Fi8000 Capital Asset Pricing Model

1
Fi8000Capital AssetPricing Model Market
Efficiency

• Milind Shrikhande

2
Today

• The Capital Asset Pricing Model
• Market Efficiency

3
The Capital Asset Pricing Model

• Sharp (1968), Black (1969) and
• Lintner (1970)
• A model that tells us the fair (risk-adjusted)
  expected return for every individual asset
• A market equilibrium model

4
The Capital Asset Pricing Model(CAPM) Outline

• The assumptions of the model
• The market equilibrium SML equation
• The two components of risk
• Systematic (non-diversifiable)
• Non-systematic (diversifiable)
• Beta as a measure of systematic risk
• The returns and the prices of risky assets

5
The Capital Asset Pricing Model(CAPM)
Assumptions

• There are many investors each investor is a
  price taker
• All investors plan for one identical holding
  period
• All risky assets are publicly traded
• All investors are risk-averse and Mean-Variance
  optimizers
• Homogeneous expectations - all investors have the
  same information and interpret it the same way

6
The CAPM Assumptions

• The perfect market assumption
• There are no taxes or transaction costs or
  information costs
• There are no frictions
• Stocks can be bought and sold in any quantity
  (even fractions)
• There is one risk-free asset and all investors
  can borrow or lend at that rate

7
The CAPM Market Equilibrium

• The market portfolio (m) is on the efficient
  frontier and on the CML. It is the Mean-Variance
  optimal portfolio of risky assets.
• All the investors will invest in the same
  portfolio of risky assets m - the market
  portfolio.
• The proportion of each asset in the market
  portfolio is simply the assets market value
  divided by the total wealth (market value of all
  assets).

8
The Market Portfolioin the µ-s Plane
The Capital Market Line µp rf(µm-rf) / smsp
µ
m
rf
s
9
The CAPM Market Equilibrium

• The risk preferences of the investors will result
  in their capital allocation between the market
  portfolio and the risk-free asset i.e. the
  location of their portfolio on the Capital Market
  Line (CML).
• (The mutual fund theorem)

10
Passive Investment Strategiesin the µ-s Plane
The CML µp rf (µm-rf) / smsp
µ
m
p
q
rf
s
11
The CAPM Market Equilibrium

• The risk premium of each risky assets will be
  proportional to the risk premium of the market
  portfolio and to the beta coefficient of the
  risky asset

12
The Capital Asset Pricing ModelThe Security
Market Line (SML)
µ
The SML µi rf µm-rfßi
q
m
p
rf
ß
13
What is Beta?

• Beta is a measure of risk
• Beta measures how sensitive are the returns of
  asset i to the returns of the market portfolio
• Beta is the slope (coefficient) in the regression
  of asset is return (risk premium) on the
  markets return (market risk premium)
• Beta is a relative measure of risk
• Beta lt 1 defensive asset
• Beta 1 neutral asset
• Beta gt 1 aggressive asset

14
Beta
Ri-rf
ßi
Rm-rf
15
Calculating Beta
16
The CAPM Market EquilibriumOutline of the Proof

• The risk-free asset is on the SML
• Calculate the beta of the risk-free asset
• The market portfolio is on the SML
• Calculate the beta of the market portfolio
• Any M-V efficient portfolio p is on the SML
• Calculate the beta of an efficient portfolio
• Any risky asset i is on the SML

17
The Benefits of Diversification
sp
Diversifiable Risk
Systematic Risk
np
18
The Risk

• The risk of any risky asset has two components
• sD - The diversifiable (non-systematic,
  idiosyncratic, firm-specific) risk can be
  eliminated by adding assets to the portfolio
• sND - The systematic (non-diversifiable, market)
  risk can not be eliminated through
  diversification
• According to the CAPM, investors are compensated
  only for the systematic component of the total
  asset risk (sND).

19
The Components of Riskin the µ-s Plane
The CML
µ
m
p
i
rf
s
sND
sD
s
20
The CAPM Market Equilibrium

• Find beta in the following planes
• Ri-Rm or (Ri-rf) (Rm-rf)
• µ-s (the CML)
• µ-ß (the SML)

21
The CAPM Market Equilibrium
µ
SML
Underpriced return is too high
m
Overpriced return is too low
rf
ß
22
The Return and the Current PriceInversely
Related

• A and B are two risky stocks. An analyst found
  that they have the following parameters
• µA15 and ßA0.5 µB22 and ßB2.
• The risk-free rate is rf10 and the expected
  return of the market portfolio is µm18.
• Relative to the CAPM equilibrium prices, which
  stock is underpriced and which is overpriced?

23
Project Valuation Example 1

• Firm XYZ usually invests in projects with a risk
  level of ß0.8. It is considering an investment
  in a new project which is expected to produce a
  CF of 12.6M a year from now, and this CF is
  expected to grow at a constant rate of 2 per
  year forever. This CF is only an expectation and
  the firms economist estimates its Std to be
  3M.
• What is the present value of the CFs of this
  project, if the expected annual return of the
  market portfolio is 12, the annual return of
  money market instruments is 4 and the market is
  in equilibrium (CAPM)?
• (k 10.4 PV 150M)

24
Project Valuation Example 2

• Joseph is looking for a treasure ship in the
  Mediterranean sea. He plans to keep looking for a
  year, and at the end of that year the value of
  his firm will be determined by the outcome of his
  quest. The probability of finding the 25M
  treasure is only 10 but he is more likely to end
  up with a smaller catch of only 5M.
• Obviously, the outcome of Josephs quest is
  independent of any macroeconomic risks, but we
  know that the expected annual return of the
  market portfolio is 14, its Std is 22 and the
  annual return of money market instruments is 6.
  What is the value of Josephs firm if the market
  is in equilibrium (CPAM)?
• (PV 6.604M)

25
CAPM Review

• Under strict assumptions, the CAPM results in a
  prescription for a fair return (price) The fair
  expected return on an asset depends on the market
  risk premium and on beta.
• Stocks with high betas have higher return, but
  there is no compensation for any risk factor
  other than the systematic market risk.

