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What are the reasons that fundamental index outperforms value-weighted index?
March/April 2005 www.cfapubs.org 83
Financial Analysts Journal
Volume 61 • Number 2
©2005, CFA Institute
Fundamental Indexation
Robert D. Arnott, Jason Hsu, and Philip Moore
A trillion-dollar industry is based on investing in or benchmarking to capitalization-weighted
indexes, even though the finance literature rejects the mean–variance efficiency of such indexes. This
study investigates whether stock market indexes based on an array of cap-indifferent measures of
company size are more mean–variance efficient than those based on market cap. These “Fundamental”
indexes were found to deliver consistent, significant benefits relative to standard cap-weighted
indexes. The true importance of the difference may have been best noted by Benjamin Graham: In the
short run, the market is a voting machine, but in the long run, it is a weighing machine.
he capital asset pricing model (CAPM)
says that the “market portfolio” is mean–
variance optimal. Although the model is
predicated on an array of assumptions,
most of which are arguably not accurate, it leads
to the conclusion that a passive investor/manager
can do no better than holding a market portfolio.
The finance industry, with considerable inspira-
tion and perspiration from Markowitz (1952,
1959), Sharpe (1965), and many others, has trans-
lated that investment advice into trillions of dollars
invested in or benchmarked to capitalization-
weighted market indexes such as the S&P 500
Index or the Russell 1000 Index.
Many academic papers, however, have
rejected the idea that cap-weighted indexes are
good CAPM market proxies, which is equivalent to
rejecting the mean–variance efficiency of those
indexes.1 It also suggests that more efficient
indexes exist. The effort to identify a better index
may be moot, however, if ex ante identification is
impossible or if cap-weighted equity market
indexes are almost optimal.2
The ex ante construction of a mean–variance-
efficient portfolio is a difficult problem; forecasting
expected stock returns and their covariance matrix
for thousands of stocks, which is necessary for
applying Markowitz’s mean–variance portfolio
construction, is intellectually challenging and
resource intensive. This is precisely why CAPM
remains so powerful: If one can find the “market”
portfolio, one simultaneously identifies a mean–
variance-optimal portfolio.
The investment industry and countless MBA
programs have promoted the belief that cap-
weighted equity market indexes are sufficiently rep-
resentative of the CAPM market portfolio to be
nearly mean–variance efficient. If we accept this
simplifying assumption, we reduce the complicated
problem of optimal portfolio construction to essen-
tially buying and holding a cap-weighted index. We
demonstrate in this article that investors can do
much better than cap-weighted market indexes: We
provide “Fundamental” equity market indexes that
deliver superior mean–variance performance.3
We constructed indexes that use gross reve-
nue, equity book value, gross sales, gross divi-
dends, cash flow, and total employment as weights.
If capitalization is a “Wall Street” definition of the
size of an enterprise, these characteristics are
clearly “Main Street” measures. When a merger is
announced, the Wall Street Journal may cite the
combined capitalization but the New York Post will
focus on the combined sales or total employment.
We show that the fundamentals-weighted, non-
capitalization-based indexes consistently provide
higher returns and lower risks than the traditional
cap-weighted equity market indexes while retain-
ing many of the benefits of traditional indexing.
Merits of Cap-Weighted and
Other
Indexes
Pension funds and endowments use investment
portfolios indexed to the S&P 500 or Russell 1000
Robert D. Arnott is chairman of Research Affiliates, LLC.
Jason Hsu is director of research at Research Affiliates,
LLC. Philip Moore is vice president of sales and market-
ing at Research Affiliates, LLC.
Note: A patent is currently pending for the construction
and management of indexes based on objective noncap-
italization measures of company size.
T
As editor of the Financial Analysts Journal, Mr. Arnott recused himself from any involvement in the refereeing or acceptance process for this article.
Copyright 2005, CFA Institute. Reproduced and republished from Financial Analysts Journal with permission from CFA Institute. All
rights reserved.
Financial Analysts Journal
84 www.cfapubs.org ©2005, CFA Institute
for many reasons other than the presumed mean–
variance efficiency of these indexes. Whatever its
shortcomings, capitalization weighting as the
basis for these portfolios has many benefits that
any alternative should largely preserve:
• Capitalization weighting is a passive strategy
requiring little trading; therefore, indexing to a
cap-weighted index incurs far lower trading
costs and fees than active management. Cap-
weighted portfolios automatically rebalance as
security prices fluctuate. Apart from the impact
of stock buybacks and secondary equity offer-
ings, the only rebalancing cost associated with
executing this strategy is the cost of replacing
a constituent security in the portfolio. The cap-
weighted indexes require material adjustment
only when new companies become large
enough to merit inclusion in an index or when
others disappear through merger, failure, or
relative changes in capitalization, collectively
referred to as “reconstitution.” Such changes
are not insignificant. A study of changes in the
composition of the S&P 500 (Blume and Edelen
2003) found that nearly half, 235 companies,
had been replaced between 1995 and 2000.
• A cap-weighted index provides a convenient
way to participate in the broad equity market.
Capitalization weighting seeks to assign the
greatest weights to the largest companies. These
companies are typically among the largest as
also measured by metrics of size other than
capitalization—including sales, book value,
cash flow, dividends, and total employment.
• Market capitalization is highly correlated with
trading liquidity, so cap weighting tends to
emphasize the more heavily traded stocks,
thereby reducing portfolio transaction costs.
• Because market capitalization is also highly
correlated with investment capacity, cap
weighting tends to emphasize the stocks with
greater investment capacities, thus allowing
the use of passive indexing on an immense
scale by large pension funds and institutions.4
In constructing our Fundamental indexes, we
sought to retain the many benefits of cap weighting
for the passive investor. Most alternative measures
of company size—such as book value, cash flow,
sales, revenues, dividends, or employment—are
highly correlated with capitalization and liquidity,
which means that the Fundamental indexes are also
primarily concentrated in the large-cap stocks and
preserve the liquidity and capacity benefits of tra-
ditional cap-weighted indexes. In addition, these
Fundamental indexes typically have volatilities
that are substantially identical to those of conven-
tional cap-weighted indexes, and their CAPM betas
and correlations average, respectively, 0.95 and
0.96. Therefore, market characteristics that inves-
tors have traditionally gained exposure to by hold-
ing cap-weighted market indexes are equally
accessible with Fundamental indexes.
Maintaining low turnover is the most challeng-
ing aspect in the construction of Fundamental
indexes. In addition to the usual reconstitution, a
certain amount of rebalancing is needed for Funda-
mental indexes. If a stock price goes up 10 percent,
its capitalization also goes up 10 percent and the
weight of that stock in the Fundamental index will
at some interval need to be rebalanced to its Funda-
mental weight in that index. If the rebalancing peri-
ods are too long, the difference between the policy
weights and actual portfolio weights becomes so
large that some of the suspected negative attributes
associated with cap weighting may be reintro-
duced. We based the Fundamental index strategies
described here on annual rebalancing as of 1 Janu-
ary. The resulting turnover only modestly exceeded
the turnover for cap-weighted indexes. Because the
Fundamental indexes are concentrated in large, liq-
uid companies, the relatively low rebalancing turn-
over translates into rebalancing costs that are nearly
as low as those for a cap-weighted strategy.5
The genesis of our non-cap-weighted market
indexes was our concern that market capitalization
is a particularly volatile way to measure a com-
pany’s size or its true fair value. If so, cap weighting
may lead to suboptimal portfolio return character-
istics because prices are too noisy relative to funda-
mentals. Mathematically, cap weighting assuredly
gives additional weight to stocks that are currently
overpriced relative to their (unknowable) dis-
counted future cash flows (the true fair value) and
reduces weights in stocks that are currently trading
below that true fair value (see Hsu 2004 and Treynor
2005) for different derivations of this result). This
mismatch leads to a natural performance drag in
cap-weighted and other price-weighted portfolios.
