T
M
A
FO
R
The Stable ROE Portfolio:
An Alternative Equity Index
Strategy Based on Common
Sense Security Analysis
IN
A
N
Y
RUSSELL J. FULLER, RAIFE GIOVINAZZO, AND YINING TUNG
R
TI
A
IS
R AIFE GIOVINAZZO
U
C
E
TH
is the director of research
at Fuller & Thaler Asset
Management in San
Mateo, CA.
[email protected]
D
YINING T UNG
IT
IS
IL
LE
G
A
L
TO
R
EP
R
O
is an investment analyst
at Fuller & Thaler Asset
Management in San
Mateo, CA.
[email protected]
3) Risk-clusters equal weighting
4) Fundamental index strategy (FI)
LE
lternative index strategies”1 are a
new and very successful investment innovation, recently gaining
many billions of dollars in new
asset inf lows. In general, these strategies
represent a combination of active decisions
and passive indexing. The alternative index
is initially based on active management decisions that determine the universe of stocks,
the individual stock weights in the index, and
the frequency of rebalancing the index. The
same rules are used over time to determine
the stocks and their weights at each rebalance
date. The most important difference between
“alternative equity indexes” and common
U.S. equity indexes such as the S&P 500 and
the Russell 1000 is that the stocks in these traditional indexes are weighted by their market
capitalization, whereas alternative indexes do
not use market-cap weighting.2
Chow et al. [2011] classified the many
different alternative equity indexes into two
general types: heuristic-based (rules-based)
and optimization-based alternative index
strategies.3 They empirically examine seven
of the more popular alternative U.S. equity
index strategies using return and fundamental
data for the 1,000 largest U.S. stocks:
“
is the chief investment
officer at Fuller & Thaler
Asset Management in San
Mateo, CA.
[email protected]
C
A
RUSSELL J. FULLER
Heuristic (Rules) Based
1) Equal weighting
2) Diversity weighting
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Optimization Based
5) Minimum-variance portfolio (MVP)
6) Maximum diversification
7) Risk-efficient indexation
For an intuitive description of each of
these seven alternative equity indexes, see
the section titled “Description of Investment
Strategies” in Chow et al. [2011], pp. 38–41.
In the same section of Chow et al. [2011],
the authors provide a relatively detailed
description of the methodology they used to
compute individual stock weights for each
of the seven alternative index strategies. In
our opinion, the classification scheme (or
taxonomy) presented in Chow et al. [2011]
of classifying alternative equity indexes as
either heuristic-based (rules-based) or optimization-based represents a nice contribution
to the literature on alternative indexes.
Chow et al. [2011] report that seven
alternative indexes have higher returns, but
also generally higher volatilities, than their
benchmark, the S&P 500.4 All seven alternative indexes have higher Sharpe ratios than
the benchmark. Among the four heuristicbased alternative indexes, FI has the highest
Sharpe ratio, the highest information ratio,
and the highest alpha. Among the optimi-
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zation-based alternative indexes, MVP has the highest
Sharpe ratio and alpha, but the lowest information
ratio.5
REPLICATING THE CHOW ET AL. [2011]
RESULTS
For this article, we first replicated the results by
Chow et al. [2011] presented in Tables 2 and 5 of their
paper. In their Table 2, they report the return and risk
characteristics of annually rebalanced alternative index
strategies for the 1,000 U.S. largest stocks at the beginning of each calendar year for the period 1964–2009
inclusive. In their Table 5, they present alphas for each
of the seven alternative indexes using the Fama/French
[1993]-Carhart [1997] methodology—also referred to
by some as the FF4 model.
Our replication is based on using the same methodologies, data sets and time periods as reported in their
paper. However, note that occasionally we had to refer
to other papers they cited to obtain the exact methodology, and for one or two procedures, we had to infer the
actual methodology (or coefficient) used in their paper.
Nevertheless, as one can see by the comparisons between
their results from their Tables 2 and 5 and our replications of their procedures in our Exhibits A1 and A2 in
Appendix A, we were able to replicate their procedures
reasonably well. None of the differences between our
mean results and the mean results in Chow et al. [2011]
were statistically significant at the 10% level. Thus, we
believe we are able to make reasonable “apples to apples”
comparisons of a new alternative index to the seven
alternative indexes in Chow et al. [2011].
