Chapter 10 - Extensions and Testing of Asset Pricing Theories

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Lecture Presentation Software to accompany

Investment Analysis and Portfolio Management

Sixth Editionby

Frank K. Reilly & Keith C. Brown

Chapter 10

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SAIF ULLAH, [email protected], +923216633271

Chapter 10 - Extensions and Testing of Asset Pricing TheoriesQuestions to be answered:

• What happens to the capital market line (CML) when you assume there are differences in the risk-free borrowing and lending rates?

• What is a zero-beta asset and how does its use impact the CML?

• What happens to the security market line (SML) when you assume transaction costs, heterogeneous expectations, different planning periods, and taxes?


Chapter 10 - Extensions and Testing of Asset Pricing Theories• What are the major questions considered when

empirically testing the CAPM?

• What are the empirical results from tests that examine the stability of beta?

• How do alternative published estimates of beta compare?

• What are the empirical test results of studies that examine the relationship between systematic risk and return?


Chapter 10 - Extensions and Testing of Asset Pricing Theories• What other variables besides beta have had a

significant impact on returns?• What is the theory and practice regarding the

“market portfolio”? How does this difference between theory and the market proxy relate to the benchmark problem?

• Assuming there is a benchmark problem, what variables are affected by it?

• What are the major assumptions not required by the APT model compared to the CAPM?


Chapter 10 - Extensions and Testing of Asset Pricing Theories• How do you test the APT by examining

anomalies found with the CAPM?

• What are the empirical test results related to the APT?

• Why do some authors contend that the APT model is untestable?

• What are the concerns related to the multiple factors of the APT model?


Relaxing the Assumptions of the CAPM

• CAPM assumption: all investors can borrow or lend at the risk-free rate - unrealistic– Differential borrowing and lending rates– Unlimited lending at risk-free rate– Borrowing at higher rate


Investment Alternatives When The Cost of Borrowing is Higher Than The Cost of LendingFigure 10.1

E(R)

Rb

RFR

Risk (standard deviation )

F

G

K



• Zero-beta portfolio: create a portfolio that is uncorrelated to the market (beta 0)– The return of the zero-beta portfolio may differ from

the risk-free rate

• Any combination of portfolios on the efficient frontier will be on the frontier

• Any efficient portfolio will have associated with it a zero-beta portfolio


Implications of Black’s Zero-beta model

• The expected return of any security can be expressed as a linear relationship of any two efficient portfolios

E(Ri) = E(Rz) + i[E(Rm) - E(Rz)]

• If CAPM defines the relationship between risk and return, then the return on the zero-beta portfolio should equal RF

• To test this - identify a market portfolio and solve for the return of a zero-beta portfolio


Security Market Line With A Zero-Beta Portfolio

Figure 10.2

E(R)

E(Rm)

i

SML

M

0.0 1.0

E(Rz)

E(Rm) - E(Rz)



• Transaction costs– affect mispricing corrections– affect diversification


Security Market Line With Transaction Costs

Figure 10.3

E(R)

E(Rm)

i

SML

0.0 1.0

E(Rz)

E(RFR) or



• Heterogenous expectations– If all investors have different expectations about risk

and return, each would have a unique CML and/or SML, and the composite graph would be a band of lines with a breadth determined by the divergence of expectations

• Planning periods– CAPM is a one period model, and the period

employed should be the planning period for the individual investor, which will vary by individual, affecting both the CML and the SML



• Taxes– Tax rates affect returns– Tax rates differ between individuals and institutions


Empirical Testing of CAPM

• How stable is the measure of systematic risk (beta)?

• Is there a positive linear relationship as hypothesized between beta and the rate of return on risky assets?

• How well do returns conform to the SML equation?



