The Oxford Guide to Financial Modeling by Ho & Lee Chapter 2. Equity Market: Capital Asset Pricing...

The Oxford Guide to Financial Modeling by Ho & Lee

Chapter 2. Equity Market:Capital Asset Pricing Model

Copyright © 2004 by Thomas Ho and Sang Bin Lee. All rights reserved.

The Oxford Guide to

Financial Modeling

Thomas S. Y. Ho and Sang Bin Lee

Chapter 2. Equity Market: The Capital Asset Pricing Model 2


2.1 Real and Financial Sectors

• Tangible assets, commodities– metals, buildings, factories, inventories,

• Intangible assets– patents, branding

• Financial securities– Stocks, bonds, options, mortgages

• Role of a corporation– Economic units– Organization of a corporation



2.2 Stocks and Stock Market

• Dividends, capital gains

– Announcement date, ex-dividends

• Types of orders

– Market orders: immediate execution at the market price

– Limit orders: wait for the execution at the stated price

• Factors affecting the bid ask spreads

– Market makers, competition, trading volume



Spot Market

• Primary market– new issuance– Investment banking

• Secondary market: – Exchanges: central location, specialists– Over-the-counter

• Open limit order book• Market makers

• Electronic Communication Network (ECN)



Future and Forward Markets

• Forward contracts

• Futures contracts

• Counter-parties

• Open interests

• Marking to market

• Indices: S&P 500, Nikkei 225



2.3 Perfect Capital Market

• All financial claims are perfectly divisible

• No transaction costs

• No taxes

• Competitive markets

• No limit in short selling

• Information symmetry

• Increasing utility of wealth and risk aversion



2.4 Efficient Capital Market Hypothesis

• Weak form efficiency

• Semi-strong form efficiency

• Strong form efficiency



2.4 Efficient Capital Market Hypothesis



2.5 Diversification

• A portfolio in general reduces the risk of an individual stock

• Contribution of risk from each stock

• A measure of risk: standard deviation

• The example of 2 coins shows that the standard deviation is lowered in betting on 2 coins than putting all the bet on one coin



Diversification (an Example)

Head/Head Head/Tail Tail/Tail

Probability 0.25 0.5 0.25

Outcomes $200 $100 0



Lognormal and normal distributions with a

mean and a standard deviation

-1.96 0 1.96

0.1

0.2

0.3

0.4

Normal Density

0.23 11.7

0.1

0.2

0.3

0.4

Lognormal Density



Diversification Effect

Systematic

Total

10 20 30 40

0.03

0.04

0.05

0.06

0.07

10 20 30 40The number of stocks

0.03

0.04

0.05

0.06

0.07

Ris

k %

Systematic Risk

Total Risk



2 2 2 22

4ABC BCD CDA DAB

k

2 2 2 2

2 2 2 2

2 2 2 2

2 2 2 2

1 1 1 2( )

9 9 9 9

1 1 1 2( )

9 9 9 9

1 1 1 2( )

9 9 9 9

1 1 1 2( )

9 9 9 9

ABC A B C AB BC CA

BCD B C D BC CD DA

CDA C D A CD DA AC

DAB D A B DA AB BD


the average risk of portfolios :

2 2 2 2

2

2

2( )1 2

3 4 3 12

1 2

3 3

A B C D AB AC AD BC BD CDk

i ij




2 2 2 2 2,

2 2 2 2, ,

2 2, ,

, ,

2

( ) ( )

P A A A B A B B B

A A A B A B A B A B B B

A A A B A B B A A B B B

A A P B B P

,

2,

( , ) ( , ) ( , ) ( , )

( , ) ( , )

A P A P A A A B B A A A A B B

A A A B A B A A B A B

Cov R R Cov R R R Cov R R Cov R R

Cov R R Cov R R



Capital Asset Pricing Model

[ ] [ ]i f i M fE R r E R r



Capital Market Line

CML

A B C

M

0

E

D



21 1 2 2cov( , ) cov( , ) .... cov( , )M M M N N MR R R R R R

1 21 22 2 2

1 1 2 2

cov( , )cov( , ) cov( , )1 ...

= ...

N MM MN

M M M

N N

R RR R R R

2

cov( , ), 1, ,i M

iM

R Ri N

the variance of the market portfolio



ˆî i i M iR R e

ˆî i MR

ˆˆ i i i MR R

î MR

î

î

ie

iR

MR

MR

O

2.7 Beta – the Systematic Risk



100

(100) Beta(5) 5

Expected Return (%)

0 10(10)

0

50

(50)

Riskless Asset

Short Stock

Buying Stock

Buying Stock at a margin

Security Market Line: relationship between expected return and beta



The Constant Growth Stock Model

• S the stock price

• D the dividends

• The required return of the stock

• The constant growth rate



2.8 The Dividend Discount Model

(1)

( )req

divS

R g

( 1) ( )(1 )div n div n g

2

2 3

(1) (1)(1 ) (1)(1 )

(1 ) (1 ) (1 )req req req

div div g div gS

R R R

( 1)(forecasted dividends over T periods)

( )(1 )Treq req

div TS PV

R g R



2.10 Empirical Tests of the Capital Asset Pricing Model

• Black, Jensen, Scholes (1972)• Fama and Macbeth (1974)

– Relate the stock betas with the long term stock returns

• Roll (1977)– Is CAPM testable?

• Stambaugh(1982)– What is the market portfolio?

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