SRP, A NEW ALTERNATIVE EQUITY INDEX
In this article, we present a new alternative equity
index that uses a single fundamental variable, ROE,
which should be related to a stock’s return over time.6
Based on common sense security analysis, simple deductive logic suggests that:
• Everything else held the same, investors should
place a higher value on a stock with a higher
ROE because it can generate a larger amount of
shareholder earnings for a given amount of equity
capital.
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• Similarly, for two stocks with the same average
ROE over time, investors should place a higher
value on the stock for which the time series of
ROE for the same time period is less volatile (more
stable).
But if enough investors mistakenly underappreciate ROE, then a portfolio consisting of high and stable
ROE stocks should outperform going forward. In the
section titled “Why SRP Works” we suggest a number
of reasons, based on cognitive psychology and behavioral finance, why investors might not fully appreciate
a portfolio of stocks which generates relatively high and
stable ROEs over time.
As our measure of a stock’s ROE and variance
of ROE as of December 31 for each year in the same
sample time period used in Chow et al. (1964–2009), we
computed the mean of each stock’s trailing 20 quarterly
observations of ROE and the variance of each stock’s
trailing 20 quarterly observations around its mean ROE
for each year. We sorted the 1,000 stocks for each year
based on each stock’s mean ROE as of December 31,
from highest (1) to lowest (1,000). We then limited
the sample to those stocks with mean ROEs above the
median, that is, stocks 1 to 500, assuming there were
1,000 stocks in the universe of U.S. large-cap stocks
with complete data to compute the stock’s mean and
variance of ROE.7
To estimate the minimum variance for our ROE
alternative index for the next year, we use similar optimization procedures to those used in forming minimum
variance (of returns) portfolios, MVPs, as summarized in
Chow et al. [2011] and described in considerable detail
in Clarke et al. [2006]. We calculated the shrinkage
target intensity as defined in Appendix A of Clarke et al.
[2006], who used a shrinkage degree of freedom less
than that of Ledoit and Wolf [2004]. In Appendix A, we
discuss a similar problem with the equal-weighted risk
clusters (RCEW), for which we did follow Ledoit and
Wolf [2004] and the results do not appear particularly
sensitive to the choice of shrinkage degree of freedom.
In Appendix A, neither our MVP nor our RCEW results
were significantly different from those reported in Chow
et al. [2011].
But, most important, rather than minimizing the
variance of stock returns, we use the optimization procedure to determine individual stock weights to minimize
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the variance of the portfolios’ ROEs for each subsequent
calendar year. In this way, we obtain the minimum variance of ROE portfolio, or what we refer to as the most
stable ROE portfolio (SRP). It turns out that the SRP
alternative index dominates all seven indexes in Chow
et al. [2011] on most relevant dimensions of risk and
return.
It is worth noting again that our choice of ROE
is based on simple deductive logic. Common sense suggests that a portfolio’s price should be positively related
to ROE. Common sense also suggests a portfolio’s price
should be negatively related to the variance of its ROE.
Thus, ROE is the only fundamental variable we examined from among the many fundamental variables available. Further, the only statistical tests we used are the
same as those used in Chow et al. [2011], as are the time
periods and data sets. Thus, our results should not be
considered an exercise in data mining.8
COMPARING SRP TO OTHER ALTERNATIVE
EQUITY INDEX STRATEGIES
Chow et al. [2011] argue that among the four heuristic-based alternative strategies they analyzed, fundamental indexing (FI) produced the best combination of
risk and return characteristics. Among the three optimization-based alternative index strategies, they suggest
that the minimum-variance portfolio (MVP) has the
best combination of risk and return characteristics. We
have no quarrel with their conclusions. Consequently, in
Exhibits 1 and 2 we compared our stable ROE portfolio
(SRP) against only FI and MVP, using the same methodology, data sets (primarily CRSP and Compustat) and
time period (1964–2009). As in Chow et al. [2011], we
used the same starting universe of stocks consisting of
the largest 1,000 U.S. stocks based on year-end market
values, although for the first five years there were not
always 1,000 stocks available with complete data (see
endnote 8). Portfolios were rebalanced annually as of
January 1 using the prior December 31 values. These
results are reported in Exhibit 1.
