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tioner community. Many investment professionals think about the distinction between firm-
specific and systematic risk and are comfortable with the use of beta to measure systematic



WEBMA STER
Beta Comparisons
Go to http://moneycentral.msn.com/investor/research and http:nasdaq.com. Obtain
the beta coefficients for IMB, PG, HWP AEIS, and INTC. (Betas on the Nasdaq site can
,
be found by using the info quotes and fundamental locations.)
Compare the betas reported by these two sites. Then, answer the following
questions:
1. Are there any significant differences in the reported beta coefficients?
2. What factors could lead to such differences?



4
ARCH stands for autoregressive conditional heteroskedasticity. This is a fancy way of saying that the volatility (and
covariance) of stocks changes over time in ways that can be at least partially predicted from their past levels.
Bodie’Kane’Marcus: II. Portfolio Theory 7. Capital Asset Pricing © The McGraw’Hill
Essentials of Investments, and Arbitrage Pricing Companies, 2003
Fifth Edition Theory




Beta Beaten
market ratios, the gap in returns between the portfolio
A battle between some of the top names in financial
with the lowest ratio and that with the highest was far
economics is attracting attention on Wall Street. Under
wider than when shares were grouped by size.
attack is the famous capital asset pricing model
So should analysts stop using the CAPM? Probably
(CAPM), widely used to assess risk and return. A new
not. Although Mr. Fama and Mr. French have produced
paper by two Chicago economists, Eugene Fama and
intriguing results, they lack a theory to explain them.
Kenneth French, explodes that model by showing that
Their best hope is that size and book-to-market ratios
its key analytical tool does not explain why returns on
are proxies for other fundamentals. For instance, a high
shares differ.
book-to-market ratio may indicate a firm in trouble; its
According to the CAPM, returns reflect risk. The
earnings prospects might thus be especially sensitive to
model uses a measure called beta”shorthand for rela-
economic conditions, so its shares would need to earn
tive volatility”to compare the riskiness of one share
a higher return than its beta suggested.
with that of the whole market, on the basis of past price
Advocates of CAPM”including Fischer Black, of
changes. A share with a beta of one is just as risky as
Goldman Sachs, an investment bank, and William
the market; one with a beta of 0.5 is less risky. Because
Sharpe of Stanford University, who won the Nobel Prize
investors need to earn more on riskier investments,
for economics in 1990”reckon the results of the new
share prices will reflect the requirement for higher-than-
study can be explained without discarding beta. In-
average returns on shares with higher betas.
vestors may irrationally favor big firms. Or they may
Whether beta does predict returns has long been
lack the cash to buy enough shares to spread risk com-
debated. Studies have found that market capitalization,
pletely, so that risk and return are not perfectly
price/earnings ratios, leverage and book-to-market ra-
matched in the market.
tios do just as well. Messrs Fama and French are clear:
Those looking for a theoretical alternative to CAPM
Beta is not a good guide.
will find little satisfaction, however. Voguish rivals, such
The two economists look at all nonfinancial shares
as the “arbitrage pricing theory,” are no better than
traded on the NYSE, Amex and Nasdaq between 1963
CAPM and betas at explaining actual share returns.
and 1990. The shares were grouped into portfolios.
Which leaves Wall Street with an awkward choice: Be-
When grouped solely on the basis of size (that is, mar-
lieve the Fama“French evidence, despite its theoretical
ket capitalization), the CAPM worked”but each port-
vacuum, and use size and the book-to-market ratios as
folio contained a wide range of betas. So the authors
a guide to returns; or stick with a theory that, despite
grouped shares of similar beta and size. Betas now
the data, is built on impeccable logic.
were a bad guide to returns.
Instead of beta, say Messrs Fama and French, dif-
SOURCE: “Beta Beaten,” The Economist, March 7, 1992, p. 87,
ferences in firm size and in the ratio of book value to based on Eugene Fama and Kenneth French, “The Cross-Section of
market value explain differences in returns”especially Expected Stock Returns,” University of Chicago Center for Research in
the latter. When shares were grouped by book-to- Security Prices, 1991.




