Investments: Analysis and Management

1
Chapter 9
Capital Market Theory
2
Learning Objectives

• Explain capital market theory and the Capital
  Asset Pricing Model (CAPM).
• Discuss the importance and composition of the
  market portfolio.
• Describe two important relationships in CAPM as
  represented by the capital market line and the
  security market line.
• Describe how betas are estimated and how beta is
  used.
• Discuss the Arbitrage Pricing Theory as an
  alternative to the Capital Asset Pricing Model.

3
Capital Market Theory

• Describes the pricing of capital assets in
  financial markets

4
Capital Asset Pricing Model

• Relates the required rate of return for any
  security with the market risk for the security as
  measured by beta
• Focus on the equilibrium relationship between the
  risk and expected return on risky assets
• Builds on Markowitz portfolio theory
• Each investor is assumed to diversify his or her
  portfolio according to the Markowitz model,
  choosing a location on the efficient frontier
  that matches his/her return-risk preferences

5
CAPM Assumptions

• All investors
• Use the same information to generate an efficient
  frontier (i.e., identical inputs E(R), s, ?)
• Have the same one-period time horizon
• Can borrow or lend money at the risk-free rate of
  return

• No transaction costs
• No personal income (i.e., indifferent between
  dividends and capital gains) taxes
• No inflation
• No single investor can affect the price of a
  stock (i.e., price-takers)
• Capital markets are in equilibrium

6
CAPM Assumptions

• These assumptions appear unrealistic
• The important issue is how well the theory
  predicts (describes) reality
• The CAPM is robust since most of its assumptions
  can be relaxed without significant effects on the
  model
• Not all of the CAPM assumptions are unrealistic
• Some institutional investors are tax-exempt
• Significant reduction in transaction costs by
  using discount brokers and/or internet
• For the one-period horizon of the model,
  inflation may be fully (or mostly) anticipated

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Market Portfolio

• Most important implication of the CAPM
• All investors hold the same optimal portfolio of
  risky assets
• As a result of the assumption that all investors
  have the same time horizon and homogenous
  expectations regarding the expected returns and
  risks for any given risky asset
• The optimal portfolio is at the highest point of
  tangency between RF and the efficient frontier
• The portfolio of all risky assets is the optimal
  risky portfolio
• Called the market portfolio

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Characteristics of the Market Portfolio (M)

• All risky assets must be in portfolio, so it is
  completely diversified
• Contains only systematic risk (cannot be
  eliminated)
• All securities included in proportion to their
  market value
• Unobservable, but proxied by SP/TSX Composite
  Index in Canada (or the SP 500 in the US)
• In theory, should contain all risky assets
  worldwide, both financial and real, in their
  proper proportions
• Is found by determining which efficient portfolio
  offers the highest risk premium, given the
  existence of a risk-free asset

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The Equilibrium Risk-Return trade-off

• The CAPM is an equilibrium model that encompasses
  two important relationships
• The capital market line (CML), specifies the
  equilibrium relationship between expected return
  and total risk for efficient portfolios
• The security market line (SML), specifies the
  equilibrium relationship between expected return
  and systematic risk

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Capital Market Line

• Line from RF to L is capital market line (CML)
• x risk premium
• E(RM) - RF
• y risk ?M
• Slope x/y market price of risk for efficient
  portfolios
• E(RM) - RF/?M
• y-intercept RF price of forgone consumption

L
M
E(RM)
x
RF
y
?M
Risk
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Example Capital Market Line

• (Pg 247) Assume that the expected return on
  portfolio M is 13, with a standard deviation of
  25, and that RF is 7
• Calculate the slope of the CML

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Capital Market Line

• Slope of the CML is the market price of risk for
  efficient portfolios, or the equilibrium price of
  risk in the market
• Relationship between risk and expected return for
  portfolio P (Equation for CML)

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Capital Market Line

• The following should be noted about the CML
• Only efficient portfolios consisting of the
  risk-free asset and portfolio M lie on the CML
• It indicates the optimal expected returns
  associated with different portfolio risk levels
• It must always be upwards sloping because the
  price of risk must always be positive
• Although, it must be upward sloping ex ante
  (before the fact), it can be, and sometimes is,
  downward sloping ex post (after the fact). This
  merely indicates that the returns actually
  realized differed from those that were expected

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Security Market Line

• CML Equation only applies to markets in
  equilibrium and efficient portfolios (i.e.,
  cannot be used to assess the expected return on
  individual securities or inefficient portfolios)
• The Security Market Line depicts the tradeoff
  between risk and expected return for individual
  securities
• Under CAPM, all investors hold the risky portion
  of their portfolio in the market portfolio
• How does an individual security contribute to the
  risk of the market portfolio?

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Security Market Line

• The expected return on any risky asset is
  directly proportional to its covariance with the
  market portfolio
• Equation for expected return for an individual
  stock similar to CML Equation

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Security Market Line

• Beta 1.0 implies as risky as market
• Securities A and B are more risky than the market
• Beta gt 1.0
• Security C is less risky than the market
• Beta lt 1.0

SML
E(R)
A
E(RM)
B
C
RF
0
1.0
2.0
0.5
1.5
BetaM
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Security Market Line

• The SML represents the trade-off between
  systematic risk (ß) and the expected return for
  all assets, whether individual securities,
  inefficient portfolios, or efficient portfolios
• Beta measures systematic risk
• Measures relative risk compared to the market
  portfolio of all stocks
• Volatility of security i is different (higher or
  lower) than that of the market if ß_i gt 1 or ß_i
  lt 1 and is equal to that of the market if ß_i 1
• ß_i 1 means that for every 1 change in the
  markets return, on average security is returns
  change 1
• ß_M 1 and ß_RF 0