First, note in Exhibit 1 that the S&P 500, constructed using the Chow et al. [2011] methodology
is a proxy for the actual S&P 500 and is always the
benchmark.9 (The top row in the upper half of Exhibit 1
presents the proxy S&P 500 results.) The alternative
index data are arranged in three rows, with the first row
presenting results for the Chow et al. [2011] choice of FI
as the best of the four heuristic-based alternative indexes,
the second row representing their choice of MVP as the
best of the three optimization-based alternative indexes,
and the third row representing results for SRP. In the top
half of Exhibit 1, for each of the three alternative index
strategies (FI, MVP, and SRP), we reproduce the same
risk and return characteristics as in Exhibit A1 (our replication of the Chow et al. [2011] Table 2), which are:
EXHIBIT 1
1964–2009 Risk & Return Attributes, and Fama/French/Carhart Results
Annually Rebalanced U.S. Strategies for Top 1,000 U.S. Market-Cap Stocks.
*Complete data for all 7 strategies are reported in table A1 in the Appendix.
*Complete data for all 7 strategies are reported in table B1 in the Appendix.
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•
•
•
•
•
•
•
total return
volatility
Sharpe ratio
excess return versus benchmark
tracking error
information ratio
one-way turnover.
Note in Exhibit 1 that SRP has the highest total
return (12.58%) and obviously the highest excess return
(3.24%) among the three alternative indexes. SRP has
the second-highest Sharpe ratio (0.42), whereas MVP
has the highest Sharpe ratio (0.49). With respect to the
information ratio, SRP has the highest (0.55) versus 0.47
for FI and 0.24 for MVP. It should be noted that FI has
the lowest (one-way) turnover of 13.6%, versus 38.6%
for SRP and 48.5% for MVP. Thus, FI’s return attributes
will be relatively less affected by transaction costs than
for MVP and SRP.10
The bottom half of Exhibit 1 reports the results
from estimating alpha using the four-factor Fama/
French/Carhart model for the three alternative indexes,
FI, MVP, and SRP. (The complete data for all seven
alternative indexes are presented in Exhibits A1 and A2
in Appendix A.) Note that SRP has by far the highest
alpha (1.83%) per year annualized, compared to FI at
0.50% and MVP at 0.30%. (SRP’s alpha is also the only
one that is statistically significantly different from zero
at the 5% level.) Given that SRP has the highest excess
return one might expect SRP to also have the highest
alpha. But, the relative spread between the alphas of the
three alternative indexes is much greater than the relative spread between their excess returns. This is because
the factor loadings for FI and MVP are higher on value
(HML) in particular than is the case for SRP.
Also, it is worth observing the factor loadings on
the market, which are the alternative indexes’ betas relative to the benchmark. FI’s beta of 1.01 is the closest to
1.00, versus SRP’s beta of 1.04. MVP’s beta of 0.71 is
substantially different from 1.00. This raises the question
of the purpose of an alternative index. If the purpose is to
provide similar risk characteristics to the index and provide higher returns, then SRP and FI do well in terms
of risk with betas close to 1.0, relatively low tracking
errors, yet have higher Sharpe ratios, information ratios,
and positive excess returns. MVP is more problematic.
Although MVP’s Sharpe ratio and excess returns certainly beat the benchmark, on the risk-profile dimension
it does not fare as well with a beta substantially less than
1.00, a relatively high tracking error and low information ratio. However, its volatility is considerably below
the benchmark’s. Thus, if one desires higher returns
and lower total volatility than the S&P 500, and is not
concerned about beta, tracking error and information
ratios, MVP may be the best choice.
