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11-0
Chapter Outline
Factor Models: Announcements, Surprises, and Expected
Returns
Risk: Systematic and Unsystematic
Systematic Risk and Betas
Portfolios and Factor Models
Betas and Expected Returns
The Capital Asset Pricing Model and the Arbitrage Pricing
Theory
Parametric Approaches to Asset Pricing
Summary and Conclusions
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-1
Arbitrage Pricing Theory
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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-2 Factor Models: Announcements,
Surprises, and Expected Returns
• 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:
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-3 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.
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11-4
Risk: Systematic and Unsystematic
• 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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-5
Risk: Systematic and Unsystematic
Systematic Risk; m
Nonsystematic Risk;
n
Total risk; U
We can break down the risk, U, of holding a stock into two
components: systematic risk and unsystematic risk:
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11-6
Systematic Risk and Betas
• The beta coefficient, b, tells us the response of the stock’s
return to a systematic risk.
• In the CAPM, b 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.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-7
Systematic Risk and Betas
• For example, suppose we have identified three
systematic risks on which we want to focus:
1. Inflation
2. GDP growth
3. The dollar-euro spot exchange rate, S($,€)
• Our model is:
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11-8
Systematic Risk and Betas: Example
• Suppose we have made the following estimates:
1. bI =
2. bGDP =
3. bS = .
• Finally, the firm was able to attract a “superstar” CEO
and this unanticipated development contributes 1% to the
return.
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-9
Systematic Risk and Betas: Example
We must decide what surprises took place in the systematic
factors.
If it was the case that the inflation rate was expected to be by
3%, but in fact was 8% during the time period, then
FI = Surprise in the inflation rate
= actual – expected
= 8% - 3%
= 5%
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-10
Systematic Risk and Betas: Example
If it was the case that the rate of GDP growth was expected
to be 4%, but in fact was 1%, then
FGDP = Surprise in the rate of GDP growth
= actual – expected
= 1% - 4%
= -3%
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-11
Systematic Risk and Betas: Example
If it was the case that dollar-euro spot exchange rate, S($,€),
was expected to increase by 10%, but in fact remained
stable during the time period, then
FS = Surprise in the exchange rate
= actual – expected
= 0% - 10%
= -10%
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-12
Systematic Risk and Betas: Example
Finally, if it was the case that the expected return on the
stock was 8%, then
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-13
Portfolios and Factor Models
• 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:
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11-14 Relationship Between the Return on the
Common Factor & Excess Return
Excess
return
The return on the factor F
If we assume
that there is no
unsystematic
risk, then ei = 0
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11-15 Relationship Between the Return on the
Common Factor & Excess Return
Excess
return
The return on the factor F
If we assume
that there is no
unsystematic
risk, then ei = 0
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11-16 Relationship Between the Return on the
Common Factor & Excess Return
Excess
return
The return on the factor F
Different
securities will
have different
betas
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11-17
Portfolios and Diversification
• We know that the portfolio return is the weighted
average of the returns on the individual assets in the
portfolio:
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11-18
Portfolios and Diversification
The return on any portfolio is determined by three sets of
parameters:
In a large portfolio, the third row of this equation
disappears as the unsystematic risk is diversified away.
1. The weighed average of expected returns.
2. The weighted average of the betas times the factor.
3. The weighted average of the unsystematic risks.
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11-19
Portfolios and Diversification
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.
In a large portfolio, the only source of uncertainty is the
portfolio’s sensitivity to the factor.
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11-20
Betas and Expected Returns
The return on a diversified portfolio is the sum of the
expected return plus the sensitivity of the portfolio to the
factor.
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11-21
Relationship Between b & Expected Return
• If shareholders are ignoring unsystematic risk, only
the systematic risk of a stock can be related to its
expected return.
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11-22
Relationship Between b & Expected Return
E
xp
ec
te
d
re
tu
rn
b
A B
C
D
SML
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-23 The Capital Asset Pricing Model and
the Arbitrage Pricing Theory
• 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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11-24
Empirical Approaches to Asset Pricing
• 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 .
– Value portfolio
– Growth portfolio
McGraw-Hill/Irwin Copyright © 2002 by The McGraw-Hill Companies, Inc. All rights reserved.
11-25
Summary and Conclusions
• 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.