26
CAPM Critique

• Roll (1977) points out that the CAPM is not
  directly testable
• It is a one period model
• The market portfolio cannot be identified
• To test the model, we need the market portfolio
  to be on the efficient frontier (proxies wont
  work)
• Indirect tests fail to support the CAPM
• Other risk factors are compensated (size,
  book-to-market ratio), but there is no
  theoretical explanation for these risk factors.

27
The Efficient Market Hypothesis

• The Efficient Markets Hypothesis (EMH) specifies
  three forms of efficiency
• Weak form market efficiency
• Semi-Strong form market efficiency
• Strong form market efficiency
• Note that EMH is an Hypothesis
• We should look for evidence that reject the
  hypothesis
• We should look for evidence to decide which form
  of EMH is more likely

28
Weak Form Efficiency

• Definition
• A market is weak form efficient if the current
  asset prices reflect all historical price
  information
• Implication
• Trading strategies based on the analysis of
  historical prices should not yield abnormal
  returns (on average!)

29
Normal and Abnormal Returns

• Normal returns
• Fair or equilibrium returns given by a
  theoretical model like the CAPM
• Abnormal returns
• Returns that are systematically higher than the
  normal returns

30
Normal and Abnormal Returns

• For each asset i the CAPM predicts a normal,
  risk-adjusted rate of return (expected return)
• E(Ri) rf ßi E(Rm) rf
• We observe asset i over time, and compare the
  realized return Ri to the expected CAPM return
• ait Rit E(Ri) Rit rf ßi E(Rmt) rf
  
• If asset i is systematically beating the CAPM
  expected return, we say that the return of asset
  i is abnormal.
• Abnormal return Average ait 1/T ai1
  ai2 aiT gt 0

31
Semi-Strong Form Efficiency

• Definition
• A market is semi-strong form efficient if the
  current asset price reflects all publicly
  available information
• Implication
• Trading strategies based on the analysis of
  publicly available information (fundamental
  analysis such as analyst reports) should not
  yield abnormal returns (on average!)

32
Strong Form Efficiency

• Definition
• A market is strong form efficient if the current
  asset price reflects all information (including
  private / insider information)
• Implication
• There is no (legal) trading strategy that yields
  abnormal returns (on average!). One cannot make
  money even by following the trades of insider
  information.

33
Nesting

• Information
• Information about past prices is included in the
  set of publicly available information, which is
  included in the complete set of information.
• Market efficiency
• The strong form of market efficiency implies the
  semi-strong, which implies the weak form. Note
  that the strongest form of the MEH is the
  strongest and the most restricting assumption.

34
Evidence of Weak Form MEH

• Consistent evidence
• Technical trading rules, based on past price
  patterns, do not appear to be profitable.
• Contradicting evidence
• The January effect almost every January,
  stock returns (usually for small stocks) are
  positive.

35
Evidence ofSemi-Strong Form MEH

• Consistent evidence
• New publicly available information (such as
  earnings release) affects prices quickly.
• Contradicting evidence
• Small stocks and stocks with high ratio of
  book-value to market-value have, on average,
  higher returns.
• Some portfolio managers consistently outperform
  the market (Peter Lynch, Warren Buffet, John
  Templeton and John Neff are in Paul Samuelsons
  hall of fame, 1989).

36
Evidence of Strong Form MEH

• Consistent evidence
• Insiders of corporations appear able to earn
  abnormal returns from their trades. On average,
  price increases just after insiders purchase the
  stock and decreases just after a they sell the
  stock.
• Contradicting evidence
• Prices react to public information that had been
  private. For example, prices react to earning
  announcements even though someone must have know
  their contents before the official announcement
  day.

37
Market Efficiency and Equilibrium

• An efficient market is a market in equilibrium
• Inefficient markets occur when asset prices are
  different from their equilibrium prices
• In theory, traders who exploit market
  inefficiencies should move the market back to
  equilibrium

38
The Joint Hypothesis Problem

• A test of market efficiency can only be conducted
  by using a theoretical model to define normal
  (fair) returns (prices)
• Finding an abnormal average return can be
  interpreted in more than one way
• Reject the Market Efficiency Hypothesis (MEH)
• Reject the theoretical model of normal returns
• Reject both

39
MEH Are Markets Efficient?

• Grossman and Stigliz (1980) the logical question
  must always be to what extent markets are
  efficient
• Empirical evidence
• Implications for trading strategies?
• Technical analysis
• Fundamental analysis
• Trading on insider information (SEC regulations)
• Is there a portfolio manager who systematically
  outperforms the market?
• Is a small abnormal return detectable?
• Will they tell us about their winning strategy
  (selection bias)?
• How can we distinguish between luck and talent?

40
Practice Problems

• BKM Ch. 9 1-2, 4-17, 21-28
• BKM Ch. 12 1-9, 14, 16-18, 25, 27-28