OUT-OF-SAMPLE RESULTS
Given the luxury of additional time since Chow
et al. [2011] did their analysis for the years 1964–2009,
we have four years (2010–2013 inclusive) of out-ofsample data. For this short time period, Exhibit 2 pres-
EXHIBIT 2
2010–2013 (Out-of-Sample) Risk & Return Attributes, and Fama/French/Carhart Results
Annually Rebalanced U.S. Strategies for Top 1,000 U.S. Market-Cap Stocks.
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erate annual portfolios that on average have relatively
ents data in the same manner as Exhibit 1: the top half
high ROEs for the next year, and the predicted ROEs
of Exhibit 2 presents data for the risk and return attrifor the SRP strategy’s portfolio are relatively stable over
butes for the three alternative indexes (FI, MVP, and
the 40 years of the study. Exhibit 4 presents the average
SRP); the bottom half of Exhibit 2 presents results from
a Fama/French/Carhart analysis.
Given the short time period (48 months
of return data and 16 quarters of fundamental E X H I B I T 3
data), we obviously don’t want to make any
1964–2013 Excess-Returns (vs. S&P 500)
strong statements about the results in Exhibit
2. But the rank order of the risk and return
attributes in Exhibit 2 are similar to the rankings in Exhibit 1, with the main exception
being that SRP has a lower volatility than
FI for this short period. With respect to the
Fama/French/Carhart results (the bottom
half of Exhibit 2), the rank orders for the
various regression coefficients are also similar to those in Exhibit 1, although the alpha
rankings are more attenuated. These results
are consistent with what is well known
about this four-year period of market history: value stocks generally performed very
well, which helped FI, and low volatility (of
returns) stocks also performed well, which
helped MVP.
This is also a good example of a small
sample size problem. Exhibit 3 has three
figures of plots of annual excess returns
over the entire in-sample time period,
1964–2013, one figure for each of the three
alternative indexes. Notice that if one constructed an arbitrary time period of five
years by including (2009–2013), instead of
the true out-of-sample four years, it would
include a pretty unusual year—2009. In
that year, MVP had a very negative excess
return whereas FI and SRP had positive
excess returns. The addition of just this one
year (2009) would favor SRP and FI more
than MSP. Thus, the safest conclusion is that
the out-of sample time period is simply too
short to draw any meaningful conclusions.
WHY SRP WORKS
First, we should point out that our
method for predicting the next year’s ROE
for the SRP portfolios does, in fact, gen-
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ROE in the first row and the standard deviation of the
annual ROEs over the years 1964–2013 in the second
row. The third and fourth rows report minimum annual
ROE and maximum annual ROE over the 40 years.
For comparison purposes, the top half of Exhibit 4
in the first column presents the average ROE for a simple
equal-weighted portfolio (13.0%); the second column
presents the average ROE for market-value-weighted
portfolios (16.3%); and the third column presents the
average ROE for stable ROE portfolios (17.6%). Since
we used only the top 50% of the universe of stocks
ranked on ROE in forming SRP portfolios, it is not
surprising that SRP has a higher ROE than would be
the case if one just randomly picked stocks (effectively
equal weighting) from the entire sample (typically 1,000
stocks, except in the earlier years) of the largest U.S.
stocks, or used a value weighting strategy.
There are much larger differences when one compares the stability of ROE over time to generic equalweighted and market-value-weighted portfolios. For
example, the standard deviation of the SRP portfolios’
ROE is only 2.9%, compared to standard deviations of
ROEs of 3.0% for the market-value-weighted portfolios and 3.1% for the equal-weighted portfolio. Perhaps
more important is the “downside risk,” which in this
case is represented by the lowest annual ROE. Again,
SRP is the most stable portfolio with respect to annual
ROEs based on the minimum annual ROE—SRP’s
worst annual ROE was 11.6%, compared to 9.1% for
the value-weighted portfolios and −0.3% for the equalweighted portfolio. Thus, SRP provides portfolios with
both higher ROEs on average, and the ROEs are more
stable whether one prefers the standard deviation of the
annual portfolios’ ROEs or the worst-year ROE as the
measure of stability. As we argued initially, if a strategy
produces generally higher ROEs and more stability (less
volatility) from year-to-year, common sense security
analysis suggests that the strategy should generate abovenormal returns.