Equal weighting, which is obviously not price
weighting, is a much studied alternative to cap
weighting. Its disadvantage is that it does not pre-
serve the benefits of cap weighting. It lacks the
liquidity and capacity found in traditional market
indexes, and its return characteristics are not rep-
resentative of the aggregate equity market. Further-
more, equal weighting has logical inconsistencies:
For instance, an equal-weighted portfolio contain-
ing the Russell 1000 stocks gives as much weight to
the 1000th largest company as to the largest com-
pany but gives no weight whatsoever to the 1001st
largest company.
Fundamental Indexation
March/April 2005 www.cfapubs.org 85
Fundamental Indexes:
Construction
Adopting Fundamental Indexation is more than
simply changing the basis for weighting the stocks
in an index. For instance, if we simply reweight the
stocks in the S&P 500 or the Russell 1000 by book
value, we miss a large number of companies with
substantial book value that are trading at a low
price-to-book ratio. We end up with a portfolio
concentrated most heavily in stocks that are large
in both capitalization and book value.
To avoid this problem, we ranked all compa-
nies by each metric, then selected the 1,000 largest
by each metric. Each of these 1,000 largest was
included in the index at its relative metric weight to
create the Fundamental index for that metric. The
measures of company size we used are as follows:
• book value (Book),
• trailing five-year average cash flow (Cash Flow),
• trailing five-year average revenue (Revenue),
• trailing five-year average gross sales (Sales),
• trailing five-year average gross dividends
(Dividends), and
• total employment (Employment).6
We also examined a composite that equally
weighted four of the fundamental metrics of size.
This composite Fundamental index (Composite
index) excluded employment because that infor-
mation is not always available, and it excluded
revenues because sales and revenues are very sim-
ilar concepts and performers. The four metrics used
in the Composite index are widely available in most
countries, so the Composite index can be easily
applied globally—even in emerging markets.
The sample period was selected to cover as
long a history as possible with data from the Comp-
ustat database. Although Compustat has data
extending back to the 1950s, the number of compa-
nies prior to 1962 that had sufficient five-year data
for our purposes is far less than 1,000.
Financial statement data are from the Comp-
ustat database. Stock price information is from the
CRSP database and was linked to the corresponding
Compustat entries by using the CRSP/Compustat
merged list. The roster of selected stocks and the
portfolio weights for 1 January of any year were
generated by using only data available on the last
trading day of the prior year. In most cases, this
process meant using data that were lagged by at
least one quarter. Each index was rebalanced on the
last trading day of each year on the basis of end-of-
day prices. We held this portfolio until the end of
the next year, at which point we used the most
recent company financial information to calculate
the following year’s index weights.
We rebalanced an index only once a year, on
the last trading day of the year, for two reasons.
First, the financial data available through Comp-
ustat are available only on an annual basis for the
earliest years of our study. Second, when we tried
monthly, quarterly, and semiannual rebalancing,
we increased index turnover but found no appre-
ciable return advantage over annual rebalancing.
Note that we did not adjust for trading costs in
the index construction, which is consistent with the
practice of providers of commercial cap-weighted
indexes and with most academic research. The
actual trading cost would be difficult to know with
any precision, but we did examine the impact of a
1 percent (each way) trading cost. Reciprocally, we
measured how large the trading cost would have
to be to completely eliminate the alpha generated
by each Fundamental index relative to cap-
weighted indexes.
We offer results for six Fundamental indexes
based on individual measures and for the Compos-
ite index. In constructing the Composite, to get the
composite weights, we combined, in equal propor-
tions, the weights each company would have in the
four Fundamental indexes (Book, Cash Flow, Sales,
and Dividends). We then selected the top 1,000
companies by composite weight and weighted
each by this composite weight.
The treatment of dividends as a metric requires
some explanation. The dividend metric excluded
all companies that did not distribute dividends.7
We recognized that nonpayment of dividends may
not be a sign of weak/small cash flows, however,
because many non-dividend-paying companies
choose not to pay out dividends for tax reasons.8
Therefore, in the Composite index, we treated non-
dividend-paying companies differently from the
way we treated low-dividend-paying companies.
When a company was not paying dividends, we
used the average of the remaining three size metrics
instead of the full four size metrics.
For the Fundamental indexes, only book value
and employment were single-year metrics; we
used trailing five-year averages wherever substan-
tial volatility in the index weights would result
from using year-to-year data. The five-year averag-
ing reduced rebalancing turnover. When fewer
than five years of data were available, we averaged
the years of data that were available. When we
tested the mean return, volatility, and equity mar-
ket beta for similar indexes constructed with single-
year cash flow or revenue, we found that the results
were not materially different from the results for
using trailing five-year data but portfolio turnover
was substantially higher.9
Financial Analysts Journal
86 www.cfapubs.org ©2005, CFA Institute
Because none of our measures of size rely on
price, none captured the current market valuations
of perceived growth opportunities of the companies.
So, young companies and fast-growing companies
were underrepresented in the Fundamental indexes
relative to their weights in cap-weighted indexes.
Ex ante, it might seem that these indexes, which
deemphasize growth characteristics, would pro-
duce lower absolute returns and lower risk than
cap-weighted indexes because growth companies
usually have the higher market beta risk and corre-
spondingly (in theory) higher expected returns. We
show later that lower absolute returns did not result.
For benchmarking purposes, we also con-
structed a 1,000-stock cap-weighted index by using
the same construction method used for the Funda-
mental indexes. Although it bears a close resem-
blance to the Russell 1000, it is not identical. The
construction of this “Reference” cap-weighed port-
folio allowed us to make direct comparisons
between it and the Fundamental indexes that were
uncomplicated by questions of float, market
impact, subjective selections, and so forth.
10
Relative Performance of
Fundamental Indexation
Table 1 shows the return attributes of the Funda-
mental indexes, the Reference cap-weighted port-
folio, and the S&P 500 for the 43 years from 1962
through 2004. We later show results decade-by-
decade and for different economic and market
environments within the 43 years. The historical
portfolio results were not adjusted for any transac-
tion costs associated with maintaining the strat-
egy; we examine the issue of turnover and trading
costs separately.
The Fundamental indexes exhibit volatility and
beta similar to those of the cap-weighted
Reference
portfolio and the S&P 500, except for the dividend-
weighted index, which, as might be expected, had
significantly lower return volatility and CAPM
beta. The dividend-weighted index is dominated by
mature companies with less risk and lower per-
ceived growth prospects than the whole group of
companies. Even so, perhaps surprisingly, it out-
paced the higher-risk conventional cap-weighted
indexes in returns.
The returns produced by the Fundamental
indexes are, on average, 1.97 percentage points
higher than the S&P 500 and 2.15 pps higher than
the Reference portfolio. The highest performing of
the Fundamental indexes (Sales) outpaced the Ref-
erence portfolio by 2.56 pps a year. The Composite
index rivaled the performance of the average Fun-
damental index, even though it excluded two of the
best single-metric Fundamental indexes. Although
we did not include this comparison in the tables,
most of these indexes also outpaced both the equal-
weighted S&P 500 and the equal-weighted CRSP
universe, with lower risk. The excess returns were
significant and had an average t-statistic of about
3.09; the Composite index came in even higher with
a t-statistic of 3.26.
As shown in Table 2, once we adjusted for the
slightly lower beta of the Fundamental indexes, the
average CAPM alpha rose to 2.37 percent with a
t-statistic of 3.41; the Composite index again,
despite excluding two of the best single-metric
indexes, delivered an even more impressive alpha
of 2.44 percent with a t-statistic of 3.87. The infor-
mation ratio is above 0.50 for the best indexes.11 The
Composite index information ratio is 0.60 on a beta-
adjusted basis.12
Over the investment period of 43 years, the
return advantages compounded to ending values
that are typically well above twice that of the end-
ing value for the Reference portfolio. Only the Book
index and Dividends index failed to double the
cumulative return of the cap-weighted indexes.
