Corporate finance 7e ross ch11

Chapter Outline11.1 Factor Models: Announcements, Surprises, and Expected Returns 11.2 Risk: Systematic and Unsystematic 11.3 Systematic Risk and Betas 11.4 Portfolios and Factor Models

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11

An Alternative View of Risk and Return: The

APT

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Chapter Outline

11.1 Factor Models: Announcements, Surprises, and

Expected Returns

11.2 Risk: Systematic and Unsystematic

11.3 Systematic Risk and Betas

11.4 Portfolios and Factor Models

11.5 Betas and Expected Returns

11.6 The Capital Asset Pricing Model and the

Arbitrage Pricing Theory

11.7 Parametric Approaches to Asset Pricing

11.8 Summary and Conclusions

11.1 Factor Models: Announcements, Surprises, and

Expected Returns

11.7 Parametric Approaches to Asset Pricing

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Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit Since no investment is required, an investor can create large positions to secure large

levels of profit.

In efficient markets, profitable arbitrage

opportunities will quickly disappear.

Arbitrage arises if an investor can construct a zero investment portfolio with a sure profit Since no investment is required, an investor can create large positions to secure large

levels of profit.

In efficient markets, profitable arbitrage

opportunities will quickly disappear.

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11.1 Factor Models: Announcements,

Surprises, and Expected ReturnsThe return on any security consists of two parts

First the expected returns Second is the unexpected or risky returns.

A way to write the return on a stock in the coming month is:

The return on any security consists of two parts

First the expected returns Second is the unexpected or risky returns.

A way to write the return on a stock in the coming month is:

return the

of part unexpected

the is

return the

of part expected

the is

where

U R

R  

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11.1 Factor Models: Announcements,

Surprises, and Expected Returns

Any announcement can be broken down into two parts, the anticipated or expected part and the

surprise or innovation:

Announcement = Expected part + Surprise.

The expected part of any announcement is part of the information the market uses to form the

expectation, R of the return on the stock.

The surprise is the news that influences the

unanticipated return on the stock, U.

Any announcement can be broken down into two parts, the anticipated or expected part and the

surprise or innovation:

Announcement = Expected part + Surprise.

The expected part of any announcement is part of the information the market uses to form the

expectation, R of the return on the stock.

The surprise is the news that influences the

unanticipated return on the stock, U.

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A systematic risk is any risk that affects a large number

of assets, each to a greater or lesser degree

An unsystematic risk is a risk that specifically affects a

single asset or small group of assets

Unsystematic risk can be diversified away

Examples of systematic risk include uncertainty about

general economic conditions, such as GNP, interest rates

or inflation

On the other hand, announcements specific to a

company, such as a gold mining company striking gold, are examples of unsystematic risk

A systematic risk is any risk that affects a large number

of assets, each to a greater or lesser degree

An unsystematic risk is a risk that specifically affects a

single asset or small group of assets

Unsystematic risk can be diversified away

Examples of systematic risk include uncertainty about

general economic conditions, such as GNP, interest rates

or inflation

On the other hand, announcements specific to a

company, such as a gold mining company striking gold, are examples of unsystematic risk

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We can break down the risk, U, of holding a stock into two

components: systematic risk and unsystematic risk:

risk ic

unsystemat the

is

risk systematic

the is

where becomes

ε m

R R

U R

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The beta coefficient, , tells us the response of the

stock’s return to a systematic risk.

In the CAPM,  measured the responsiveness of a

security’s return to a specific risk factor, the return

on the market portfolio.

We shall now consider many types of systematic

risk.

The beta coefficient, , tells us the response of the

stock’s return to a systematic risk.

In the CAPM,  measured the responsiveness of a

security’s return to a specific risk factor, the return

on the market portfolio.

We shall now consider many types of systematic

risk.

) (

R

R R

Cov



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For example, suppose we have identified three systematic risks

on which we want to focus:

Our model is:

For example, suppose we have identified three systematic risks

on which we want to focus:

unsystemat the

is

beta rate

exchange spot

the is

beta GDP

the is

beta inflation

the is

ε β β β

ε F

β F

β R

R

ε m

R R

S GDP I

S S GDP

GDP I

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Systematic Risk and Betas: Example

Suppose we have made the following estimates:

ε F

β F

β R

% 1



ε

% 1 50

0 50

1 30

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We must decide what surprises took place in the systematic

factors

If it was the case that the inflation rate was expected to be

by 3%, but in fact was 8% during the time period, then

F I = Surprise in the inflation rate

If it was the case that the inflation rate was expected to be

by 3%, but in fact was 8% during the time period, then

F I = Surprise in the inflation rate

= actual – expected

= 8% – 3%

= 5%

% 1 50

0 50

1 30

0 50

1

% 5 30



R

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If it was the case that the rate of GDP growth was expected

to be 4%, but in fact was 1%, then

F GDP = Surprise in the rate of GDP growth

= 1% – 4%

= – 3%

If it was the case that the rate of GDP growth was expected

to be 4%, but in fact was 1%, then

F GDP = Surprise in the rate of GDP growth

= 1% – 4%

= – 3%

% 1 50

0 50

1

% 5 30

0

%) 3 ( 50 1

% 5 30



R

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If it was the case that dollar-euro spot exchange rate, S($,

