Corporate finance chapter 013 the capital asset pricing model

Chapter 13: The Capital
Asset Pricing Model

Objective
1

•The Theory of the CAPM
•Use of CAPM in benchmarking
• Using CAPM to determine
correct rate for
discounting


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
2


Introduction
• 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
3


Specifying the Model
• We also observed that in the limit as the
number of securities becomes large, we
obtained the formula
σ portfioio = σ exemplar ρ exemplari ,exemplarj

– This formula tells us that the correlations are
of crucial importance in the relationship
between a portfolio risk and the stock risk
4


CAPM Formula
µ m − rf
µr =
σ r + rf
σm
µ m − rf
slope =
σm

5


13.2 Determining the Risk
Premium on the Market

Portfolio
• CAPM states that
– 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

µ rm − rf = Aσ

2
M
6


Example: To Determine ‘A’
µ rM = 0.14, σ rM = 0.20, rf = 0.06,
µ rM − rf = Aσ

2
rM

µ rM − rf
⇒ A=
2
σ rM

0.14 − 0.06
A=
= 2 .0

2
0.20
7


CAPM Risk Premium on any
Asset
• According the the CAPM, in equilibrium,
the risk premium on any asset is equal
the product of
– β (or ‘Beta’)
– the risk premium on the market portfolio

µ ri − rf = ( µ m − rf ) β i ⇒ µ ri = rf + ( µ m − rf ) β i
8


Security Prices
70
60

Value

50
40
30
20

Market_Price

Stock_Z_Price

10
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
Years
9


Table of Prices
month
0
1
2
3
4
5
6
7
8
9
10
11
12

Mkt_Price Z_Price
hpr_Mkt hpr_Z
50.00
30.00 hpr_Mkt hpr_Z
annual_cont_mkt
annual_cont_z

reg_line
55.84
33.87
11.68%
12.90% 132.55% 145.56% 176.82%
52.87
33.65
-5.32%
-0.64% -65.59%
-7.75% -64.54%
58.19
39.19
10.07%
16.47% 115.15% 182.98% 155.62%
60.33
41.30
3.66%
5.38%
43.19%
62.90%
67.97%
56.97
38.93
-5.57%
-5.74% -68.71% -70.89% -68.35%
51.52
34.20
-9.56% -12.15% -120.56% -155.40% -131.50%
52.80
35.88

2.47%
4.91%
29.32%
57.54%
51.08%
55.04
38.24
4.24%
6.56%
49.83%
76.22%
76.06%
55.76
40.64
1.32%
6.28%
15.70%
73.08%
34.48%
62.20
46.26
11.55%
13.83% 131.12% 155.46% 175.09%
56.84
41.01
-8.62% -11.34% -108.23% -144.43% -116.49%
55.30
39.54
-2.71%
-3.58% -32.93% -43.78% -24.76%

an_an_fact 1.105934 1.318151
an_cont_rate 0.10069 0.27623

mu
sig
rho
beta

10.07%
27.62%
0.259099 0.325796
0.968777
1.218157
10


Regression of Returns of Z on Market
200%
150%

Return on Z

100%
50%
0%
-150%

-100%

-50%

0%

50%

-50%
-100%
-150%
-200%
Market Return
11

100%

150%


Model and Measured Values
of Statistical Parameters
µm

σm

µz

σz

ρ

β

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

12


Market
Portfolio

Security Market Line
20%

Expected Risk Premium

15%
10%
5%
0%
-2.0

-1.5

-1.0

-0.5

0.0

0.5

-5%
-10%
-15%
-20%
Beta (Risk)
13

1.0

1.5

2.0


The Beta of a Portfolio
• When determining the risk of a portfolio
– using standard deviation results in a formula
that’s quite complex

σ w1r1 + w2 r2 +...+ wn rn


=  ∑ wiσ ri
 i =1,n

(

)

2

(

+ 2∑ wi w jσ ri σ r j ρ i , j
i> j

)






1
2

– using beta, the formula is linear

β w1r1 + w2 r2 +...+ wn rn = w1 β r1 + w2 β r2 + ... + wn β rn = ∑ wi β ri
i

14


Computing Beta
• Here are some useful formulae for
computing beta

σ i , M σ iσ M ρ i , M σ i ρ i , M
β i = β i,M = 2 =
=
2
σM
σM
σM
µ ri − rf
βi =
µ M − rf
15


Valuation and Regulating
Rates of Return
• Assume the market rate is 15%, and the riskfree rate is 5%

• Compute the beta of betaful’s operations

β company = wequity β equity + wbond β bond
β company = 0.80 *1.3 + 0.20 * 0
β company = 1.04
16


Valuation and Regulating
Rates of Return
• Beta of betaful’s operations is equal to
the beta of our new operation
• To find the required return on the new

project, apply the CAPM

µ r = rf + β ( rm − rf )

= 0.05 + 1.04( 0.15 − 0.05)
= 15.4%

17


Valuation and Regulating
Rates of Return
• Assume that your company is just a
vehicle for the new project, then the
beta of your unquoted equity is

β company = wequity β equity + wbond β bond
1.04 = 0.60 * β equity + 0.40 * 0

β equity = 1.73
18


Valuation and Regulating
Rates of Return
• Assume that your company has an
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

D1
6
p0 =
=
= $52.63
r − g 0.154 − 0.04
19