To close the loop: Given that SRP generated
higher, more stable ROEs than typical stock indexes
(as presented in the top half of Exhibit 4) and better
risk/return characteristics and higher alphas (as shown
in Exhibit 1), we should also look at the comparative
magnitude of average ROEs over time and the stability
of ROEs for FI and MVP versus SRP. The bottom
half of Exhibit 4 presents these results. With respect to
average annual ROE, SRP’s 17.6% result is well above
the average ROE for MVP (12.4%) and FI (12.2%).
With respect to stability of ROE, SRP’s standard deviation of annual ROE (0.9%) is below MVP (3.4%) and
FI (3.5%).
Using the worst-year, or minimum annual, ROE
(during the 40 years of the study) as another measure
of ROE stability, or downside risk, SRP’s worst annual
ROE was 11.6% compared to 1.6% for MVP and 0.6%
for FI.
Thus, compared to the naïve weighting schemes of
equal-weighted and value-weighted indexes, as well as
the two best performing alternative equity indexes (FI
and MVP) identified in Chow et al. [2011], SRP did
generate a higher average ROE with substantially lower
variation of annual ROEs. Consequently, the data in this
study supports the notion, based on common sense and
basic security analysis, that a strategy which generates
portfolios that have a higher average ROE and a more
stable time series of ROE over a period of time should
generate better risk and return characteristics than strategies that don’t generate as good a ROE profile.
An important question with any anomaly study
is why does alpha exist? The stable ROE portfolio by
construction selects 1) individual stocks with higher
ROE, 2) individual stocks with more stable ROE and 3)
a portfolio of stocks whose combined ROE is more stable
EXHIBIT 4
1964–2013, Top 1,000 Stocks
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than merely equal weighting the high ROE individual
stocks. In our unpublished tests, we find all three elements add alpha. A full explanation of the stable ROE
portfolio would provide an explanation for each of the
three contributing elements.
Research in the last few years has provided increasingly precise explanations for why individual stocks with
high ROE may have higher returns. The best recent
paper on this topic is by Wang and Yu [2013]. They
find little evidence that high ROE stocks have more
macro-economic risk, and instead find evidence consistent with investor under-reaction due to inattention
to public news. Namely, stock returns for high ROE
stocks do not later reverse and are higher among stocks
with less attentive investors.
We do not know of any existing research on why
individual stocks with stable ROE or a portfolio of
stocks with stable ROE should earn higher returns, so
our explanations must be more speculative. We suspect
three possible reasons: investor inattention, lottery preferences, and a predictability bias.
We suspect the most likely explanation for why
more stable ROE stocks earn higher returns is due to
investor inattention, consistent with the inattention
causing high-ROE stocks to earn higher returns. Stocks
with unstable earnings—like unstable celebrities—naturally gain more attention, whereas stocks with more stable
ROE are more boring and receive less attention. Recent
research on predictably higher returns around entirely
predictable dates of earnings announcements, dividend
announcements, or seasonal earnings are consistent with
the idea that regular, boring patterns may receive little
attention precisely because they are regular and boring
(Chang et al. [2014]). Stable ROE stocks are likely more
boring and thus likely receive less attention.
A second possible explanation for why stable ROE
firms earn higher returns is that some investors seem
to prefer stocks that have lotterylike payoffs—see Barberis and Huang [2008]. Volatile ROE stocks may be
similar to lottery payoffs. If investors overbid for volatile, lotterylike payoffs, then more volatile stocks will
earn lower returns. Both the stable ROE portfolio and
the minimum volatility portfolio would benefit from
avoiding volatile stocks that are overbid. SRP will put
a low-weight on high-volatility ROE stocks and avoid
the negative returns associated with lotteries.
A third possible explanation for why stable ROE
stocks earn higher returns may be related to predict-
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ability bias. Huberts and Fuller [1995] classify stocks by
how easy or hard it is for analysts to predict company
earnings. Their surprising result is that stocks whose
earnings are hardest to predict provide below-normal
returns, and stocks whose earnings are easiest to predict
provide above-normal returns. One possible cause: when
earnings are hard to predict, it is easy to be biased and
overly optimistic. Obviously, stocks (or portfolios) with
high volatility of ROE are going to generate earnings
that are relatively hard to predict, and SRP will put a
low weight on these stocks.