Table 1. Return Characteristics of Alternative Indexing Metrics, 1962–2004
Portfolio/
Index
Ending
Value of $1
Geometric
Return Volatility
Sharpe
Ratio
Excess
Return
vs. Reference
Tracking Error
vs. Reference
Information
Ratio
t-Statistic for
Excess Return
S&P 500 $ 73.98 10.53% 15.1% 0.315 0.18 pps 1.52% 0.12 0.76
Reference 68.95 10.35 15.2 0.301 — — — —
Book 136.22 12.11 14.9 0.426 1.76 3.54 0.50 3.22
Income 165.21 12.61 14.9 0.459 2.26 3.94 0.57 3.72
Revenue 182.05 12.87 15.9 0.448 2.52 5.03 0.50 3.25
Sales 184.95 12.91 15.8 0.452 2.56 4.93 0.52 3.36
Dividends 131.37 12.01 13.6 0.458 1.66 5.33 0.31 2.02
Employment 156.83 12.48 15.9 0.423 2.13 4.64 0.46 2.98
Composite 156.54 12.47 14.7 0.455 2.12 4.21 0.50 3.26
Average (ex Composite) $159.44 12.50% 15.2% 0.444 2.15 pps 4.57% 0.47 3.09
Fundamental Indexation
March/April 2005 www.cfapubs.org 87
Portfolio Liquidity
In Table 3, we present liquidity/capacity character-
istics of the Fundamental indexes. In conjunction
with the information on annual portfolio turnover,
this information allowed us to assess the impact of
transaction costs on the excess returns of the Fun-
damental indexes.
There are several useful ways to gauge liquid-
ity. We measured the relative capacity of each Fun-
damental index by dividing the fundamentals-
weighted average capitalization of that index by
the cap-weighted average capitalization of the Ref-
erence portfolio. This “CAP ratio” measure helped
us assess the investment capacity of each index. A
CAP ratio of 0.66 for the Composite index suggests
that the weighted-average capitalization of the
companies in the Composite index is two-thirds as
large as that of the Reference portfolio. A possible
inference is that the aggregate amount of money
that can be benchmarked to or invested in the Com-
posite index is approximately two-thirds the
amount that could be benchmarked to or invested
in the Reference portfolio.
In addition, we examined the average dollar
trading volume of the Fundamental indexes and
the average number of trading days required to
trade a billion-dollar portfolio. For these two mea-
sures, we used only the data from 1993 through
2003 in order to report numbers that are relevant to
the current environment. These two metrics sug-
gest that, apart from the Employment index, the
Fundamental indexes have liquidity that is more
than half that of the Reference portfolio. Given that
more than $1 trillion is passively managed in some
variant of cap-weighted index portfolios, this find-
ing does not seem to be a serious constraint.13
We also measured the concentration of the port-
folio in the large-cap stocks by examining the frac-
tion of the total index capitalization that belonged
to the top 100 stocks by metric weight in each index.
Table 3 shows these concentration ratios to be simi-
lar for all the indexes, including the Reference port-
folio. Most are between 51 percent and 57 percent,
nearly identical to the 55 percent concentration ratio
for the cap-weighted Reference portfolio.
Table 2. CAPM Characteristics of Alternative Indexing Metrics, 1962–2004
Portfolio/Index
Ending
Value of $1
Geometric
Return
Correlation
with
Reference
CAPM
Beta vs.
Reference
Excess
Return vs.
Reference
CAPM
Alpha vs.
Reference
Information
Ratio of Alpha
t-Statistic for
CAPM Alpha
S&P 500 $ 73.98 10.53% 100% 0.99 0.18 pps 0.23% 0.16 1.00
Reference 68.95 10.35 — — — — — —
Book 136.22 12.11 97 0.95 1.76 1.98 0.57 3.71
Income 165.21 12.61 97 0.95 2.26 2.51 0.65 4.21
Revenue 182.05 12.87 95 0.99 2.52 2.57 0.51 3.32
Sales 184.95 12.91 95 0.99 2.56 2.63 0.53 3.46
Dividends 131.37 12.01 94 0.84 1.66 2.39 0.49 3.17
Employment 156.83 12.48 96 1.00 2.13 2.15 0.46 3.00
Composite 156.54 12.47 96 0.93 2.12 2.44 0.60 3.87
Average (ex Composite) $159.44 12.50% 96% 0.95 2.15 pps 2.37% 0.53 3.41
Table 3. Liquidity Characteristics of Alternative Indexing Metrics, 1962–2004
Portfolio/Index
Ending
Value of $1
CAP
Ratio
Concentration
Ratio
Weighted
$ Trading
Volumea
(millions)
Weighted
Trading Daysa Turnover
Excess
Return at 1%
Trade Cost
Trade Cost
for No
Excess Return
Reference $ 68.95 1.00 55.06% $191 0.9 6.30% — —
Book 136.22 0.64 51.46 134 1.5 13.20 1.62% 12.73%
Income 165.21 0.65 57.06 126 1.3 12.14 2.14 19.34
Revenue 182.05 0.55 54.66 105 2.0 14.15 2.36 16.05
Sales 184.95 0.54 52.48 99 1.7 13.41 2.42 17.99
Dividends 131.37 0.71 61.99 110 1.6 11.10 1.56 17.27
Employment 156.83 0.38 42.76 70 9.3 14.56 1.96 12.89
Composite 156.54 0.66 51.76 102 1.5 10.55 2.03 24.93
Average (ex Composite) $159.44 0.58 53.40% $107 2.9 13.09% 2.01% 16.04%
aInformation for 1962–2003.
Financial Analysts Journal
88 www.cfapubs.org ©2005, CFA Institute
Table 3 also shows average annual index turn-
over. Recall that the indexes were reconstituted and
rebalanced once a year at the end of the year.
Observe that the Reference portfolio has lower
turnover than the others. This result is expected
because virtually the entire turnover in this portfo-
lio arises from reconstitution. The Fundamental
indexes, in contrast, must adjust the index holdings
also to (1) reflect the deviation in the index weights
from the beginning-of-year policy weights and (2)
reflect changes in prices. These changes increase
turnover from the 6.3 percent for the Reference
portfolio to an average of 13.1 percent for the Fun-
damental indexes. The Composite index produced
a surprisingly modest average of 10.6 percent.
The pertinent issue in measuring turnover is
the erosion of any excess return relative to the cap-
weighted index because of transaction costs.
When we assumed a 2 percent round-trip transac-
tion cost (including transaction fees and price
impact), the excess return fell from an average of
2.15 percent to 2.01 percent. To completely erode
the excess return would require a one-way trans-
action cost greater than 16 percent for each trade,
and a 24.9 percent transaction cost each way
would be needed to eliminate the alpha of the
lower-turnover Composite index.
Outliers and Market Environment
We report here a series of tests of the robustness of
our findings. From a mean–variance perspective,
the Fundamental indexes appear to be superior to
cap-weighted market indexes. In the results of
skewness and kurtosis tests reported in Table 4, we
show that, on average, skewness was similar to
that of the cap-weighted indexes and kurtosis was
slightly higher, which suggests modestly more
outliers in the historical returns of the Fundamen-
tal indexes. The Fundamental indexes were
slightly more exposed to extreme one-month and
three-month events than a cap-weighted market
index would have been.
The pattern for various indexes in Table 4 is
interesting. For the Dividends index compared
with the cap-weighted index, the return for the
worst month (“Minimum Monthly Return”) was
sharply higher but the return for the best month
(“Maximum Monthly Return”) was not degraded.
For the Employment, Revenue, and Sales indexes,
however, the range between best and worst months
is wider than for other indexes. The observed
extreme events across all of the indexes do not
appear to be large enough to account for the high
excess return for the Fundamental indexes. Indeed,
the extremes are dampened in the Composite index,
so it outperformed the Reference portfolio and the
S&P 500 for their best and worst month and quarter.
Furthermore, the broad dispersion between
best and worst did not carry through to spans
longer than a quarter. The 12-month results, with
one exception, favored all the Fundamental
indexes over the Reference portfolio: Best outcome
was better and worst outcome was better. The
exception is the low-beta Dividends index, which
lagged the best 12-month span for the cap-
weighted indexes.