€), was expected to increase by 10%, but in fact remained stable during the time period, then

F S = Surprise in the exchange rate

= 0% – 10%

= – 10%

If it was the case that dollar-euro spot exchange rate, S($,

€), was expected to increase by 10%, but in fact remained stable during the time period, then

F S = Surprise in the exchange rate

= 0% – 10%

= – 10%

% 1 50

0

%) 3 ( 50 1

% 5 30

%) 10 (

50 0

%) 3 ( 50 1

% 5 30



R

R

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Finally, if it was the case that the expected return on

the stock was 8%, then

Finally, if it was the case that the expected return on

the stock was 8%, then

% 1 50

0

%) 3 ( 50 1

% 5 30

% 1

%) 10 (

50 0

%) 3 ( 50 1

% 5 30 2

% 8



R

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Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-

factor model.

We will create portfolios from a list of N stocks

and will capture the systematic risk with a

1-factor model.

The ith stock in the list have returns:

Now let us consider what happens to portfolios of stocks when each of the stocks follows a one-

factor model.

We will create portfolios from a list of N stocks

and will capture the systematic risk with a

1-factor model.

The ith stock in the list have returns:

i i

i

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Relationship Between the Return on the

Common Factor & Excess Return

Excess return

The return on the factor F

i



i i

i

R   

If we assume that there is no unsystematic risk, then i = 0

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Excess return

If we assume that there is no unsystematic risk, then i = 0

F β R

R i  i  i

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Excess return

Different securities will have different

betas

0 1



B

β

50 0



C

β

5 1



A

β

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Portfolios and Diversification

We know that the portfolio return is the weighted average of the returns on the individual assets in the portfolio:

N N i

i

R  1 1  2 2   

)(

)

1

N N

P

ε F

β R

X

ε F

β R

X ε

F β R

N N

N

P

ε X F

β X R

X

ε X F

β X R

X ε

X F

β X R

2 2

2 1

1 1

1

i i

i

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The return on any portfolio is determined by three sets of

R  1 1  2 2 

1 The weighed average of expected returns.

F β

X β

X ε

X   

 1 1 2 2 

3 The weighted average of the unsystematic risks.

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So the return on a diversified portfolio is

determined by two sets of parameters:

1. The weighed average of expected returns

2. The weighted average of the betas times the factor F.

So the return on a diversified portfolio is

determined by two sets of parameters:

1. The weighed average of expected returns

2. The weighted average of the betas times the factor F.

F β

X β

X

R X

R X R

X R

N N

P

)( 1 1 2 2

2 2 1

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The return on a diversified portfolio is the sum of the

expected return plus the sensitivity of the portfolio to the factor

The return on a diversified portfolio is the sum of the

expected return plus the sensitivity of the portfolio to the factor

F β

X β

X R

X

R P  1 1  N N ( 1 1   N N )

F β R

R P  P  P

N N

R  1 1 

that Recall

N N

β  1 1 and

P

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Relationship Between  & Expected Return

If shareholders are ignoring unsystematic

risk, only the systematic risk of a stock can

be related to its expected return.

If shareholders are ignoring unsystematic

risk, only the systematic risk of a stock can

be related to its expected return.

F β

R

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Relationship Between  & Expected Return

R

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APT applies to well diversified portfolios and not necessarily to individual stocks.

With APT it is possible for some individual

stocks to be mispriced - not lie on the SML.

APT is more general in that it gets to an expected return and beta relationship without the

assumption of the market portfolio.

APT can be extended to multifactor models.

APT applies to well diversified portfolios and not necessarily to individual stocks.

With APT it is possible for some individual

stocks to be mispriced - not lie on the SML.

APT is more general in that it gets to an expected return and beta relationship without the

assumption of the market portfolio.

APT can be extended to multifactor models.

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Be aware that correlation does not imply causality.

Related to empirical methods is the practice of

classifying portfolios by style e.g.

Value portfolio Growth portfolio

Both the CAPM and APT are risk-based models There are alternatives

Empirical methods are based less on theory and more on looking for some regularities in the historical record

Be aware that correlation does not imply causality

Related to empirical methods is the practice of

classifying portfolios by style e.g.

Value portfolio Growth portfolio

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The APT assumes that stock returns are generated according to

factor models such as:

As securities are added to the portfolio, the unsystematic risks of the individual securities offset each other A fully diversified

portfolio has no unsystematic risk.

The CAPM can be viewed as a special case of the APT.

Empirical models try to capture the relations between returns and stock attributes that can be measured directly from the data

without appeal to theory.

The APT assumes that stock returns are generated according to

factor models such as:

As securities are added to the portfolio, the unsystematic risks of the individual securities offset each other A fully diversified

portfolio has no unsystematic risk.

The CAPM can be viewed as a special case of the APT.

Empirical models try to capture the relations between returns and stock attributes that can be measured directly from the data

without appeal to theory.

ε F

β F

β R

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