Ultimately, our best conjecture is that the stable
ROE portfolio earns higher returns due to investor inattention to boring, stable ROE—although possibly due
to other investor biases such as lottery preferences or
predictability bias. But until more research is provided
on these conjectures, one should view them as just that,
conjectures. This is a topic for future research.
CONCLUSIONS
In this article, we present a new and different candidate to be used as an alternative equity index for the
U.S large-cap sector. We focus on the single fundamental variable that common sense suggests should be
strongly related to stock returns and this is a company’s
return on equity, ROE. We use standard minimumvariance techniques in constructing minimum-variance
(of returns) portfolios, except in this case we use these
minimization techniques to determine individual stock
weights that will minimize the variance of the portfolio’s
return on equity over time. Thus, the resulting portfolio
of stocks is the set of stocks whose weights provide the
lowest variance of ROE over time, or what we call the
most stable ROE portfolio.
It turns out that SRP provides risk and return
characteristics that are at least as good as, and generally
better than, the seven alternative indexes analyzed by
Chow et al. [2011] in their interesting paper. SRP does
provide the highest excess return, the second-highest
Sharpe ratio, the highest information ratio, and, by a
substantial margin, the highest alpha based on the fourfactor Fama/French/Carhart methodology over the 46
years of 1964–2009 inclusive. Consequently, SRP is a
good candidate for those investors who want an alternative index that provides exposure to the U.S. large-cap
stock universe, as represented by the S&P 500.
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APPENDIX A
REPLICATION OF THE CHOW ET AL.
[2011] RESULTS REPORTED IN THEIR
TABLES 2 AND 5
If we can replicate the results in Chow et al. [2011] with
reasonable precision, then using the same methodology, we
can compute results for the stable ROE portfolio (SRP) that
can be compared to the various alternative indexes analyzed
in Chow et al. [2011] on an apples-to-apples basis. Exhibit
A1 lists the results of our attempt to replicate the risk/return
analysis for the seven alternative index strategies presented in
Table 2 of Chow et al. [2011]. We tried to follow as closely as
possible the procedures they used, as described in their sections
titled “Descriptions of Investment Strategies” and “Empirical
Results and Discussion” on pages 38–41 of their paper. Exhibit
A1 presents the empirical results reported in Table 2 of Chow
et al. [2011], side-by-side with our replications of their results
for all seven of the alternative indexes, so the reader can quickly
compare their results with our replication of their results.
There are several points that should be mentioned about
any differences between the results we report versus the results
reported in Chow et al. [2011]: First, although we tried to
follow their methodology as closely as possible, in some cases
the actual methodological choices they made were based on
other published papers, which they reference in their paper.
In particular, judgments as to the number of clusters used to
determine the return and risk characteristics for the equalweighted risk clusters (RCEW) are problematic in that they
have to be made arbitrarily, but the number of clusters used
by Chow et al. [2011] was not explicitly identified. In this
case, we used what we believed to be the most likely number
of clusters used by in Chow et al. [2011], which was seven
clusters. Our choice of seven clusters is also consistent with
the k-medoid approach favored by Kaufman and Rousseeuw
[1990] and cited by Chow et al. [2011].
Another source of difference between the results
reported in Chow et al. [2011] and our attempts to replicate
their work could simply be due to changes in the available
data. Although we used the exact same data sets (primarily
CRSP and Compustat data) for the same time period as Chow
et al. [2011] 1964–2009, with the passage of time since their
empirical work (four years in this case), minor changes tend
to be made to data sets as new data become available that were
not available during earlier time periods in the same data sets
used by Chow et al. [2011] in 2010, and changes can be made
to past data as the data vendors, or users of the data, discover
data errors, that are subsequently changed by the data vendors
over time. Our experience is that these types of data issues
tend to be minor for the major financial data sets.
