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FIN 504: Financial Management

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Title: FIN 504: Financial Management


1
FIN 504 Financial Management
  • Lecture 13 The Capital Asset Pricing Model
    (CAPM)

2
Topics
  • Measurement of Market Risk
  • The Capital Asset Pricing Model (CAPM)
  • Assumptions and Flaws of the Model
  • Application of the Model
  • Some Extensions of the Model

3
Measurement of Market Risk
4
Measurement of Market Risk
  • If standard deviation and variance have failed as
    adequate measures of market risk, we need a new
    measure.
  • The new measure is called beta (b).
  • Beta is a measure of the sensitivity of changes
    in the return of an asset to changes in the
    market.

5
Measurement of Market Risk
  • If the market were to go up by 10, how much
    would a particular stock change on average?
  • Up by 15
  • Up by 10
  • Up by 5
  • No Change
  • Down by 10

6
Beta
  • Beta is a measure of this average change in
    response to changes in the market.
  • Beta is the correct approach to step two Measure
    risk.
  • Beta, e.g., average change can be
  • Equal to the market
  • Greater than the market, or
  • Less than the market.

7
b 1
  • If the stock return moves up and down with the
    market, b 1.
  • It has the same sensitivity to market risk as the
    market as a whole.
  • It has average sensitivity to market risk.
  • The return on this stock should be the same as
    the return on the market as a whole, i.e., the
    average return on the market.

8
b gt 1
  • If the stock return moves up and down more than
    the market, b gt 1.
  • It has greater sensitivity to market risk than
    the market as a whole.
  • It has more than average sensitivity to market
    risk.
  • The return on this stock should be greater than
    the return on the market as a whole, i.e., the
    average return on the market.

9
b lt 1
  • If the stock return moves up and down less than
    the market, b lt 1.
  • It has lesser sensitivity to market risk than the
    market as a whole.
  • It has less than average sensitivity to market
    risk.
  • The return on this stock should be less than the
    return on the market as a whole, i.e., the
    average return on the market.

10
Two Known Betas
  • The market portfolio has, by definition, a beta
    of 1, i.e., bM 1.
  • The market moves exactly with itself.
  • Risk free assets have a beta of 0, i.e., brf 0.
  • If they are risk free, then their return is
    determined in advance.
  • If it is determined in advance, it is not at all
    sensitive to changes in the market.

11
All the Other Betas
  • We need a method to find the betas of assets
    other than the market and fixed income
    securities.
  • If beta is a sensitivity, then we can use linear
    regression to estimate it.
  • Linear regression estimates the average response
    of a dependent variable to an independent
    variable.

12
Beta from Linear Regression
  • Linear Regression Model for Beta
  • The market return is the independent variable.
  • The return on a stock is the dependent variable.
  • Beta is the slope of the line that best captures
    the linear relationship between the two.

13
Linear Regression Example
14
Linear Regression Example
  • Intercept 0.222
  • Coefficient (Beta) 0.067
  • R2 0.118
  • Standard Error 0.290

15
Beta Formula
  • There is also a formula for beta

16
Negative Betas
  • For the formula, we see that beta is negative iff
    covariance is negative.
  • A negative beta would imply a counter-cyclical
    stock.
  • What is the return on a negative beta stock?
  • Would anyone invest in such an asset?

17
The Capital Asset Pricing Model (CAPM)
18
The Capital Asset Pricing Model
  • We have completed the first two steps in our risk
    analysis
  • 1) Identify Risk Market Risk
  • 2) Measure Risk Beta
  • We now need (3) to find a formula for pricing
    risk.
  • How much greater return should an investor expect
    from a stock with a beta of 2.3 than one with a
    beta of 0.9?

19
Building the SML
  • We can start by graphing the relationship between
    beta and return, then we will find a formula that
    is more practical to use.

20
Building the SML
Return
Return
Beta
0
21
Building the SML
  • Begin with the two points we know

22
Building the SML
Return
Return
rM
Market
rf
Risk Free Asset
Beta
0
1
23
Building the SML
  • Where would we find portfolios that contain
    combinations of the risk free asset and the
    market?

24
Security Market Line (SML)
Return
Return
rM
rf
Beta
0
1
25
Building the SML
  • What would happen if we could borrow to enlarge
    our portfolio?

26
Building the SML
Return
Return
rM
rf
Beta
0
1
27
Building the SML
  • What would happen if there were a stock below the
    line?

28
Building the SML
Return
Return
rM
rf
Beta
0
1
29
Building the SML
Return
Return
rM
rf
Beta
0
1
30
Building the SML
  • What would happen if there were a stock above the
    line?

31
Building the SML
Return
Return
rM
rf
Beta
0
1
32
Building the SML
Return
Return
rM
rf
Beta
0
1
33
Building the SML
  • Market equilibrium forces all stocks to be on the
    line, which is called the Security Market Line
    (SML).

34
Security Market Line (SML)
SML
Return
Return
rM
rf
Beta
0
1
35
The CAPM Equation
  • It is easier to calculate with a formula than a
    graph, so we can also express the SML as the CAPM
    equation

36
The CAPM Equation
  • The CAPM equation only requires one input from
    the firm data and two from market data
  • Firm
  • Beta
  • Market
  • The risk free rate
  • The return on the market

37
The CAPM Equation
  • Market Data
  • The risk free rate
  • For the risk free rate we normally use the return
    on a Treasury security whose maturity is equal to
    the period for which we are applying the CAPM.
  • The return on the market
  • For the return on the market, we use the return
    on a broad market portfolio, such as the SP 500.

38
The CAPM Equation
  • Firm Datum
  • The beta for the firm is, as we have seen,
    usually calculated using linear regression.
  • Again, for the return on the market, we use the
    return on a broad market portfolio, such as the
    SP 500.

39
The CAPM Equation Examples
  • We can use the following, to fins the expected
    return
  • rf 4.5
  • rM 12.3
  • Find the expected return on the following three
    stocks
  • bA 1.02
  • bB 0.89
  • bC 1.34

40
The CAPM Equation Examples
41
Assumptions and Problems of the CAPM Model
42
CAPM Assumptions
  • It is extremely important to keep in mind that
    the basic CAPM model uses a number of
    assumptions
  • Homogeneous Beliefs
  • One-Period
  • Constant rf
  • Constant b
  • Normally Distributed Assets

43
CAPM Problems
  • It also has some practical and theoretical flaws
  • Empirical Testing
  • Rolls Critique

44
CAPM Extensions
  • Given that many of the assumptions of CAPM are
    highly restrictive, many of the attempts to
    improve the predicative ability of CAPM have
    focused on models that do not need these.
  • Unfortunately, it is the assumptions that keep
    the models simple.
  • As soon as you remove them, the models be come
    very mathematically complex.
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