How Robust Are the Findings?
If the goal of earning higher returns with lower
risk is the raison d’être for the finance community,
the evidence for indexing to these Fundamental
indexes is convincing. Figure 1 vividly demon-
strates the superior performance of the Funda-
mental indexes. Panel A shows the cumulative
growth of a $1 investment in the Reference portfo-
lio, the Composite index, the top-performing
(Sales) index, and the bottom-performing (Divi-
dends) index.14 Panel B shows the cumulative
Table 4. Outlier Risks of Alternative Indexing Metrics, 1962–2004
Portfolio/Index Skewness
Excess
Kurtosis
Maximum
Monthly
Return
Minimum
Monthly
Return
Maximum
3-Month
Return
Minimum
3-Month
Return
Maximum Trail-
ing 12-Month
Return
Minimum Trail-
ing 12-Month
Return
S&P 500 –0.32 1.79 17.0% –21.7% 21.7% –29.7% 61.6% –39.0%
Reference –0.36 1.69 17.5 –21.3 27.0 –28.8 62.4 –4
1.0
Book –0.30 1.94 17.9 –21.3 27.2 –28.3 62.8 –32.9
Income –0.30 2.01 18.4 –21.0 28.0 –28.7 64.6 –34.3
Revenue –0.33 2.36 21.3 –23.3 33.1 –30.7 72.9 –33.9
Sales –0.33 2.38 21.2 –23.3 33.1 –30.7 72.8 –33.9
Dividends –0.23 2.00 17.8 –19.1 25.8 –26.3 58.8 –32.7
Employment –0.36 2.45 21.3 –23.5 32.2 –29.4 69.7 –36.8
Composite –0.29 2.11 18.9 –21.2 27.8 –28.5 64.4 –33.4
Average (ex Composite) –0.31 2.19 19.7% –21.9% 29.9% –29.0% 66.9% –34.1%
Fundamental Indexation
March/April 2005 www.cfapubs.org 89
wealth relative to the Reference portfolio of the
S&P 500 as well as the Composite index, the top-
performing index according to this measure
(Sales), and the bottom-performing (Dividends)
index.
Note in Panel B that the S&P 500 closely tracked
the Reference portfolio in this period except during
the technology/media/telecommunications (TMT)
bubble toward the end of the sample period. The
Fundamental indexes did not keep pace with the
cap-weighted indexes in times of large-cap high-
multiple bull markets (the Nifty Fifty age of 1972,
the TMT bubble of 1998–1999, and to a lesser extent,
the TMT-dominated rallies of 1980 and 1989–1991).
Such markets are characterized by narrow high-
multiple leadership, which leaves the “average
stock” far behind. The Fundamental indexes did
keep pace with the cap-weighted indexes in average
bull markets.
Table 5 presents the performance of the cap-
weighted and Fundamental indexes in various
decades. The Fundamental indexes beat the
Figure 1. Wealth Accumulation: Various Indexation Metrics, 1962–2004
Note: Dates as of December each year.
Growth of $1 ($)
A. Growth of $1.00
200
100
80
60
40
180
160
140
1
20
20
0
12/61 12/73 12/85 12/97 6/0412/9112/67 12/79
Relative Growth of $1 ($)
B. Cumulative Performance of Indexes Relative to Reference Portfolio
3.0
2.6
2.2
1.8
1.4
1.0
0.6
12/61 12/73 12/85 12/97 6/0412/9112/67 12/79
Reference S&P 500 Dividends
Composite Sales
Financial Analysts Journal
90 www.cfapubs.org ©2005, CFA Institute
cap-weighted indexes, often by a wide margin, in
four of the five spans. The only shortfall was in the
1990s, and even during the 1990s, the Composite
index was ahead of the Reference portfolio until
the end of May 1999, just 10 months before the
bubble burst. This decade was dominated by
“mega-cap” companies, fueled in part by a massive
flow of investment assets into cap-weighted index
funds—in short, a decade in which anything other
than the largest companies lagged. Comparing any
of the Fundamental indexes with the S&P 500 in
that decade is an apples-to-oranges comparison.
Table 5. Return Characteristics of Alternative Indexing Metrics by Decade,
1962–2004
Portfolio/Index 1/62–12/69 1/70–12/79 1/80–12/89 1/90–12/99 1/00–12/04
A. Geometric return
S&P 500 6.58% 5.86% 17.71% 18.57% –2.15%
Reference 6.80 5.90 17.00 17.94 –1.73
Book 6.94 8.72 18.29 17.09 5.84
Income 7.04 8.64 19.04 17.65 7.60
Revenue 8.26 8.67 19.32 16.99 8.38
Sales 8.26 8.70 19.47 16.84 8.66
Dividends 6.37 8.48 19.15 15.42 7.98
Employment 9.94 8.69 17.74 15.65 7.82
Composite 7.13 8.63 19.04 16.95 7.59
Average (ex Composite) 7.80% 8.65% 18.83% 16.61% 7.71%
B. Value added relative to Reference portfolio
S&P 500 –0.22 pps –0.05 pps 0.71 pps 0.63 pps –0.43 pps
Reference — — — — —
Book 0.13 2.81 1.29 –0.85 7.57
Income 0.23 2.73 2.04 –0.29 9.33
Revenue 1.46 2.77 2.32 –0.95 10.10
Sales 1.46 2.79 2.47 –1.10 10.39
Dividends –0.44 2.57 2.15 –2.52 9.71
Employment 3.14 2.78 0.74 –2.29 9.55
Composite 0.33 2.73 2.04 –1.00 9.32
Average (ex Composite) 1.00 pps 2.74 pps 1.84 pps –1.33 pps 9.44 pps
C. Annualized standard deviation of returns
S&P 500 12.38% 16.11% 16.56% 13.55% 17.98%
Reference 12.61 16.62 16.40 13.46 18.07
Book 12.40 16.58 15.61 13.22 18.18
Income 12.27 16.55 15.81 13.52 17.63
Revenue 13.38 18.23 16.59 13.96 18.22
Sales 13.38 18.21 16.60 13.64 18.15
Dividends 11.80 15.47 14.45 11.95 15.27
Employment 12.88 18.63 16.50 13.75 18.56
Composite 12.43 16.63 15.56 12.99 17.22
Average (ex Composite) 12.69% 17.28% 15.93% 13.34% 17.67%
D. Sharpe ratio
S&P 500 0.19 –0.03 0.53 1.01 0.27
Reference 0.20 –0.03 0.49 0.97 –0.24
Book 0.22 0.14 0.60 0.93 0.17
Income 0.23 0.14 0.64 0.95 0.28
Revenue 0.30 0.13 0.63 0.87 0.31
Sales 0.30 0.13 0.64 0.88 0.33
Dividends 0.18 0.14 0.71 0.89 0.35
Employment 0.44 0.12 0.53 0.79 0.28
Composite 0.23 0.14 0.65 0.93 0.28
Average (ex Composite) 0.28 0.13 0.62 0.88 0.28
Fundamental Indexation
March/April 2005 www.cfapubs.org 91
Even in such a comparison, the Composite index
held a lead relative to the Reference portfolio until
the last eight months of the decade. Then, as the
TMT bubble burst, the Fundamental indexes
pulled ahead by an average of 9.44 pps a year for
January 2000 through December 2004.
Table 6 shows the performance of the indexes
in the recessionary and expansionary phases of the
business cycle as defined by the National Bureau
of Economic Research. The excess returns were
particularly strong in the recessionary phases of
the business cycle; they averaged 4.13 percent a
year versus 1.80 percent a year during expansions.
Still, value was added during expansions as well
as recessions.
In Table 7, we show the performance in bear
and bull markets, where a bull market is defined
simplistically (and ex post) by a 20 percent rally
from the previous low and a bear market, by a 20
percent decline from the previous high. The Fun-
damental indexes outperformed by an average 6.40
pps a year in bear markets and a still-respectable
0.55 pps a year in bull markets. Given the value bias
of the Fundamental indexes, the superior perfor-
mance in bear markets is not surprising, but the
indexes also matched the cap-weighted indexes in
the typical bull market, despite the growth bias of
the cap-weighted indexes.