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Security Market Line

• ß is useful for comparing the relative systematic
  risk of different stocks and, in practice, is
  used by investors to judge a stocks riskiness
• ßs may vary widely across companies in different
  industries and within a give industry (e.g., ß
  for Barrick Gold Corp. is 0.63 and for Eldorado
  Gold Corp. is 1.2)
• All securities should lie on the SML
• The expected return on the security should be
  only that return needed to compensate for
  systematic risk

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SML and Asset Values
Er
Underpriced SML Er rf ? (Erm rf)
Overpriced rf
ß
Underpriced ? expected return gt
required return according to CAPM ? lie
above SML Overpriced ? expected return lt
required return according to CAPM ? lie
below SML Correctly priced ? expected return
required return according to CAPM ? lie along
SML
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CAPMs Expected Return-Beta Relationship

• Required rate of return on an asset (ki) is
  composed of
• risk-free rate (RF)
• risk premium (?i E(RM) - RF )
• Market risk premium adjusted for specific
  security
• ki RF ?i E(RM) - RF
• The greater the systematic risk, the greater the
  required return

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Example Expected Return-Beta Relationship

• (Pg 252) If the ß estimate for security i is
  1.04, the RF is 0.0241, and the expected return
  on the market is estimated to be 0.10.
• Calculate the required return on security i

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Estimating the SML

• To use the SML, an investor needs estimates of
  the return on the risk-free asset, the expected
  return on the market index, and the ß for an
  individual security
• Treasury Bill rate used to estimate RF
• Expected return for the market index in not
  observable
• Estimated using past market returns and taking an
  expected value
• Estimating individual security betas is difficult
• ß is only company-specific factor in CAPM
• Requires asset-specific forecast

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Estimating Beta

• Market model
• Relates the return on each stock to the return on
  the market, assuming a linear relationship with
  an intercept and slope
• Rit ?i ?i RMt eit
• It is identical to the single-index model except
  that it does not make the assumption that the
  error terms of the different securities are
  uncorrelated
• The Market Model produces an estimate of return
  for any stock

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Estimating Beta

• Characteristic line
• A regression equation used to estimate ß by
  regressing stock returns on market returns
• Line fitted to total returns for a security
  relative to total returns for the market index
  (Fig 9.6 pg 255)
• ß is the slope of the characteristic line

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How Accurate Are Beta Estimates?

• Betas change with a companys situation (e.g.,
  earnings cash flows)
• Not stationary over time
• Estimating a future beta
• May differ from the historical beta
• RMt represents the total of all marketable assets
  in the economy
• Approximated with a stock market index, which, in
  turn, approximates return on all common stocks

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How Accurate Are Beta Estimates?

• No one correct number of observations and time
  periods for calculating beta. As a result,
  estimates of ß will vary
• The regression estimates of the true ? and ? from
  the characteristic line are subject to estimation
  error
• Portfolio betas more reliable than individual
  security betas
• ßs for large portfolios are stable (show less
  change from period to period) because of the
  averaging effect (i.e., errors involved in
  estimating ßs tend to cancel out)

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Test of CAPM

• Previous empirical results indicate that
• Ri a1 ?i a2
• The SML appears to be linear (i.e., the trade-ff
  between expected return and risk is an upward
  sloping straight line
• The intercept term, a1, is generally found to be
  higher than RF
• The slope of the CAPM, a2, is generally found to
  be less steep than predicted by the theory (i.e.,
  overpredicts returns for low-ß stocks and
  underpredicts returns for high-ß stock)

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Test of CAPM

• Fama and French (1992)
• Indicate that the CAPMs sole risk factor, market
  risk ß, posses no explanatory power in
  discriminating among the cross-sectional returns
  of US stocks
• Common market equity (ME) and the ratio of book
  equity to market equity (BE/ME) combine to
  explain the cross-section of expected returns
• Three-factor model (overall market factors,
  factors related to firm size, BE/ME ratio)

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Test of CAPM

• Empirical SML is flatter than predicted SML
• Fama and French (1992)
• Market
• Size
• Book-to-market ratio
• Rolls Critique
• True market portfolio is unobservable
• Tests of CAPM are merely tests of the
  mean-variance efficiency of the chosen market
  proxy

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Arbitrage Pricing Theory

• Based on the Law of One Price
• Two otherwise identical assets cannot sell at
  different prices
• Equilibrium prices adjust to eliminate all
  arbitrage opportunities
• Unlike CAPM, APT does not assume
• single-period investment horizon, absence of
  personal taxes, riskless borrowing or lending,
  mean-variance decisions

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Factors

• APT assumes returns generated by a factor model
• Factor Characteristics
• Each risk must have a pervasive influence on
  stock returns
• Risk factors must influence expected return and
  have nonzero prices
• Risk factors must be unpredictable to the market

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APT Model

• Most important are the deviations of the factors
  from their expected values
• The expected return-risk relationship for the APT
  can be described as
• E(Rit) a0bi1 (risk premium for factor 1) bi2
  (risk premium for factor 2) bin (risk
  premium for factor n)

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APT Model

• Reduces to CAPM if there is only one factor and
  that factor is market risk
• Roll and Ross (1980) Factors
• Changes in expected inflation
• Unanticipated changes in inflation
• Unanticipated changes in industrial production
• Unanticipated changes in the default risk premium
• Unanticipated changes in the term structure of
  interest rates

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Problems with APT

• Factors are not well specified ex ante
• To implement the APT model, the factors that
  account for the differences among security
  returns are required
• CAPM identifies market portfolio as single factor
• Neither CAPM or APT has been proven superior
• Both rely on unobservable expectations