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First, note that in Exhibit A1 the S&P 500, constructed
using the Chow et al. [2011] methodology, is always the
benchmark. The alternative index data are arranged in rows,
with the first four rows presenting results for the four heuristic-based alternative indexes and the next three rows presenting results for the optimization-based alternative indexes.
For each of the seven alternative index strategies, Chow et al.
[2011] estimate seven commonly used variables:
•
•
•
•
•
•
•
total return
volatility
Sharpe ratio
excess return versus benchmark
tracking error
information ratio
one-way turnover.
For each of these seven variables, there are two columns
for each variable; the first column simply being results reported
by Chow et al. [2011] and the next adjacent column being the
results of our replication of Chow et al. [2011]. For example,
the total return for the equal-weighted alternative index (EW)
over the period 1964–2009 for a universe of stocks drawn
from the top 1,000 cap-weighted U.S. stocks was reported in
Chow et al. [2011] to be 11.78% annualized, whereas the result
for our replication was 11.58%. Although the reader will find
minor discrepancies between the Chow et al. [2011] results
and our results across all variables, none of the differences are
large enough to be statistically significant.
For example, the largest difference between the Chow
et al. [2011] results for total return and our results is 10.91% −
11.59% = 0.68% for the risk-clustering/equal-weighted
(RCEW) alternative index. However, the t-statistic for the
difference between these two mean returns is only 0.198.
(As noted above, we view the replication of their risk-cluster
equal-weighted to be the most problematic.) On balance, we
view our replication of the Chow et al. [2011] risk and return
characteristics to be reasonably close.
Exhibit A2 presents results in the same format as Exhibit
A1, but for the Fama/French/Carhart methodology for estimating alphas, which Chow et al. [2011] report their results in
their Table 5. Our results for Fama/French/Carhart estimates
are placed side-by-side to those of Chow et al. [2011]. Again,
there are small differences between the Chow et al. [2011]
results and the results of our replication.
Thus, we are reasonably confident that our replications
of the Chow et al. [2011] reported results are reasonably close
and reliable. We believe that the same methodology and data
we used to estimate results for SRP are good approximations
of what Chow et al. [2011] would find today if they had
known about SRP and ran the same tests over the same time
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Annually Rebalanced U.S. Strategies for Top 1,000 U.S. Market-Cap Stocks.
Replication of Chow et al. [2011] Results Reported in Their Table 5: 1964–2009 Factor Fama/French/Carhart Alphas & Factor Loadings
EXHIBIT A2
Replication of Chow et al. [2011] Results Reported in Their Table 2: 1964–2009 Risk & Return Characteristics of Annually Rebalanced
U.S. Strategies for Top 1,000 U.S. Market-Cap Stocks
EXHIBIT A1
period, 1964–2009 for all seven alternative index strategies,
but using data sets available in 2014.
ENDNOTES
We should acknowledge the participants at the Spring
JOIM Conference, who offered several helpful comments.
A special acknowledgement must be given to our former colleague Wei Su, who provided some of the original insights
for this paper while at Fuller & Thaler.
1
The majority of alternative index strategies represent
an alternative to investing in several different and commonly
known equity indexes. However, there can be alternative
indexes for widely used bond indexes, currency indexes, and
so forth. From this point forward, we will simply use the
term “alternative index” to refer to “alternative equity index,”
since that is the only type of alternative index examined in
this paper and in Chow et al. [2011].
2
The well-known Dow Jones indexes are an exception
in that they use price weighting for the individual stocks in
their indexes. Interestingly, Treynor [2005] shows that almost
any weighting scheme not based on market-cap weights will
generate higher returns than the commonly used market-cap
indexes. Fuller et al. [2012] devise a methodology for estimating the maximum amount market-cap weighting reduces
the return for various market-cap-weighted indexes.
3
These general types of strategies are also referred to
as “alternative beta” strategies, or sometimes “smarter beta
indexes.” We will use the term “alternative equity index strategies” to represent all three names.