Table 8 shows the performance in rising-
interest-rate and falling-interest-rate regimes,
where a rising-rate regime is defined (simplistically
and ex post) by the U.S. 90-day T-bill yield rising
more than 20 percent from the previous low and a
falling-rate regime is defined by the T-bill yield
falling more than 20 percent since the previous
high. The Fundamental indexes outperformed the
Reference portfolio by an average of 2.54 pps a year
in falling-interest-rate environments and 1.87 pps
a year in rising-interest-rate environments.
Table 6. Return Characteristics of Alternative Indexing Metrics in NBER
Business Cycles, 1962–2004
Portfolio/Index
Expansions Recessions
Geometric
Return Volatility
Sharpe
Ratio
Geometric
Return Volatility
Sharpe
Ratio
S&P 500 11.75% 14.13% 0.45 3.15% 20.34% –0.25
Reference 11.66 14.13 0.44 2.46 20.90 –0.28
Book 13.19 13.89 0.56 5.51 20.13 –0.13
Income 13.60 13.94 0.59 6.55 20.03 –0.08
Revenue 13.82 14.74 0.57 7.03 21.75 –0.05
Sales 13.84 14.67 0.58 7.24 21.62 –0.05
Dividends 12.70 12.75 0.57 7.74 18.36 –0.03
Employment 13.63 14.61 0.56 5.49 22.24 –0.12
Composite 13.40 13.75 0.58 6.77 19.93 –0.07
Average (ex Composite) 13.46% 14.10% 0.57 6.59% 20.69% –0.08
Table 7. Return Characteristics of Alternative Indexing Metrics in Bull and
Bear Markets, 1962–2004
Bull Markets Bear Markets
Portfolio/Index
Geometric
Return Volatility
Sharpe
Ratio
Geometric
Return Volatility
Sharpe
Ratio
S&P 500 20.81% 13.62% 1.21 –24.02% 16.49% –1.89
Reference 20.89 13.56 1.22 –24.89 17.01 –1.89
Book 21.20 13.51 1.25 –19.30 16.77 –1.58
Income 21.63 13.64 1.27 –18.62 16.49 –1.56
Revenue 22.24 14.46 1.24 –19.36 17.90 –1.48
Sales 22.27 14.38 1.25 –19.30 17.85 –1.48
Dividends 19.68 12.63 1.21 –15.27 14.84 –1.51
Employment 21.62 14.34 1.20 –19.08 18.43 –1.42
Composite 21.26 13.48 1.25 –18.09 16.37 –1.54
Average (ex Composite) 21.44% 13.83% 1.23 –18.49% 17.05% –1.51
Financial Analysts Journal
92 www.cfapubs.org ©2005, CFA Institute
Tables 4 through 8 address the concern that the
excess returns of the Fundamental indexes are
driven by exposure to macroeconomic risks that are
not captured fully by the CAPM model. These
tables suggest that weighting by the Main Street
definitions of the size of a company is surprisingly
robust in improving on the mean–variance effi-
ciency of cap-weighted indexes.
Panel A of Table 9 compares the correlations
of the Fundamental indexes and the cap-weighted
indexes with an array of asset-class returns. The
results are, for the most part, surprisingly bland:
The Fundamental indexes have largely the same
correlations that the cap-weighted indexes do
with this assortment of assets. The notable excep-
tion is that the Fundamental indexes are more
Table 8. Return Characteristics of Alternative Indexing Metrics in Rising-
and Falling-Interest-Rate Regimes, 1962–2004
Falling Rates Rising Rates
Portfolio/Index
Geometric
Return Volatility
Sharpe
Ratio
Geometric
Return Volatility
Sharpe
Ratio
S&P 500 18.05% 16.31% 0.75 5.08% 13.99% –0.05
Reference 18.13 16.31 0.76 4.73 14.19 –0.07
Book 19.81 16.04 0.87 6.53 13.78 0.06
Income 20.94 16.04 0.94 6.61 13.80 0.06
Revenue 20.99 16.84 0.90 7.00 14.91 0.08
Sales 21.02 16.74 0.91 7.06 14.86 0.09
Dividends 20.38 14.47 1.01 5.99 12.75 0.02
Employment 20.87 17.13 0.88 6.44 14.62 0.05
Composite 20.56 15.74 0.94 6.63 13.75 0.06
Average (ex Composite) 20.67% 16.21% 0.92 6.60% 14.12% 0.06
Table 9. Correlations of Indexes with Major Asset Classes, 1988–2004
Portfolio/Index S&P 500
Hedged
EAFEa
Wilshire
REIT
Lehman
Aggregate
U.S. Bond
Lehman
U.S. TIPSb
Merrill U.S.
High-Yield
B–BB
JP Morgan
Unhedged
Non-U.S.
Bonds
JP Morgan
Emerging
Markets
Bonds
Dow Jones
AIG
Commodity
A. Correlation of index returns
S&P 500 1.00 0.54 0.30 0.20 –0.22 0.49 0.01 0.54 –0.05
Reference 0.99 0.54 0.31 0.19 –0.22 0.51 0.01 0.55 –0.04
Book 0.96 0.52 0.41 0.19 –0.18 0.52 –0.01 0.54 –0.01
Income 0.95 0.51 0.42 0.21 –0.16 0.53 –0.02 0.55 –0.03
Revenue 0.92 0.50 0.46 0.17 –0.15 0.56 –0.04 0.52 –0.03
Sales 0.92 0.51 0.46 0.16 –0.15 0.56 –0.03 0.52 –0.02
Dividends 0.90 0.45 0.42 0.25 –0.13 0.48 0.03 0.50 –0.03
Employment 0.93 0.51 0.46 0.18 –0.15 0.55 –0.02 0.55 0.01
Composite 0.94 0.50 0.43 0.20 –0.16 0.53 –0.01 0.53 –0.02
Average (ex Composite) 0.93 0.50 0.44 0.19 –0.16 0.53 –0.02 0.53 –0.02
B. Correlation of index value added over Reference portfolio
S&P 500 0.12 0.01 –0.08 0.09 0.03 –0.11 0.05 –0.06 –0.07
Reference — — — — — — — — —
Book –0.17 –0.12 0.32 –0.03 0.12 0.00 –0.06 –0.05 0.09
Income –0.17 –0.13 0.28 0.02 0.16 0.02 –0.06 –0.03 0.04
Revenue –0.14 –0.08 0.36 –0.05 0.15 0.12 –0.11 –0.07 0.03
Sales –0.17 –0.08 0.37 –0.08 0.15 0.10 –0.09 –0.09 0.05
Dividends –0.44 –0.31 0.10 0.05 0.19 –0.20 0.03 –0.23 0.03
Employment –0.14 –0.09 0.44 –0.04 0.17 0.13 –0.06 –0.02 0.15
Composite –0.26 –0.18 0.26 –0.01 0.16 –0.03 –0.05 –0.12 0.05
Average (ex Composite) –0.21 –0.13 0.31 –0.02 0.16 0.03 –0.06 –0.08 0.06
aEurope/Australasia/Far East Index.
bFrom February 1997; U.S. TIPS did not previously exist. TIPS is the short name commonly given to Treasury Inflation-Indexed
Securities.
Fundamental Indexation
March/April 2005 www.cfapubs.org 93
strongly correlated than the cap-weighted indexes
with the Wilshire REIT Index. All correlations
larger than 0.11 are statistically significant at the
90 percent level in a two-tailed test; a correlation
of 0.18 or above is significant at the 99 percent
level.15 Accordingly, most of these correlations are
highly significant.
Panel B of Table 9 goes a step farther than Panel
A: It examines the correlation of the value added
for the various indexes, net of the return for the
Reference portfolio, with an array of asset classes.
