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Intern. J. of Research in Marketing 26 (2009) 164–165
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Intern. J. of Research in Marketing
j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / i j r e s m a r
Measuring alpha: The consequences of ignoring the four-factor model
In response to the commentary: "The statistical significance of portfolio returns" by
Claes Fornell, Sunil Mithas and Forrest Morgeson
Don O'Sullivan a ,⁎, Mark C. Hutchinson b ,c, Vincent O'Connell d
a
Melbourne Business School, University of Melbourne, Australia
Department of Accounting, Finance and Information Systems, University College Cork, College Road, Cork, Ireland
c
Centre for Investment Research, University College Cork, College Road, Cork, Ireland
d
Korea University Business School, Korea University, Anam Dong, Seongbuk-Gu, Seoul 136-701, Republic of Korea
b
To begin, we complement Fornell, Mithas, Morgeson, and Krishnan
(2006) for raising important issues with respect to the relationship
between customer satisfaction and stock prices. Fornell et al. (2006)
present evidence of a new anomaly in efficient market theory, specifically the theory that portfolios formed from firms with high levels of
customer satisfaction generate consistently abnormal returns — high
returns at low risk. While we disagree with the conclusion that their
ACSI-based trading strategies lead to abnormal stock returns, we
strongly believe that customer satisfaction is an important determinant
of firm value — one that firm executives ignore at their peril.
Our paper demonstrates that the ACSI-based trading strategy
proposed by Fornell et al. (2006) does not offer abnormal returns when
taking into account the following four factors: market risk, book-tomarket ratio, firm size, and momentum. Starting with the pioneering
work of Sharpe (1964) and Lintner (1965), and continuing with Fama
and French (1993) and Carhart (1997), contemporary finance theory
has evolved to the point where the four-factor model is the conventionally accepted benchmark for judging whether returns are
abnormal. Our analysis demonstrates that the abnormal returns
documented in Fornell et al. (2006) evaporate when the aforementioned four factors are properly accounted for.
We now turn our attention to some of the specific comments
offered by Fornell, Mithas, and Morgeson (2009-this issue). Fornell
et al. (2009-this issue) note that our findings point to “a cumulative
return of 164% vs. 98% for the market (S&P 500), corresponding to
above-market annualized returns of +3.8%. To put this in perspective,
less than 10% of actively managed portfolios generate even a positive
alpha, let alone returns as high as 3% per year (Barras, Scaillet, &
Wermers, 2008).” As Barras et al. (2008) do not report the abovemarket annualized returns of their sample, it is not possible to directly
compare the above-market annualized returns of + 3.0% with their
results. However, as in our study, Barras et al. (2008) provide estimates
of alpha (also using a four-factor model specification) to measure
performance. They find that over 75% of funds deliver zero alpha, just
as we find that a portfolio formed following Fornell et al. (2006)
⁎ Corresponding author. Tel.: +61 3 9349 8223.
E-mail address: d.o'[email protected] (D. O'Sullivan).
generates zero alpha; this demonstrates the difficulties faced even by
professional stock pickers when generating statistically significant
performance. Barras et al. (2008) further demonstrate that even in
cases where positive alpha is discovered for a fund, it is often due to
chance and should be treated with caution.
Fornell et al. (2009-this issue) raise interesting questions about the
adequacy of the four-factor model used in our analysis, noting that
“Under the market efficiency hypothesis, the predictor variables in
these models are interpreted as risk factors and a positive and
significant intercept (alpha) as indicative of abnormal returns. Under
the same hypothesis, the predictor variables must completely account
for the returns. For example, Fama and French (1996) report R2s close
to 1.0.” In Fama and French (1996) the authors report R2, whereas our
study reports adjusted R2, which accounts for the incremental
explanatory power of individual variables. These adjusted R2 values
(ranging from 0.62 to 0.88) are in line with recent studies in both
marketing (e.g., Aksoy, Cooil, Groening, Keiningham, & Yalcin, 2008)
and finance (e.g., Sadka, 2006).
Fornell et al. (2009-this issue) make the observation that “Rather
than subjecting the returns to an analysis model that assumes market
efficiency, it may make more sense to simply ask what the probability
would be that returns of 164% vs. 98% ( a difference of 66%) over a 10year period is due to chance.” In addressing this question, we note that
the ACSI survey focuses primarily on large firms. Firm size is a well
known driver of stock returns. Thus, a more appropriate question in
the present context is — What is the probability that the returns from a
trading strategy based on ACSI outperform those of a trading strategy
based on a random selection of stocks of equivalent firm size?
Obviously, this question can be easily extended to other factors (i.e.,
momentum and book-to-market).
We agree with Fornell et al. (2009-this issue) that “Back testing can
only get us so far. It always has an element of capitalizing on chance.
Real data and real portfolios would be better.” Real world applications
are the acid test of the Fornell et al. (2006) findings. In that spirit, let us
temporarily set aside the debate with respect to the four-factor model
that is discussed earlier. Apart from any theoretical considerations, our
paper highlights two issues that are important in the real world of
investment: transaction costs and the Sharpe ratio. Real world rebalancing requires significant transaction costs, and any serious claim of
0167-8116/$ – see front matter. Crown Copyright © 2009 Published by Elsevier B.V. All rights reserved.
doi:10.1016/j.ijresmar.2009.03.003
D. O'Sullivan et al. / Intern. J. of Research in Marketing 26 (2009) 164–165
inefficiency must take these costs into account. For example, Bernard
and Thomas (1990) show that the well-known post-earningsannouncement drift anomaly is robust to transaction and other trading
costs. Is this the case with the proposed ACSI-based anomaly? Equally,
consider the Sharpe ratio, a widely used ‘rule of thumb’ measurement
that relates excess return to portfolio standard deviation. The Sharpe
ratio of Portfolio 1 in our Table 2 is 0.27, which is barely higher than the
0.24 for Portfolio 3 in the same table. The mean annual Sharpe ratio in
the U.S. between 1970 and 2000 was 0.44 (as reported in Shackman,
2006). Based on this perspective and the results of the four-factor
model, we believe that significantly more proof is needed before the
proposed ACSI-based anomaly can be accepted.
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