4
Chow et al. [2011] do not use the actual S&P 500
returns. Rather, they construct a proxy for the actual S&P
returns that are computed in a manner consistent with the
way they compute returns for the seven alternative indexes
in their study. Specifically, at the end of each year, they select
the 500 largest U.S. stocks and use the stocks’ market values
to construct the weights for these stocks. For the actual S&P
500 index, the universe of 500 stocks are determined by a
committee of analysts at Standard & Poor’s Corporation, at
arbitrary dates in time, and then the stocks’ market values are
used to weight those 500 stocks in the S&P 500 index. As a
general rule, the S&P 500 holds most of the largest 500 U.S.
stocks at any point in time. However, there is no defined time
designated for rebalancing, versus Chow et al. [2011] consistent end-of-year rebalance. Thus, there are small differences
between the returns of the actual S&P 500 Index and Chow
et al. [2011] proxy for the S&P 500 Index.
5
The main reason MVP has a relatively high tracking
error, resulting in the lowest information ratio, is that it minimizes the variance of the portfolio’s returns. In general, any
optimization procedure that minimizes the variance of a port-
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THE STABLE ROE PORTFOLIO
folio’s returns will result in a low-beta portfolio, thus giving
the strategy a relatively high tracking error and a low information ratio. If one is not concerned with the alternative-index
strategy having a different risk profile versus the cap-weighted
index for which it serves as an alternative, this is not an issue;
however, if one is using MVP as an alternative for a capweighted index and wants both higher returns and a similar
risk profile, this type of approach to constructing an alternative index is problematic with respect to the risk profile.
6
Every security analysis textbook we are aware of (and
most introductory investments textbooks) emphasizes that
return on equity, and the risk associated with ROE, is a
critical fundamental variable that investors should consider
in determining the price they are willing to pay for a stock,
relative to other stocks.
7
It should be noted that in some years (particularly
1963–1967), not all stocks had the necessary five years of
ROE data to compute a mean and variance. (Chow et al.
[2011] also had the same problem for the alternative index
strategies they examined that used fundamental data.) In these
cases, we simply used the median ROE for all stocks that had
the necessary data as the cut-off point. For example, if 600
stocks had complete data, the SRP portfolio was formed using
the top 300 ROE stocks. We also constructed SRP portfolios using all stocks with complete data, up to the top 1,000
market-value stocks, and the results were qualitatively similar
to those reported in Exhibits A1 and A2 in Appendix A. In
general, the measures of SRP returns were slightly higher
using stocks with above median ROEs, but the measures of
volatility were also slightly higher. For example, it turned out
that the average Sharpe ratios (the SRP portfolio excess return
divided by its volatility) were exactly the same (0.42) for both
universes, that is, stocks 1 to 500 and stocks 1 to 1,000. We
used the smaller number of stocks mostly as a measure of
convenience because the process of minimizing a 500 × 500
covariance matrix is obviously much faster than a 1,000 ×
1,000 covariance matrix and less prone to data errors.
8
Personally, it is somewhat disconcerting that a great
deal of financial research is based on inductive logic—that
is, sorting through vast amounts of data, finding historical
correlations, and drawing conclusions based on those correlations—this type of research is precisely where “black swans”
come from.
9
The proxy benchmark for the S&P 500 is the only
index constructed by Chow et al. [2011] using the 500 largest
market-cap stocks, instead of the 1,000 largest market-cap
stocks, and a few of these 500 stocks are not the same as the
actual 500 stocks in the S&P 500. To be consistent with
Chow et al. [2011], we use the same starting universe of
the 500 largest-capitalization stocks at the beginning of each
yearly rebalance period to form a proxy for the S&P 500
benchmark.
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10
Estimating transaction costs is difficult and Chow
et al. [2011] report all of their results before transaction costs.
In other work we have done, for U.S. large-cap stocks we
have estimated transaction costs as 20 basis points one-way,
or 40 basis points round trip. Assuming 40 basis points round
trip transaction cost is reasonable, this will reduce the relative returns for SRP versus FI by about 12 basis points per
year, given the estimated one-way turnover of 38.6% per year
for SRP versus 13.6% per year for FI. Although the return
advantage of SRP relative to FI is reduced after estimated
transaction costs, SRP still dominates after transaction costs
estimated at 40 basis points round trip, which we believe is
conservative.
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