Here, we found differences that may be more inter-
esting than those shown in Panel A, although these
results often lack statistical significance. The value
added by the S&P 500 apparently outpaced that of
the Reference portfolio when the stock market was
rising, the broad U.S. bond market was rising (i.e.,
interest rates were falling), and high-yield bonds,
emerging market bonds, and REITS were perform-
ing badly. The Fundamental indexes reveal mostly
the opposite characteristics, performing best when
U.S. and non-U.S. stocks were falling and REITS
were rising. Curiously, the Fundamental indexes
generally performed well when high-yield bonds
were rising but emerging market bonds were fall-
ing. Also, they tended to perform well when TIPS
were rising (i.e., real interest rates were falling).
Most of these results are not surprising, but, apart
from the S&P, REIT, and TIPS correlations, most are
also not statistically significant.
Intuition for Fundamental Indexes
We believe the performance of these Fundamental
indexes is largely free of data mining. Our selection
of size metrics was intuitive; the metrics were not
selected ex post on the basis of results. Nor was the
composite constructed by “cherry picking” the best
metrics; we chose the obvious ones—measures that
are readily available worldwide. For example,
although we also examined reported and operating
earnings, both raw and smoothed, we have not
shown those results in tables here because cash
flow is slightly less subject to manipulation and
global accounting differences than earnings.16 We
used no subjective stock selection or weighting
decisions in the indexes’ construction, and the port-
folios were not fine-tuned in any way. For the Com-
posite index, we did not optimize the weighting of
the constituent measures in any way.
Even so, we acknowledge that our research
may be subject to at least two criticisms:
• Part of the motivation for this research is that
the authors lived through the 1962–2004
period; we experienced bubbles in which cap
weighting caused severe destruction of inves-
tor wealth, which contributed to our concern
about the efficacy of cap-weighted indexation.
• The fundamental metrics of size all implicitly
introduce a value bias into the indexes, which
has been amply documented as possibly the
result of market inefficiencies or as priced risk
factors. (Reciprocally, it can be argued that cap-
weighted indexes have a growth bias.)
To explore the second point, we compared a list
of the largest companies by capitalization (the Ref-
erence portfolio) as of the end of 2004 with the
largest as measured by the Composite index. Table
10 shows the results. With few exceptions, the stocks
on both of these lists are intuitive and unsurprising.
What is also evident is that the cap-weighted list has
a marked bias, relative to the Composite index, in
favor of high-multiple stocks with strong perceived
growth opportunities. Whether this growth bias
will prove profitable in the future is not known, but
it has not proven profitable in the past.
Although the top three stocks on both indexes
are the same, albeit in a different order, few aspects
of the Fundamental indexes more starkly highlight
the difference with cap-weighted indexes than the
fourth largest companies on the two lists. Microsoft
is unequivocally an important part of today’s—
and tomorrow’s—economy, and its weight in the
cap-weighted portfolio is 2.0 percent. Its place
accords with the market’s view of future profits. In
the Composite index, where companies are
weighted in accordance with the current scale of an
enterprise in today’s economy, Microsoft occupies
11th place, with a more modest 1.3 percent of the
index. From the perspective of Main Street, Wal-
Mart occupies a larger share of the economy; it
pays larger dividends, earns larger profits, and
includes more of the nation’s capital stock (book
value) than Microsoft. Wal-Mart also accounts for
more of our consumption basket (sales) and
employs more people, although this last metric
was not included in the Composite index. Accord-
ingly, the Composite index weights Wal-Mart 4th,
at 1.6 percent of today’s economy, even though it
ranks 13th in capitalization.
Of course these index weights do not suggest
that Microsoft is overvalued or that Wal-Mart is
undervalued. The weights merely indicate that
Microsoft’s scale in the current economy is smaller
than Wal-Mart’s current scale. Empirically, the vol-
atility associated with the shifting perceptions of
future scale for individual companies creates a per-
formance drag on the cap-weighted indexes. Wall
Street is making the judgment that Wal-Mart will be
45 percent smaller in the future economy than
Microsoft, but Fundamental indexing (Main Street)
pegs Wal-Mart as 25 percent larger in the current
Financial Analysts Journal
94 www.cfapubs.org ©2005, CFA Institute
economy than Microsoft. That is a big gap; the mar-
ket’s perception that Microsoft will be larger in the
future than it is today may or may not prove true.
Figure 2 illustrates the stability of the sector
allocations of the Fundamental indexes over
time.17 The cap-weighted index (Panel A) has
reacted strongly to shifting investor preferences,
with a huge spike and collapse in the allocation to
energy in the early 1980s and in the allocation to
technology stocks in 1998–2001. In contrast, the
Fundamental indexes closely reflect the steady evo-
lution of the economy at large, with a gradual
change in sector allocations in response to the shift-
ing composition of the economy.
Performance Attribution
The excess return of the Fundamental indexes we
observed is consistent with the hypothesis that
stock prices are inefficient, but the incremental per-
formance is also consistent with explanations not
based on price inefficiency. We explore here the
possible reasons behind the performance of the
Fundamental indexes and provide evidence sup-
porting both views.
Table 2 shows that the CAPM betas and corre-
lations for the Fundamental indexes averaged 0.95
and 0.96; the notable outlier is Dividends, which
had an average beta of 0.84. Adjusted for beta risk,
the average excess return for the Fundamental
indexes increases from 2.15 pps to 2.37 pps a year.
The t-statistics are significant for all the Fundamen-
tal indexes, approaching 4.0 for the Composite
index. How does one explain these alphas?
Much of the work on explaining the Funda-
mental index alphas builds on existing knowledge:
Alphas have been used repeatedly in the academic
literature to reject (1) the S&P 500 as a good market
proxy, (2) the link between noise in asset pricing
and the factor returns observed for value and size,
(3) the CAPM’s single-factor framework, and (4)
price efficiency.
Many theoretical reasons have been given for
why the S&P 500 and other cap-weighted indexes
do not proxy well for the “true” equity market
portfolio, so our identification of a better equity
market index is not surprising. That cap-weighted
indexes fall short of proxying the market is a defen-
sible interpretation of our empirical results, but it
does not provide an ex ante reason to believe these
Fundamental indexes are a better proxy for the true
CAPM market portfolio than is, for example, the
S&P 500.
Hsu demonstrated that cap-weighted portfo-
lios suffer from a return drag if prices are noisy
relative to movements in company fundamentals.
Treynor shows that random pricing errors lead to
Table 10. Largest by Capitalization and by Fundamental Composite,
31 December 2004
20 Largest by Reference Portfolio
Weight in
Index 20 Largest by Fundamental Composite
Weight in
Index
General Electric 3.19% ExxonMobil 2.763%
ExxonMobil 2.75 Citigroup 2.482
Citigroup 2.05 General Electric 2.455
Microsoft 2.03 Wal-Mart Stores 1.610
Pfizer 1.70 Fannie Maea 1.492
Bank of America 1.58 Bank of America 1.485
Johnson & Johnson 1.56 SBC Communications 1.468
International Business Machines 1.37 ChevronTexaco 1.377
American International 1.24 General Motors 1.335
Intel 1.24 American International Group 1.311
Procter & Gamble 1.18 Microsoft 1.310
JPMorgan Chase & Co. 1.15 Ford Motor 1.232
Wal-Mart Stores 1.12 Verizon Communications 1.220
Cisco Systems 1.08 JP Morgan Chase & Co. 1.189
Altria Group 1.03 Altria Group 1.14 0
Verizon Communications 0.93 Pfizer 1.003
ChevronTexaco 0.93 Merck & Co. 0.947
Dell 0.88 Morgan Stanley 0.935
Wells Fargo & Co. 0.87 International Business Machines 0.913
Home Depot Inc. 0.79 Wells Fargo & Co. 0.845
aFederal National Mortgage Association.
Fundamental Indexation
March/April 2005 www.cfapubs.org 95
a negative alpha for any price-weighted or cap-
weighted portfolio relative to a price-indifferent
portfolio, such as the Fundamental indexes (or
equal weighting).
