no expected excess return for any security)
Index model (average realized alpha is 0)
Fig 10.3
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34. Market Model Idea Equivalence use realized excess returns
CAPM + Market model = Index model
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35. Summary CAPM Factor model Index model Market model
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36. Arbitrage Pricing Theory and Multifactor Models of Risk and Return
CHAPTER 10

37. Single Factor Model Returns on a security come from two sources
Common macro-economic factor
Firm specific events
Possible common macro-economic factors
Gross Domestic Product Growth
Interest Rates
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38. Single Factor Model Equation
ri = Return for security I
= Factor sensitivity or factor loading or factor beta
F = Surprise in macro-economic factor
(F could be positive, negative or zero)
ei = Firm specific events
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39. Multifactor Models 1 Necessity Solution CAPM not practical Index model
unique factor is unsatisfactory
example: Table 10.2 (very small R2)
Solution
multiple factors
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40. Multi-factor Models 2 Factors in practice business cycles factors
examples (Chen Roll Ross)
industrial production % change
expected inflation % change
unanticipated inflation % change
LT corporate over LT gvt. bonds
LT gvt. bonds over T-bills
interpretation
residual variance = firm specific risk
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41. Multi-factor Models 3 Factors in practice
firm characteristics (Fama and French)
firm size
difference in return
between firms with low vs. high equity market value
proxy for business cycle sensitivity?
market to book
between firms with low vs. high BTM ratio
proxy for bankruptcy risk?
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42. Multifactor Models 4
Use more than one factor in addition to market return
Examples include gross domestic product, expected inflation, interest rates etc.
Estimate a beta or factor loading for each factor using multiple regression.
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43. Multifactor Model Equation
ri = E(ri) GDP GDP IR IR + ei
ri = Return for security I
GDP= Factor sensitivity for GDP
IR = Factor sensitivity for Interest Rate
ei = Firm specific events
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44. Multifactor SML Models
E(r) = rf + GDPRPGDP + IRRPIR
GDP = Factor sensitivity for GDP
RPGDP = Risk premium for GDP
IR = Factor sensitivity for Interest Rate
RPIR = Risk premium for Interest Rate
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45. Arbitrage Pricing Theory (APT)
Nature of arbitrage
APT
well-diversified portfolios
individual assets
APT vs. CAPM
APT vs. Index models
single factor
multi-factor
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46. Arbitrage Pricing Theory
Arbitrage - arises if an investor can construct a zero investment portfolio with a sure profit
Since no investment is required, an investor can create large positions to secure large levels of profit
In efficient markets, profitable arbitrage opportunities will quickly disappear
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47. APT & Well-Diversified Portfolios
rP = E (rP) + bPF + eP
F = some factor
For a well-diversified portfolio:
eP approaches zero
Similar to CAPM,
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48. Figure 10.1 Returns as a Function of the Systematic Factor
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49. Figure 10.2 Returns as a Function of the Systematic Factor: An Arbitrage Opportunity
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50. Figure 10.3 An Arbitrage Opportunity
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51. Figure 10.4 The Security Market Line
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52. APT and CAPM Compared
APT applies to well diversified portfolios and not necessarily to individual stocks
With APT it is possible for some individual stocks to be mispriced - not lie on the SML
APT is more general in that it gets to an expected return and beta relationship without the assumption of the market portfolio
APT can be extended to multifactor models
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53. Multifactor APT Use of more than a single factor
Requires formation of factor portfolios
What factors?
Factors that are important to performance of the general economy
Fama-French Three Factor Model
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54. Two-Factor Model The multifactor APR is similar to the one-factor case
But need to think in terms of a factor portfolio
Well-diversified
Beta of 1 for one factor
Beta of 0 for any other
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55. Example of the Multifactor Approach
Work of Chen, Roll, and Ross
Chose a set of factors based on the ability of the factors to paint a broad picture of the macro-economy
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56. Another Example: Fama-French Three-Factor Model
The factors chosen are variables that on past evidence seem to predict average returns well and may capture the risk premiums
Where:
SMB = Small Minus Big, i.e., the return of a portfolio of small stocks in excess of the return on a portfolio of large stocks
HML = High Minus Low, i.e., the return of a portfolio of stocks with a high book to-market ratio in excess of the return on a portfolio of stocks with a low book-to-market ratio
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57. The Multifactor CAPM and the APM
A multi-index CAPM will inherit its risk factors from sources of risk that a broad group of investors deem important enough to hedge
The APT is largely silent on where to look for priced sources of risk
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