risk. Still, the nuances of the CAPM are not nearly as well established in the community. For
example, the compensation of portfolio managers is not based on appropriate performance
measures (see Chapter 20). What can we make of this?
New ways of thinking about the world (that is, new models or theories) displace old ones
when the old models become either intolerably inconsistent with data or when the new model
is demonstrably more consistent with available data. For example, when Copernicus over-
threw the age-old belief that the Earth is fixed in the center of the Universe and that the stars
orbit about it in circular motions, it took many years before astronomers and navigators re-
placed old astronomical tables with superior ones based on his theory. The old tools fit the data
available from astronomical observation with sufficient precision to suffice for the needs of
the time. To some extent, the slowness with which the CAPM has permeated daily practice in
the money management industry also has to do with its precision in fitting data, that is, in pre-
cisely explaining variation in rates of return across assets. Let™s review some of the evidence
on this score.
240
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Essentials of Investments, and Arbitrage Pricing Companies, 2003
Fifth Edition Theory




241
7 Capital Asset Pricing and Arbitrage Pricing Theory


The CAPM was first published by Sharpe in the Journal of Finance (the journal of the
American Finance Association) in 1964 and took the world of finance by storm. Early tests by
Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973) were only partially sup-
portive of the CAPM: average returns were higher for higher-beta portfolios, but the reward
for beta risk was less than the predictions of the simple theory.
While all this accumulating evidence against the CAPM remained largely within the ivory
towers of academia, Roll™s (1977) paper “A Critique of Capital Asset Pricing Tests” shook the
practitioner world as well. Roll argued that since the true market portfolio can never be ob-
served, the CAPM is necessarily untestable.
The publicity given the now classic “Roll™s critique” resulted in popular articles such as “Is
Beta Dead?” that effectively slowed the permeation of portfolio theory through the world of
finance.5 This is quite ironic since, although Roll is absolutely correct on theoretical grounds,
some tests suggest that the error introduced by using a broad market index as proxy for the
true, unobserved market portfolio is perhaps the lesser of the problems involved in testing the
CAPM.
Fama and French (1992) published a study that dealt the CAPM an even harsher blow.
They claimed that once you control for a set of widely followed characteristics of the firm,
such as the size of the firm and its ratio of market value to book value, the firm™s beta (that is,
its systematic risk) does not contribute anything to the prediction of future returns. This time,
the piece was picked up by The Economist and the New York Times (see the nearby box) even
before it was published in the Journal of Finance.
Fama and French and several others have published many follow-up studies of this topic.
We will review some of this literature in the next chapter. However, it seems clear from these
studies that beta does not tell the whole story of risk. There seem to be risk factors that affect
security returns beyond beta™s one-dimensional measurement of market sensitivity. In fact, in
the next section of this chapter, we will introduce a theory of risk premiums that explicitly al-
lows for multiple risk factors.
Liquidity, a different kind of risk factor, has been ignored for a long time. Although first an-
alyzed by Amihud and Mendelson as early as 1986, it is yet to be accurately measured and in-
corporated in portfolio management. Measuring liquidity and the premium commensurate
with illiquidity is part of a larger field in financial economics, namely, market structure. We
now know that trading mechanisms on stock exchanges affect the liquidity of assets traded on
these exchanges and thus significantly affect their market value.
Despite all these issues, beta is not dead. Other research shows that when we use a more in-
clusive proxy for the market portfolio than the S&P 500 (specifically, an index that includes
human capital) and allow for the fact that beta changes over time, the performance of beta in
explaining security returns is considerably enhanced (Jagannathan and Wang, 1996). We know
that the CAPM is not a perfect model and that ultimately it will be far from the last word on
security pricing. Still, the logic of the model is compelling, and more sophisticated models of
security pricing all rely on the key distinction between systematic versus diversifiable risk.
The CAPM therefore provides a useful framework for thinking rigorously about the relation-
ship between security risk and return. This is as much as Copernicus had when he was shown
the prepublication version of his book just before he passed away.