Portfolio managers like to believe that
observed superior performance is alpha and is
driven by price inefficiency, but they recognize that
any assumption of price inefficiency is significantly
difficult to defend. We understand this point and
do not wish to overstate our case. Many practitio-
ners and academics do believe, however, that the
extraordinary run-up in share valuations and the
subsequent crash of 1998–2002 was a bubble; this
experience adds support to the contention that
price fluctuations sometimes do not reflect changes
in company fundamentals.
What if the assumption of price inefficiency is
true? After all, Fischer Black famously observed
that the markets are far more efficient when viewed
from the banks of the Charles than from the banks
Figure 2. Sector Weightings
(12-month centered moving average, 1962–2004)
Portion of Portfolio (%)
A. Reference Portfolio
B. Fundamental Composite Index
100
50
40
30
20
90
80
70
60
10
Utilities
Telecommunications
Electronic Equipment
Chemicals
Consumer Durables
Financial
Energy
Manufacturing
Health Care
Consumer Nondurables
Retail
Other
0
62 66 82 9470 86 9874 78 90 02 04
Portion of Portfolio (%)
100
50
40
30
20
90
80
70
60
10
0
62 66 82 9470 86 9874 78 90 02 04
Utilities
Telecommunications
Electronic Equipment
Chemicals
Consumer Durables
Financial
Energy
Manufacturing
Health Care
Consumer Nondurables
Retail
Other
Financial Analysts Journal
96 www.cfapubs.org ©2005, CFA Institute
of the Hudson. Price inefficiency need not immedi-
ately suggest easy money. Suppose we merely
know that some companies are overvalued and
others are undervalued. We have no simple way to
trade away this idiosyncratic noise in prices
because we do not know which stock is currently
overvalued and which stock is undervalued.
Any price deviation from “true fair value”
implies, however, that cap weighting will over-
weight all currently overpriced stocks and under-
weight all undervalued ones. An overreliance on
overpriced stocks and underreliance on under-
priced stocks leads to lower risk-adjusted perfor-
mance relative to hypothetical fair value–weighted
strategies—and probably also relative to strategies
that randomize these errors. The size metrics that
we explored are valuation indifferent and, there-
fore, will not be subject to this bias or the corre-
sponding performance drag in cap-weighted
indexes. Admittedly, they could introduce other
(potentially more costly) biases, but we found no
evidence of that in the data.
The literature on stock return predictability in
which price-related ratios, such as dividend yield
and earnings yield, appear to forecast next-period
stock returns is also consistent with price ineffi-
ciency.18 This evidence of return predictability is a
stronger form of price inefficiency than simply idio-
syncratic price noise because the pattern of price
deviation in the studies is systematic (e.g., high-P/E
stocks have a greater tendency to underperform)
and because there are obvious strategies to profit
from the inefficiency.19 Return predictability sug-
gests a systematic inefficiency that can be exploited
by using companies’ financial ratios as trading sig-
nals. The Fundamental indexes implicitly condition
on company financial ratios through their annual
reconstitution and reweighting, which allows these
indexes to benefit from the documented predictive
relationships between dividend yields and other
value measures of future stock returns.
Although the construction of the Fundamental
indexes systematically underweights growth
stocks relative to a cap-weighted portfolio, a better
way to state what is going on is that the cap-
weighted Wall Street indexes systematically over-
weight growth stocks relative to a Main Street Fun-
damental index. A Fama–French three-factor
regression shows that the Fundamental indexes
have exposure to the value factor and, to a lesser
extent, the size factor. Accordingly, the Fundamen-
tal indexes, net of the effects of the value and size
factors, earned an estimated alpha of –0.1 percent.
Three observations are noteworthy here. First, we
were not seeking Fama–French “alpha”; this
approach is a passive method with no stock selec-
tion. Second, most value indexes earn an estimated
Fama–French alpha of –1.5 percent or worse, mean-
ing that their CAPM alphas could be far higher if
they were better constructed. No existing indexes
that we are familiar with earn as much value added
relative to capitalization weighting as the Funda-
mental indexes or avoid a large negative Fama–
French alpha in the process. Finally, we question
whether the returns on the Fama–French factors
create the alpha for Fundamental Indexation or
whether they are themselves generated by the same
negative-alpha driver that cuts returns on the cap-
weighted indexes. One can adopt the interpretation
that the value premium is an anomaly and is a pure
alpha because of a systematic price inefficiency.20
The cap-weighted index underperformance is
positively related to the size of the price deviation,
whether that deviation is idiosyncratic or system-
atic (see Hsu). Table 5 provides a powerful illustra-
tion in the data showing that the cap-weighted
market portfolio underperformed the Fundamen-
tal indexes in the current decade—after high-tech
share prices began to revert to a level of normalcy
relative to their fundamentals—by an average of
9.44 pps.
The observed excess returns could also be
attributed to hidden risk exposures rather than
return anomalies from price inefficiency. Under-
weighting growth stocks relative to a cap-weighted
index may expose the Fundamental indexes to more
risks, such as economywide liquidity or distress risk,
than a cap-weighted index is exposed to. Although
the history of stock returns we analyzed does not
provide support for this view (except, weakly, in the
worst single month for a few of the Fundamental
indexes), the proposition that hidden risk factors are
behind the performance is conceivable.
These explanations are not mutually exclusive.
That is, the superior performance of the Fundamen-
tal indexes may be attributable in part to market
mispricing and in part to the index taking on addi-
tional hidden risk exposure. A common denomina-
tor in all three explanations, however, should be
kept in mind: In any but the simplest CAPM defi-
nition of alpha, this value added is attributable
more to a structural negative return bias from cap-
weighted or price-weighted indexes than to any
positive alpha from Fundamental Indexation.
We remain agnostic as to the true driver of the
Fundamental indexes’ excess return over the cap-
weighted indexes; we simply recognize that they
outperformed significantly and with some
consistency across diverse market and economic
environments. Our research suggests little reason
to believe that this pattern will not continue.21
Fundamental Indexation
March/April 2005 www.cfapubs.org 97
Conclusion
We have described a group of fundamentals-based
market portfolios whose construction method is
based on selection and weighting with metrics of
company size other than cap weighting. These size
measures include book value, revenues, dividends,
and others. The resulting portfolios outperformed
the S&P 500 by an average of 1.97 pps a year over
the 43-year span tested. The performance was
robust across time, across phases of the business
cycle, across bear and bull stock markets, and
across rising- and falling-interest-rate regimes. Our
work suggests that indexes constructed using Main
Street measures of company size are significantly
better than the cap-weighted Wall Street indexes.
The excess return of the Fundamental index
portfolios over the S&P 500 could arise from (1)
superior market portfolio construction, (2) price
inefficiency, (3) additional exposure to distress risk,
or (4) a mixture of the three. Whether the superior
performance is driven by better market index con-
struction, by pure CAPM alpha (driven by a struc-
tural negative return bias in cap-weighted
portfolios), or by beta exposure to additional risk,
historically, the Fundamental indexes are materi-
ally more mean–variance efficient than standard
cap-weighted indexes.
We believe these results are not mere accidents
of history but are likely to persist into the future.
The mean–variance superiority of the Fundamental
indexes is robust and significant. We offered our
interpretations of the results and explained why the
results should not be dismissed as active manage-
ment anomalies or the product of data mining or
data snooping.
We are pursuing additional research related to
Fundamental Indexation in numerous directions
that are beyond the scope of this article. A particu-
larly worthy question is whether the Fundamental
indexes have a value bias relative to the cap-
weighted indexes—or whether the cap-weighted
indexes have a growth bias relative to the “average
company” (the Fundamental indexes). Other areas
include performance in comparison with the “next
2,000 stocks” (roughly equivalent to the Russell
2000), performance outside the United States, per-
formance in comparison with active managers,
why the Fundamental indexes sharply outpace the
cap-weighted indexes in bear markets but not bull
markets, risk premium implications, the superior
performance we have found for the Fundamental
indexes in relation to conventional value indexes,
and the role of mean reversion in the Fundamental
indexes’ performance.
