Title: FIN 504: Financial Management
1FIN 504 Financial Management
- Lecture 13 The Capital Asset Pricing Model
(CAPM)
2Topics
- 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
3Measurement of Market Risk
4Measurement 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.
5Measurement 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
6Beta
- 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.
7b 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.
8b 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.
9b 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.
10Two 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.
11All 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.
12Beta 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.
13Linear Regression Example
14Linear Regression Example
- Intercept 0.222
- Coefficient (Beta) 0.067
- R2 0.118
- Standard Error 0.290
15Beta Formula
- There is also a formula for beta
16Negative 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?
17The Capital Asset Pricing Model (CAPM)
18The 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?
19Building 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.
20Building the SML
Return
Return
Beta
0
21Building the SML
- Begin with the two points we know
22Building the SML
Return
Return
rM
Market
rf
Risk Free Asset
Beta
0
1
23Building the SML
- Where would we find portfolios that contain
combinations of the risk free asset and the
market?
24Security Market Line (SML)
Return
Return
rM
rf
Beta
0
1
25Building the SML
- What would happen if we could borrow to enlarge
our portfolio?
26Building the SML
Return
Return
rM
rf
Beta
0
1
27Building the SML
- What would happen if there were a stock below the
line?
28Building the SML
Return
Return
rM
rf
Beta
0
1
29Building the SML
Return
Return
rM
rf
Beta
0
1
30Building the SML
- What would happen if there were a stock above the
line?
31Building the SML
Return
Return
rM
rf
Beta
0
1
32Building the SML
Return
Return
rM
rf
Beta
0
1
33Building the SML
- Market equilibrium forces all stocks to be on the
line, which is called the Security Market Line
(SML).
34Security Market Line (SML)
SML
Return
Return
rM
rf
Beta
0
1
35The CAPM Equation
- It is easier to calculate with a formula than a
graph, so we can also express the SML as the CAPM
equation
36The 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
37The 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.
38The 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.
39The 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
40The CAPM Equation Examples
41Assumptions and Problems of the CAPM Model
42CAPM 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
43CAPM Problems
- It also has some practical and theoretical flaws
- Empirical Testing
- Rolls Critique
44CAPM 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.