• Beta is not stable for individual stocks over short periods of time (52 weeks)

• Stability for portfolios increase significantly

• The larger the portfolio and the longer the period, the more stable the beta of the portfolio

• Betas tend to regress toward the mean



• Different estimates of beta for a stock vary typically in data used

• Value Line estimates use 260 weekly observations

• Merrill Lynch estimates using 60 monthly observations

• Securities market value affects the size and direction of the interval affect


Relationship Between Systematic Risk and Return

• Sharpe and Cooper: positive, but non-linear• Douglas: intercept higher than the risk-free rate

• Miller and Scholes: possible error in Douglas findings• Black, Jensen, and Scholes: positive linear relationship

between monthly excess return and portfolio beta• Fama and McBeth: supported the CAPM with the

intercept equal to the RFR


Relationship Between Systematic Risk and Return

• Effect of skewness on the relationship– preference for high risk and returns

• Effect of size, P/E and leverage

• Effect of book-to-market value– The Fama-French Study


The Market Portfolio: Theory Versus Practice

• Difficult to test full market

• Portfolio used as market proxy may be correlated to true market portfolio

• Benchmark error


Criticism of CAPM by Richard Roll

• Limits on tests: only testable implication from CAPM is whether the market portfolio lies on the efficient frontier

• Range of SML’s - infinite number of possible SML’s, each of which produces a unique estimate of beta


Criticism of CAPM by Richard Roll

• Market efficiency effects - substituting a proxy, such as the S&P 500 creates two problems– Proxy does not represent the true market

portfolio– Even if the proxy is not efficient, the market

portfolio might be


Criticism of CAPM by Richard Roll • Conflicts between proxies - different

substitutes may be highly correlated even though some may be efficient and others are not, which can lead to different conclusions regarding beta risk/return relationships

• So, CAPM is not testable - but it still has value and must be used carefully

• Stephen Ross devised an alternative way to look at asset pricing - APT


Arbitrage Pricing Theory - APT

• Arbitrage is a process of buying a lower priced asset and selling a higher priced asset, both of similar risk, and capturing the difference in arbitrage profits

• The general arbitrage principle states that two identical securities will sell at identical prices

• Price differences will immediately disappear as arbitrage takes place


Arbitrage Pricing Theory - APTThree major assumptions:

1. Capital markets are perfectly competitive

2. Investors always prefer more wealth to less wealth with certainty

3. The stochastic process generating asset returns can be expressed as a linear function of a set of K factors or indexes


Arbitrage Pricing Theory - APT

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Roll-Ross Study

1. Estimate the expected returns and the factor coefficients from time-series data on individual asset returns

2. Use these estimates to test the basic cross-sectional pricing conclusion implied by the APT


Extensions of the Roll-Ross Study

• Cho, Elton, and Gruber examined the number of factors in the return-generating process that were priced

• Dhrymes, Friend, and Gultekin (DFG) reexamined techniques and their limitations and found the number of factors varies with the size of the portfolio


The APT and Anomalies• Small-firm effect

Reinganum - results inconsistent with the APT

Chen - supported the APT model over CAPM

• January anomalyGultekin - APT not better than CAPM

Burmeister and McElroy - effect not captured by model, but still rejected CAPM in favor of APT

• APT and inflationElton, Gruber, and Rentzler - analyzed real returns


The Shanken Challenge to Testability of the APT

• If returns are not explained by a model, it is not considered rejection of a model; however if the factors do explain returns, it is considered support

• APT has no advantage because the factors need not be observable, so equivalent sets may conform to different factor structures

• Empirical formulation of the APT may yield different implications regarding the expected returns for a given set of securities

• Thus, the theory cannot explain differential returns between securities because it cannot identify the relevant factor structure that explains the differential returns


Alternative Testing Techniques

• Jobson proposes APT testing with a multivariate linear regression model

• Brown and Weinstein propose using a bilinear paradigm

• Others propose new methodologies


The InternetInvestments Online

www.barra.com

www.wsharpe.com

www.cob.ohio-state.edu/~fin/journal.jof.htm

www3.oup.co.uk/revfin/scope

http://www.barra.com/

http://www.wsharpe.com/

http://www.cob.ohio-state.edu/~fin/journal.jof.htm


End of Chapter 10–Extensions and Testing of Asset Pricing Theories


Future topicsChapter 11

• Derivative Markets

• Forwards

• Futures

• Options

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Chapter 10 - Extensions and Testing of Asset Pricing Theories