We find it refreshing that Main Street indexing
outperforms Wall Street indexing. When the pop-
ular press describes mergers and other corporate
actions, the size of the companies is generally
described in revenues, profits, employees, or other
Main Street measures. The true significance of the
difference between these two forms of viewing the
stock market may have been best noted by Ben-
jamin Graham: In the short run, the market is a
voting machine, but in the long run, it is a weigh-
ing machine.
We are indebted to George Keane and Marty Leibowitz
for sowing the seeds for this research in many discussions
about improved ways to manage passive portfolios. We
also appreciate the valued feedback and suggestions of
Peter Bernstein, Burton Malkiel, Harry Markowitz, and
Jack Treynor, with additional help from Cliff Asness,
Michael Brennan, Bob Greer, Philip Halpern, Bing Han,
Max Moroz, Richard Roll, Glenn Swartz, and Ashley
Wang. Special thanks go to Yuzhao Zhang for assistance
with CRSP/Compustat data issues.
Notes
1. The CAPM market portfolio should theoretically be a
portfolio that includes all assets in positive net supply,
including all financial instruments backed by physical
assets as well as nontraded capital assets. Thus, the true
market portfolio should include (at least) U.S. and
international stocks plus corporate bonds, commodities,
real estate, and human capital. Thus, a globally diversified
all-asset portfolio is closer to being mean–variance efficient
than is a diversified stock portfolio. Mayers (1976) was the
first to point out that the CAPM market portfolio should
include all assets in positive net supply and, therefore, the
equity market portfolio cannot be a reasonable proxy for it.
Traditional CAPM tests using a cap-weighted equity mar-
ket portfolio have found the CAPM relationship to not hold,
which represents either a rejection of the equity market
portfolio as the CAPM portfolio or a rejection of the mean–
variance optimality of the market portfolio. Stambaugh
(1982) extended Mayers’ idea and tested the CAPM with a
market portfolio that included nonequity asset classes; the
result was improved success over traditional CAPM tests.
Roll and Ross (1994, p. 101) stated “. . . it is well known that
a positive and exact cross-sectional relation between ex ante
expected returns and betas must hold if the market index
against which betas are computed lies on the positively
sloped segment of the mean–variance efficient frontier. Not
finding a positive cross-sectional relation suggests that the
index proxies used in empirical testing are not ex ante
mean–variance efficient.” See Roll (1977) and Ross (1977)
for excellent reviews of this topic. Papers that rejected the
efficiency of various cap-weighted market indexes include
Ross (1978), Gibbons (1982), Jobson and Korkie (1982),
Shanken (1985), Kandel and Stambaugh (1987), Gibbons,
Ross, and Shanken (1989), Zhou (1991), and MacKinlay and
Richardson (1991).
Financial Analysts Journal
98 www.cfapubs.org ©2005, CFA Institute
2. Roll and Ross suggested that the standard cap-weighted
market indexes may be located within 22 bps below the true
market index in mean–variance space.
3. We are not the first to explore weighting by fundamental
factors, although none of these works came to our attention
before our research was completed. Goldman Sachs man-
aged an earnings-weighted S&P 500 Index during the early
1990s, as did Global Wealth Allocation from 1999 to 2003.
Barclays Global Investors recently introduced a dividend-
weighted strategy. Paul Wood manages an earnings-
weighted 100 (out of the S&P 500) strategy (see Wood and
Evans 2003). All of these strategies, however, use as a com-
pany universe an existing cap-weighted index. Each strat-
egy, therefore, requires that companies be large in both
capitalization and the other selected metric of size. None of
the organizations have published a theoretical basis for the
success of their strategies.
4. A cap-weighted index has the added intellectual satisfaction
of macro consistency. All investors can hold a cap-weighted
portfolio without violating market clearing. The alternative
indexes we propose would not be market-clearing
portfolios. But the CAPM is predicated on an array of
simplifying assumptions that are not factually correct; these
assumptions have been repeatedly shown to invalidate the
mean–variance efficiency of that market-clearing portfolio.
Accordingly, investors seeking better indexes have little
reason to care greatly about the market-clearing property.
5. Turnover is surprisingly high on the most widely used
“passive” indexes. For example, the widely respected Frank
Russell Company makes available data on “annual index
portfolio turnover,” which is defined as “the percentage of
an index fund that must be ‘traded out’ at reconstitution to
maintain an exact replication of the index in the Russell
1000, which represents 92 percent of all domestic equity
market value.” Russell states that this turnover has aver-
aged 9.2 percent a year during the 1983–2000 period. The
Russell 3000, which represents 98 percent of all domestic
market value, has averaged 9.0 percent turnover.
6. We are indebted to Burton Malkiel for suggesting that we
test this measure of company size. In addition to the number
of employees, we also looked at dollar payroll, with results
nearly identical to those for number of employees.
7. Empirical studies have shown that zero-yield stocks out-
pace low-yield stocks with some regularity. Yet, even
though zero-yield stocks were excluded from the Dividends
index while low-yield stocks were not, the index still hand-
ily outpaced the traditional cap-weighted indexes in the
long run, with markedly lower risk.
8. These companies tend either to be fast growing enough for
shareholders to accept a policy of 100 percent earnings
retention or struggling enough to have canceled the divi-
dend and be marked down in price as a consequence. See
Arnott (1988).
9. The differences in annual returns between the indexes that
used five-year trailing average statistics versus one-year
trailing statistics were within ±10 bps, whereas turnover
increased uniformly by more than 2 percentage points.
10. The Russell indexes are weighted by float, not aggregate
capitalization, and are rebalanced annually at midyear.
11. The information ratio is the value added divided by the
standard deviation of value added (or the “tracking error”).
12. Given that Warren Buffett’s lifetime information ratio is
about 0.70, we found this result to be very satisfactory,
particularly for a process that is not seeking alpha.
13. We found also (not shown in Table 3) that the Fundamental
indexes have roughly twice the liquidity and half the turn-
over of an equally weighted portfolio of the Reference
index holdings.
14. By each metric, Revenue nearly duplicates Sales perfor-
mance. Results for every Fundamental index are available
from the authors or online at www.researchaffiliates.com/
index.
15. The required significance data for TIPS (Treasury Inflation-
Indexed Securities) correlations, because of the limited his-
tory of TIPS, are 0.18 for the 90 percent level and 0.29 for the
99 percent level.
16. The results for earnings were nearly identical to the results
for the Cash Flow index.
17. We used stocks of the merged Compustat/CRSP database
grouped by the 12 S&P industrial sector groupings.
18. See Blume (1980); Campbell and Shiller (1988); Fama (1990);
Chen, Grundy, and Stambaugh (1990); Hodrick (1992);
Campbell and Hamao (1992); Goetzmann and Jorion (1993,
1995); Fama and French (1992,1995); Lamont (1998); Barberis
(2000); Arnott and Asness (2003). Cochrane (1999) contains
an excellent review of return predictability. The particular
return predictabilities explored in most academic general
equilibrium models are not related to price inefficiencies but
are related to time-varying risk premiums.
19. See Bansal, Dahlquist, and Harvey (2004) for a trading
strategy based on the literature of return predictability to
enhance buy-and-hold portfolio returns.
20. This stance is not as controversial as it might seem. The
academic finance literature has still not reached a consensus
on the source of the value premium, and journals continue
to publish general equilibrium models demonstrating how
the Fama–French value factor may be a proxy for an under-
lying risk factor. Little convincing evidence is available,
however, on the value factor proxying a macroeconomic
risk factor. In contrast, the most popular interpretations of
the value factor as a systematic distress-risk factor have
failed to identify economywide distress scenarios that coin-
cided with price collapses in value stocks. The finance
literature on return anomalies, and on systematic market
inefficiencies driven by behavioral biases, certainly lends
support to the interpretation that Fundamental indexes
capture the value premium as pure alpha.
21. For example, the capitalization ratios of the Fundamental
indexes are currently well within normal ranges, which
suggests that the excess return is not merely a function of a
42-year revaluation of the Fundamental Indexation metrics.
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