7.5 ARBITRAGE PRICING THEORY
In the 1970s, as researchers were working on test methodologies for variants of the CAPM,
Stephen Ross (1976) stunned the world of finance with the arbitrage pricing theory (APT).
5
A. Wallace, “Is Beta Dead?” Institutional Investor 14 (July 1980), pp. 22“30.
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Essentials of Investments, and Arbitrage Pricing Companies, 2003
Fifth Edition Theory




242 Part TWO Portfolio Theory


Moving away from construction of mean-variance efficient portfolios, Ross instead calculated
relations among expected rates of return that would rule out riskless profits by any investor in
well-functioning capital markets. This generated a theory of risk and return similar to the
CAPM.

Arbitrage Opportunities and Profits
To explain the APT, we begin with the concept of arbitrage, which is the exploitation of rel-
arbitrage
ative mispricing among two or more securities to earn risk-free economic profits.
Creation of riskless
A riskless arbitrage opportunity arises when an investor can construct a zero-investment
profits made possible
portfolio that will yield a sure profit. Zero investment means investors need not use any of
by relative mispricing
among securities. their own money. To construct a zero-investment portfolio, one has to be able to sell short at
least one asset and use the proceeds to purchase (go long) one or more assets. Even a small in-
zero-investment vestor, using borrowed money in this fashion, can take a large position in such a portfolio.
portfolio An obvious case of an arbitrage opportunity arises in the violation of the law of one price:
When an asset is trading at different prices in two markets (and the price differential exceeds
A portfolio of zero net
transaction costs), a simultaneous trade in the two markets will produce a sure profit (the net
value, established by
buying and shorting price differential) without any net investment. One simply sells short the asset in the high-
component securities, priced market and buys it in the low-priced market. The net proceeds are positive, and there is
usually in the context
no risk because the long and short positions offset each other.
of an arbitrage
In modern markets with electronic communications and instantaneous execution, such op-
strategy.
portunities have become rare but not extinct. The same technology that enables the market to
absorb new information quickly also enables fast operators to make large profits by trading
huge volumes at the instant an arbitrage opportunity opens. This is the essence of program
trading and index arbitrage, to be discussed in Part Five.
From the simple case of a violation of the law of one price, let us proceed to a less obvious
(yet just as profitable) arbitrage opportunity. Imagine that four stocks are traded in an econ-
omy with only four possible scenarios. The rates of return on the four stocks for each infla-
tion-interest rate scenario appear in Table 7.10. The current prices of the stocks and rate of
return statistics are shown in Table 7.11.
The rate of return data give no immediate clue to any arbitrage opportunity lurking in this
set of investments. The expected returns, standard deviations, and correlations do not reveal
any abnormality to the naked eye.
Consider, however, an equally weighted portfolio of the first three stocks (Apex, Bull, and
Crush), and contrast its possible future rates of return with those of the fourth stock, Dreck.
We do this in Table 7.12.
Table 7.12 reveals that in all four scenarios, the equally weighted portfolio will outperform
Dreck. The rate of return statistics of the two alternatives are


Mean Standard Deviation Correlation
Three-stock portfolio 25.83 6.40
0.94
Dreck 22.25 8.58

The two investments are not perfectly correlated and are not perfect substitutes. Neverthe-
less, the equally weighted portfolio will fare better under any circumstances. Any investor, no
matter how risk averse, can take advantage of this dominance by taking a short position in
Dreck and using the proceeds to purchase the equally weighted portfolio. Let us see how it
would work.
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Essentials of Investments, and Arbitrage Pricing Companies, 2003
Fifth Edition Theory




243
7 Capital Asset Pricing and Arbitrage Pricing Theory


High Real Interest Rates Low Real Interest Rates
TA B L E 7.10
High Inflation Low Inflation High Inflation Low Inflation
Rate of return
projections
Probability: 0.25 0.25 0.25 0.25
Stock
Apex (A) 20 20 40 60
Bull (B) 0 70 30 20
Crush (C ) 90 20 10 70
Dreck (D) 15 23 15 36




Correlation Matrix
TA B L E 7.11 Current Expected Standard

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