Version 1.2 Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make...

Version 1.2Copyright © 2000 by Harcourt, Inc.All rights reserved. Requests for permission to make copies of any part of the work should be mailed to:

Permissions DepartmentHarcourt, Inc.6277 Sea Harbor DriveOrlando, Florida 32887-6777

Lecture Presentation Software to accompany

Investment Analysis and Portfolio Management

Sixth Editionby

Frank K. Reilly & Keith C. Brown

Chapter 10

Copyright © 2000 by Harcourt, Inc. All rights reserved.

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 original CAPM defines the relationship between risk

and return, then the return on the zero-beta portfolio should equal RF – Typically, in real world, RFR < E(RZ), so the zero-beta SML

would be less steep than the original SML– Consistent with empirical results of tests of original CAPM

• To test directly - identify a market portfolio and solve for the return of a zero-beta portfolio– Leads to less consistent results


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)



• Another assumption of CAPM – zero transactions costs

• 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 investor would have a different idea about the position and composition of the efficient frontier, hence would have a different idea about the location and composition of the tangency portfolio, M

– Hence, 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

– Since each investor would have a different idea about where the SML lies, each would also have unique conclusions about which securities are under- and which are over-valued

– Also note that small differences in initial expectations can lead to vastly different conclusions in this regard!



• 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

Key questions asked:• 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?


Empirical Testing of CAPM

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

• Stability increases significantly for portfolios

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

• Betas tend to regress toward the mean


Empirical Testing of CAPM• Different estimates of beta for a stock vary typically

in data used• Value Line estimates use 260 weekly observations

and compare to the NYSE Composite Index• Merrill Lynch estimates use 60 monthly

observations and compare to the S&P 500 ML 0.127 + 0.879VL • Securities market value affects the size and direction

of the interval affect• Trading volume also affects the beta estimates


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 – need to account for effects of skewness

• Black, Jensen, and Scholes: positive linear relationship between monthly excess return and portfolio beta

• Fama and McBeth: support 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 and French Study (discussed in

Introductory notes)


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 – 2 possible effects:– Beta will be wrong– SML will be wrong


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 (or vice versa)


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– “Law of One Price”

• 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

NibbbERi ikikiii to1for 2211

assets ofnumber error) (randomreturn s'asset on effect unique a

assets all of returns theinfluencesmean that zero a with indexesor factorscommon ofset a

index or factor comon ain movements toreturns s'asset in reaction

changes zero have indexes or factors theall if asset for return expected

period timespecified a during asset on return

Ni

KKib

iEiRi

i

k

ik

i


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 7

• Importance of Efficient Capital Markets• Alternative Efficient Market Hypotheses• Efficient Markets and

– Technical Analysis– Fundamental Analysis– Portfolio Management

• “Shift Happens” - Mauboussin• “The Wrong 20-Yard Line” - Haugen

Version 1.2 Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make...

Documents

Transcript of Version 1.2 Copyright © 2000 by Harcourt, Inc. All rights reserved. Requests for permission to make...