Corporate finance chapter 013 the capital asset pricing model

Chapter 13: The Capital Asset Pricing Model Objective •The Theory of the CAPM •Use of CAPM in benchmarking • Using CAPM to determine... Chapter 13 Contents13.1 The Capital Asset Pricing

Chapter 13: The Capital

Asset Pricing Model

Objective

•The Theory of the CAPM

•Use of CAPM in benchmarking

• Using CAPM to determine

Chapter 13 Contents

13.1 The Capital Asset Pricing Model in Brief 13.2 Determining the Risk Premium on the Market Portfolio

13.3 Beta and Risk Premiums on Individual Securities

13.4 Using the CAPM in Portfolio Selection 13.5 Valuation & Regulating Rates of Return

• CAPM is a theory about equilibrium prices

in the markets for risky assets

• It is important because it provides

– a justification for the widespread practice of

passive investing called indexing

– a way to estimate expected rates of return

for use in evaluating stocks and projects

Specifying the Model

number of securities becomes large, we obtained the formula

– This formula tells us that the correlations are

of crucial importance in the relationship

between a portfolio risk and the stock risk

j

i ,exemplar exemplar

exemplar

CAPM Formula

m

f m

f

r m

f

m r

r slope

r r

σ µ

σ σ

µ µ

−

=

+

−

=

13.2 Determining the Risk

Premium on the Market

Portfolio

– the equilibrium risk premium on the market

portfolio is the product of

• variance of the market, σ2M

• weighted average of the degree of risk

aversion of holders of risk, A

2

M f

Example: To Determine ‘A’

0

2 20

0

06 0 14

0

, 06

0 ,

20

0 ,

14 0

2

2 2

=

−

=

−

=

⇒

=

−

=

=

=

A

r A

A r

r

M

M M

M

M M

r

f

r r

f r

f r

r

σ

µ σ

µ

σ µ

CAPM Risk Premium on any

Asset

the risk premium on any asset is equal the product of

– β (or ‘Beta’)

– the risk premium on the market portfolio

( m f ) i r f ( m f ) i f

i

Security Prices

10

20

30

40

50

60

70

0.000 0.083 0.167 0.250 0.333 0.417 0.500 0.583 0.667 0.750 0.833 0.917 1.000

Market_Price Stock_Z_Price

Table of Prices

0 50.00 30.00 hpr_Mkt hpr_Z annual_cont_mktannual_cont_zreg_line

Regression of Returns of Z on Market

-200%

-150%

-100%

-50%

0%

50%

100%

150%

200%

-150% -100% -50% 0% 50% 100% 150%

Model and Measured Values

of Statistical Parameters

modl 15% 20% 12% 25% 90% 1.13 Meas 10% 26% 28% 33% 97% 1.22

Security Market Line Market

Portfolio

-20%

-15%

-10%

-5%

0%

5%

10%

15%

20%

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

The Beta of a Portfolio

– using standard deviation results in a formula

that’s quite complex

– using beta, the formula is linear

∑

= +

+ +

= w β w β w β w β

1

, ,

1

2

2 2 1

1 + + + =   ∑= + ∑i>j  

j i r r j

i n

i

r i r

w r

w r

w n n w σ i w w σ iσ j ρ σ

Computing Beta

computing beta

f M

f

r i

M

M i i M

M i M i

M

M

i M

i i

r

r i

−

−

=

=

=

=

=

µ

µ β

σ

ρ

σ σ

ρ σ

σ σ

σ β

2

, 2

, ,

Valuation and Regulating

Rates of Return

• Assume the market rate is 15%, and the

risk-free rate is 5%

04 1

0

* 20 0 3

1

* 80

0

bond

=

+

=

+

=

company

company

bond equity

equity

β

β

β β

β

Valuation and Regulating

Rates of Return

the beta of our new operation

project, apply the CAPM

04 1 05

.

=

− +

r r β r r

µ

Valuation and Regulating

Rates of Return

vehicle for the new project, then the beta of your unquoted equity is

73

1

0

* 40 0

* 60 0 04

.

1

bond

=

+

=

+

=

equity

equity

bond equity

equity

β

β

β β

β

Valuation and Regulating

Rates of Return

expected dividend of $6 next year, and that it will grow annually at a rate of 4% for ever, the value of a share is

63

52

$ 04

0 154

0

6

1

−

=

−

=

g r

D p