Fi8000 Capital Asset Pricing Model - PowerPoint PPT Presentation

1 / 40
About This Presentation
Title:

Fi8000 Capital Asset Pricing Model

Description:

Beta measures how sensitive are the returns of asset i to the returns of the market portfolio ... D - The diversifiable (non-systematic, idiosyncratic, firm ... – PowerPoint PPT presentation

Number of Views:112
Avg rating:3.0/5.0
Slides: 41
Provided by: isabel8
Category:

less

Transcript and Presenter's Notes

Title: 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
Write a Comment
User Comments (0)
About PowerShow.com