Factor Models: Announcements, Surprises, and Expected Returns

Сентябрь 10, 2022

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Factor Models: Announcements, Surprises, and Expected Returns

Содержание

2. 11.1 Factor Models: Announcements, Surprises, and Expected Returns The return on any security consists of two
3. 11.1 Factor Models: Announcements, Surprises, and Expected Returns A way to write the return on a
4. 11.1 Factor Models: Announcements, Surprises, and Expected Returns Any announcement can be broken down into two
5. 11.2 Risk: Systematic and Unsystematic A systematic risk is any risk that affects a large number
6. 11.2 Risk: Systematic and Unsystematic Systematic Risk; m Nonsystematic Risk; ε n σ Total risk; U
7. 11.2 Risk: Systematic and Unsystematic Systematic risk is referred to as market risk. m influences all
8. 11.3 Systematic Risk and Betas The beta coefficient, β, tells us the response of the stock’s
9. 11.3 Systematic Risk and Betas For example, suppose we have identified three systematic risks on which
10. Systematic Risk and Betas: Example Suppose we have made the following estimates: βI = -2.30 βGDP
11. Systematic Risk and Betas: Example We must decide what surprises took place in the systematic factors.
12. Systematic Risk and Betas: Example If it was the case that the rate of GDP growth
13. Systematic Risk and Betas: Example If it was the case that dollar-pound spot exchange rate, S($,£),
14. Systematic Risk and Betas: Example Finally, if it was the case that the expected return on
15. 11.4 Portfolios and Factor Models Now let us consider what happens to portfolios of stocks when
16. Relationship Between the Return on the Common Factor & Excess Return Excess return The return on
17. Relationship Between the Return on the Common Factor & Excess Return Excess return The return on
18. Relationship Between the Return on the Common Factor & Excess Return Excess return The return on
19. Portfolios and Diversification We know that the portfolio return is the weighted average of the returns
20. Portfolios and Diversification The return on any portfolio is determined by three sets of parameters: In
21. Portfolios and Diversification So the return on a diversified portfolio is determined by two sets of
22. 11.5 Betas and Expected Returns The return on a diversified portfolio is the sum of the
23. Relationship Between β & Expected Return The relevant risk in large and well-diversified portfolios is all
24. Relationship Between β & Expected Return Expected return β A B C D SML
25. 11.6 The Capital Asset Pricing Model and the Arbitrage Pricing Theory APT applies to well diversified
26. Multi-factor APT Example: A Canadian study (Otuteye, CIR 1991) with five factors: the rate of growth
27. 11.7 Empirical Approaches to Asset Pricing Both the CAPM and APT are risk-based models. There are
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11.1 Factor Models: Announcements, Surprises, and Expected Returns
The return on any

security consists of two parts.
1) the expected or normal return: the return that shareholders in the market predict or expect
2) the unexpected or risky return: the portion that comes from information that will be revealed .
Examples of relevant information:
Statistics Canada figures (e.g., GNP)
A sudden drop in interest rates
News that the company’s sales figures are higher than expected

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11.1 Factor Models: Announcements, Surprises, and Expected Returns
A way to write

the return on a stock in the coming month is:

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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.

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11.2 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.

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11.2 Risk: Systematic and Unsystematic
Systematic Risk; m
Nonsystematic Risk; ε
n
σ
Total risk;

We can break down the risk, U, of holding a stock into two components: systematic risk and unsystematic risk:

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11.2 Risk: Systematic and Unsystematic
Systematic risk is referred to as market

risk.
m influences all assets in the market to some extent.
Is specific to the company and unrelated to the specific risk of most other companies.

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11.3 Systematic Risk and Betas
The beta coefficient, β, tells us the

response of the stock’s return to a systematic risk.
In the CAPM, β 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.

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11.3 Systematic Risk and Betas
For example, suppose we have identified three

systematic risks on which we want to focus:
Inflation
GDP growth
The dollar-pound spot exchange rate, S($,£)
Our model is:

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Systematic Risk and Betas: Example
Suppose we have made the following estimates:
βI

= -2.30
βGDP = 1.50
βS = 0.50.
Finally, the firm was able to attract a “superstar” CEO and this unanticipated development contributes 1% to the return.

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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 3%, but in fact was 8% during the time period, then
FI = Surprise in the inflation rate
= actual – expected
= 8% - 3%
= 5%

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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%

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Systematic Risk and Betas: Example
If it was the case that dollar-pound

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%

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Systematic Risk and Betas: Example
Finally, if it was the case that

the expected return on the stock was 8%, then

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11.4 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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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 εi = 0

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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 εi = 0

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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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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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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.

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Portfolios and Diversification
So the return on a diversified portfolio is determined

by two sets of parameters:
The weighed average of expected returns.
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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11.5 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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Relationship Between β & Expected Return
The relevant risk in large and

well-diversified portfolios is all systematic, because unsystematic risk is diversified away.
If shareholders are ignoring unsystematic risk, only the systematic risk of a stock can be related to its expected return.

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Relationship Between β & Expected Return
Expected return
β
A
B
C
D
SML

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11.6 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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Multi-factor APT
Example: A Canadian study (Otuteye, CIR 1991)
with five factors:
the rate

of growth in industrial production
the changes in the slope of the term structure of interest rates
the default risk premium for bonds
inflation
The value-weighted return on the market portfolio (TSE 300)

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11.7 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 e.g.,
Value portfolio
Growth portfolio

Factor Models: Announcements, Surprises, and Expected Returns

Содержание

11.1 Factor Models: Announcements, Surprises, and Expected ReturnsThe return on any

11.1 Factor Models: Announcements, Surprises, and Expected ReturnsA way to write

11.1 Factor Models: Announcements, Surprises, and Expected ReturnsAny announcement can be

11.2 Risk: Systematic and UnsystematicA systematic risk is any risk that

11.2 Risk: Systematic and UnsystematicSystematic Risk; m Nonsystematic Risk; εnσTotal risk;

11.2 Risk: Systematic and Unsystematic Systematic risk is referred to as market

11.3 Systematic Risk and BetasThe beta coefficient, β, tells us the

11.3 Systematic Risk and BetasFor example, suppose we have identified three

Systematic Risk and Betas: ExampleSuppose we have made the following estimates:βI

Systematic Risk and Betas: ExampleWe must decide what surprises took place

Systematic Risk and Betas: ExampleIf it was the case that the

Systematic Risk and Betas: ExampleIf it was the case that dollar-pound

Systematic Risk and Betas: ExampleFinally, if it was the case that

11.4 Portfolios and Factor ModelsNow let us consider what happens to

Relationship Between the Return on the Common Factor & Excess ReturnExcess

Relationship Between the Return on the Common Factor & Excess ReturnExcess

Relationship Between the Return on the Common Factor & Excess ReturnExcess

Portfolios and DiversificationWe know that the portfolio return is the weighted

Portfolios and DiversificationThe return on any portfolio is determined by three

Portfolios and DiversificationSo the return on a diversified portfolio is determined

11.5 Betas and Expected ReturnsThe return on a diversified portfolio is

Relationship Between β & Expected ReturnThe relevant risk in large and

Relationship Between β & Expected ReturnExpected returnβABCDSML

11.6 The Capital Asset Pricing Model and the Arbitrage Pricing TheoryAPT

Multi-factor APTExample: A Canadian study (Otuteye, CIR 1991)with five factors:the rate

11.7 Empirical Approaches to Asset PricingBoth the CAPM and APT are

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Relationship Between the Return on the Common Factor & Excess Return
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