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Chapter 7. Capital Asset Pricing and Arbitrage Pricing Theory. CAPM: Simplifying Assumptions. Individual investors are price takers Single-period investment horizon Investments are limited to traded financial assets No taxes and no transaction costs

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chapter 7

Chapter 7

Capital Asset Pricing and Arbitrage Pricing Theory

capm simplifying assumptions
CAPM: Simplifying Assumptions

Individual investors are price takers

Single-period investment horizon

Investments are limited to traded financial assets

No taxes and no transaction costs

Information is costless and available to all investors

Investors are rational mean-variance optimizers

Homogeneous expectations

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alpha and beta
alpha and beta

E(rM) =

βS =

rf =

Required return = rf + βS [E(rM) – rf]

=

If you believe the stock will actually provide a return of ____, what is the implied alpha?

 =

Portfolio Beta is the weighted average of underlying Betas

14%

1.5

5%

5 + 1.5 [14 – 5] = 18.5%

17%

17% - 18.5% = -1.5%

7-3

adjusted betas
Adjusted Betas

Adjusted β =

=

=

1

1

Calculated betas are adjusted to account for the empirical finding that betas different from _ tend to move toward _ over time.

A firm with a beta __ will tend to have a ___________________ in the future. A firm with a beta ___ will tend to have a ____________________ in the future.

>1

lower beta (closer to 1)

< 1

higher beta (closer to 1)

2/3 (Calculated β) + 1/3 (1)

2/3 (1.276) + 1/3 (1)

1.184

7-4

evaluating the capm
Evaluating the CAPM

The CAPM is “false” based on the ____________________________.

validity of its assumptions

The CAPM could still be a useful predictor of expected returns. That is an empirical question.

Huge measurability problems because the market portfolio is unobservable.

Conclusion: As a theory the CAPM is untestable.

7-5

evaluating the capm1
Evaluating the CAPM

However, the __________ of the CAPM is testable.

Betas are ___________ at predicting returns as other measurable factors may be.

More advanced versions of the CAPM that do a better job at ___________________________ are useful at predicting stock returns.

practicality

not as useful

estimating the market portfolio

Still widely used and well understood.

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slide7
Fama-French (FF) 3 factor Modelhttp://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html

Fama and French noted that stocks of ____________ and stocks of firms with a _________________ have had higher stock returns than predicted by single factor models.

smaller firms

high book to market

Problem: Empirical model without a theory

Will the variables continue to have predictive power?

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fama french ff 3 factor model
Fama-French (FF) 3 factor Model

FF proposed a 3 factor model of stock returns as follows:

rM – rf = Market index excess return

Ratio of ______________________________________ measured with a variable called ____:

HML: High minus low or difference in returns between firms with a high versus a low book to market ratio.

_______________ measured by the ____ variable

SMB: Small minus big or the difference in returns between small and large firms.

book value of equity to market value of equity

HML

SMB

Firm size variable

7-8

arbitrage pricing theory apt
Arbitrage Pricing Theory (APT)

Arbitrage:

Zero investment:

Efficient markets:

Arises if an investor can construct a zero investment portfolio with a

sure profit, e.g. Credit Card B/T

Since no net investment outlay is required, an investor can create arbitrarily large positions to secure large levels of profit

With efficient markets, profitable arbitrage opportunities will quickly disappear

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arbitrage pricing example
Arbitrage Pricing Example

Suppose Rf = ___ and a well diversified portfolio P has a beta of ___ and an alpha of ___ when regressed against a systematic factor S. Another well diversified portfolio Q has a beta of ___ and an alpha of ___.

If we construct a portfolio of P and Q with the following weights:

What should αp = ___

3.25

-2.25

Note: Σ W = 1

1.3

6%

2%

0.9

1%

WP = and WQ = ;

Then βp =

αp =

(-2.25 x 1.3) + (3.25 x 0.9) = 0

(-2.25 x 2%) + (3.25 x 1%) = - 1.25%

0

αp = -1.25% means an investor will earn rf – 1.25% or 4.75% on portfolio PQ.

In theory one could short this portfolio and pay 4.75%, and invest in the riskless asset and earn 6%, netting the 1.25% difference.

Arbitrage should eliminate the negative portfolio alpha quickly.

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arbitrage pricing model
Arbitrage Pricing Model

The result: For a well diversified portfolio

Rp = βpRS (Excess returns)

(rp,i – rf) = βp(rS,i – rf)

and for an individual security

(rp,i – rf) = βp(rS,i – rf) + ei

Advantage of the APT over the CAPM:

RS is the excess return on a portfolio with a beta of 1 relative to systematic factor “S”

  • No particular role for the “Market Portfolio,” which can’t be measured anyway
  • Easily extended to multiple systematic factors, for example
    • (rp,i – rf) = βp,1(r1,i – rf) + βp,2(r2,i – rf) + βp,3(r3,i – rf) + ei

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