Transcript of CHAPTER 9 The Capital Asset Pricing Model. It is the equilibrium model that underlies all modern...
- Slide 1
- CHAPTER 9 The Capital Asset Pricing Model
- Slide 2
- 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 CAPITAL ASSET PRICING MODEL (CAPM)
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 2
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- Individual investors are price takers Single-period investment
horizon Investments are limited to traded financial assets There
are homogeneous expectations ASSUMPTIONS: INVESTORS BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 3
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- 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 ASSUMPTIONS: ASSETS BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 4
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- 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 RESULTING
EQUILIBRIUM CONDITIONS BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 5
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- 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 RESULTING
EQUILIBRIUM CONDITIONS CONTINUED BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 6
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- FIGURE 9.1 THE EFFICIENT FRONTIER AND THE CAPITAL MARKET LINE
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- 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: BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 8
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- The risk premium on individual securities is a function of the
individual securitys contribution to the risk of the market
portfolio An individual securitys risk premium is a function of the
covariance of returns with the assets that make up the market
portfolio RETURN AND RISK FOR INDIVIDUAL SECURITIES BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 9
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- USING GE TEXT EXAMPLE Covariance of GE return with the market
portfolio: Therefore, the reward-to-risk ratio for investments in
GE would be: BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 10
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- 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: BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 11
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- EXPECTED RETURN-BETA RELATIONSHIP CAPM holds for the overall
portfolio because: This also holds for the market portfolio:
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 12
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- FIGURE 9.2 THE SECURITY MARKET LINE BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 13
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- FIGURE 9.3 THE SML AND A POSITIVE-ALPHA STOCK BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 14
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- THE INDEX MODEL AND REALIZED RETURNS To move from expected to
realized returnsuse 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 BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 15
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- FIGURE 9.4 ESTIMATES OF INDIVIDUAL MUTUAL FUND ALPHAS,
1972-1991 BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 16
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- 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 BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 17
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- 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 BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 18
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- 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 Mertons
Multiperiod Model and hedge portfolios Incorporation of the effects
of changes in the real rate of interest and inflation BAHATTIN
BUYUKSAHIN, JHU, INVESTMENT 19
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- EXTENSIONS OF THE CAPM CONTINUED A consumption-based CAPM
Models by Rubinstein, Lucas, and Breeden Investor must allocate
current wealth between todays consumption and investment for the
future BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 20
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- LIQUIDITY AND THE CAPM Liquidity Illiquidity Premium Research
supports a premium for illiquidity. Amihud and Mendelson Acharya
and Pedersen BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 21
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- FIGURE 9.5 THE RELATIONSHIP BETWEEN ILLIQUIDITY AND AVERAGE
RETURNS BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 22
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- THREE ELEMENTS OF LIQUIDITY Sensitivity of securitys
illiquidity to market illiquidity: Sensitivity of stocks return to
market illiquidity: Sensitivity of the security illiquidity to the
market rate of return: BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 23
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- CAPM: EXAMPLES OF PRACTICAL PROBLEMS 1 BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS1/16/2010 24
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 25 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 2
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 26 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 3
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 27 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 4
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 28 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 5
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 29 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 6
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 30 CAPM: EXAMPLES
OF PRACTICAL PROBLEMS 7
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- BAHATTIN BUYUKSAHIN, JHU INVESTMENTS1/16/2010 CAPM: EXAMPLES OF
PRACTICAL PROBLEMS 8
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- INDEX MODEL VS. CAPM BAHATTIN BUYUKSAHIN, JHU INVESTMENTS Risk
CAPM (theoretical, unobservable portfolio) Index model (observable,
proxy portfolio) 1/16/2010 32
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- INDEX MODEL VS. CAPM 2 BAHATTIN BUYUKSAHIN, JHU INVESTMENTS
Beta Relationship CAPM (no expected excess return for any security)
Index model (average realized alpha is 0) Fig 10.3 1/16/2010
33
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- MARKET MODEL BAHATTIN BUYUKSAHIN, JHU INVESTMENTS Idea use
realized excess returns Equivalence CAPM + Market model = Index
model 1/16/2010 34
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- SUMMARY BAHATTIN BUYUKSAHIN, JHU INVESTMENTS CAPM Factor model
Index model Market model 1/16/2010 35
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- CHAPTER 10 Arbitrage Pricing Theory and Multifactor Models of
Risk and Return
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- 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
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 37
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- SINGLE FACTOR MODEL EQUATION r i = 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) e i =
Firm specific events BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 38
- Slide 39
- MULTIFACTOR MODELS 1 BAHATTIN BUYUKSAHIN, JHU INVESTMENTS
Necessity CAPM not practical Index model practical unique factor is
unsatisfactory example: Table 10.2 (very small R 2 ) Solution
multiple factors 1/16/2010 39
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- MULTI-FACTOR MODELS 2 BAHATTIN BUYUKSAHIN, JHU INVESTMENTS
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 1/16/2010 40
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- MULTI-FACTOR MODELS 3 BAHATTIN BUYUKSAHIN, JHU INVESTMENTS
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
difference in return between firms with low vs. high BTM ratio
proxy for bankruptcy risk? 1/16/2010 41
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- 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. BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 42
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- MULTIFACTOR MODEL EQUATION r i = E(r i ) + GDP GDP + IR IR + e
i r i = Return for security I GDP = Factor sensitivity for GDP IR =
Factor sensitivity for Interest Rate e i = Firm specific events
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 43
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- MULTIFACTOR SML MODELS E(r) = r f + GDP RP GDP + IR RP IR GDP =
Factor sensitivity for GDP RP GDP = Risk premium for GDP IR =
Factor sensitivity for Interest Rate RP IR = Risk premium for
Interest Rate BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 44
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- ARBITRAGE PRICING THEORY (APT) BAHATTIN BUYUKSAHIN, JHU
INVESTMENTS Nature of arbitrage APT well-diversified portfolios
individual assets APT vs. CAPM APT vs. Index models single factor
multi-factor 1/16/2010 45
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- 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 BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 46
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- APT & WELL-DIVERSIFIED PORTFOLIOS r P = E (r P ) + P F + e
P F = some factor For a well-diversified portfolio: e P approaches
zero Similar to CAPM, BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 47
- Slide 48
- FIGURE 10.1 RETURNS AS A FUNCTION OF THE SYSTEMATIC FACTOR
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 48
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- FIGURE 10.2 RETURNS AS A FUNCTION OF THE SYSTEMATIC FACTOR: AN
ARBITRAGE OPPORTUNITY BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 49
- Slide 50
- FIGURE 10.3 AN ARBITRAGE OPPORTUNITY BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 50
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- FIGURE 10.4 THE SECURITY MARKET LINE BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 51
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- 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 APT AND CAPM COMPARED BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 52
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- 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 BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 53
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- 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
BAHATTIN BUYUKSAHIN, JHU, INVESTMENT 54
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- 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 BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 55
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- 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 BAHATTIN BUYUKSAHIN, JHU,
INVESTMENT 56
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- 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 BAHATTIN BUYUKSAHIN,
JHU, INVESTMENT 57