1. Exploring Index Effects
A look at index and index constituent returns
around rebalancing dates
Tamas Toth, CFA

2. 1
Table of Contents
Introduction.............................................................................................................................................2
Financial Environment.........................................................................................................................2
Principal-agent problem.......................................................................................................................4
Index reconstitution.............................................................................................................................4
Impact on market efficiency.................................................................................................................5
Hypotheses for Index Effects...............................................................................................................5
Data and methodology.............................................................................................................................7
Evaluation of the Index Effect in Canada.............................................................................................7
Data Sources .......................................................................................................................................8
Investigation of the existence of index effect in the SP/TSX Composite ...........................................8
Methodology.......................................................................................................................................8
S&P/TSX Composite...........................................................................................................................9
Eligibility ........................................................................................................................................9
Index and Stock Price Data................................................................................................................10
Cumulative Abnormal Returns...........................................................................................................10
Additions.......................................................................................................................................10
Deletions .......................................................................................................................................12
Findings ................................................................................................................................................13
Extensions.............................................................................................................................................14
Appendix I – S&P/TSX Composite Rebalancing Methodology..............................................................15
Works Cited..........................................................................................................................................16

3. 2
Introduction
Financial Environment
The current dynamics in financial markets made passive investment strategies very attractive for a broad
range of investors. Passive investment strategies provide exposure to a specific market, sector or style by
attempting to replicate the returns of a market index. One of the main drivers of growth in financial assets
is the aging population in developed countries. Figure 1 shows that Canada’s population of 65 years and
over is expected to grow from 14.4 percent in 2011 to 22.8 percent in 2031.
Figure 1 - Canada's Aging Population
Source: http://www4.hrsdc.gc.ca/.3ndic.1t.4r@-eng.jsp?iid=33
As people get older, a larger portion of their total wealth is stored in financial capital (investments) than
in human capital (future income). Figure 2 graphically displays this trend of shifting source of wealth.

4. 3
Figure 2- Source of Wealth in Life's Stages
While this trend supports the growth of all financial assets in the market, there has been a trend that tilted
the growth of passive investments from those of active ones. Passive investments differ from active
investments in that there is no stock-picking or timing ability is expected by the investor. The rationale for
investing in passive funds over actively manages ones is that study after study shows that only very few
active managers can outperform their benchmarks (Walker, 2013). Further, since no active management is
required, fees in passive funds tend to be much lower. Competition and economies of scale have been
driving fees lower every year. While Vanguard has earned the reputation of offering the lowest fees,
Charles Schwab grabbed headlines in September of 2013 by cutting its fees on its US Broad Market ETF
from 6 basis points to 4 bps (Walker, 2013).
Figure 3 - Share of Equity Index Mutual Funds over Time

5. 4
Source: http://www.icifactbook.org/pdf/2013_factbook.pdf
Figure 3 shows the rise of the share of equity index mutual funds in the United States (Investment
Company Institute, 2013). The trend has been study in growth of passive funds from 1998 to 2007, but a
significant jump can be observed in 2008.
The financial crisis of 2008 prompted many investors to re-evaluate their investment portfolios and the
returns they were receiving (or not receiving) for the fees they were paying for active management.
Confirming the trend in Figure 3, Lipper also reported that since 2004, assets held in passive funds –
excluding ETFs – as a portion of all equity products increased from 12 percent to 21 percent (Walker,
2013). This trend resulted in the doubling of assets held in passive investment funds over the past four
years, ending 2013 with $1.3 trillion of US investors’ assets (Walker, 2013). In 2013 specifically a record
$115 billion has been piled into index mutual funds, which is nearly 4 times the $38.3 billion invested in
actively managed funds (Condon, 2014).
Principal-agent problem
The financial crisis not only reminded investors of the high costs they were paying for no apparent
superior performance, but also of the lack of downside protection active investors are supposed to provide
their investors. There have been multiple studies exploring the principal-agent problem in the money
management framework. One way investors can overcome this issue is to constrain managerial risk by
tying the performance of the fund to a benchmark. The effectiveness of the manager can then be evaluated
based on the “absolute difference between each month’s index return and the fund return summed over
the time frame in question” (Chen, Noronha, & Singal, 2006), which is referred to as the fund’s tracking
error. By monitoring the tracking error of the fund, the investor can evaluate how well the manager is
performing his mandate.
Index reconstitution
When an investor selects a benchmark they would like to gain exposure to through a passive investment,
they consider the market or style the benchmark is set out to represent. For example, the “S&P/TSX
indices are designed to be both representative of the Canadian equity market and its sectors, and liquid, to
support investment products such as index mutual funds, exchange traded funds, index portfolios, and
index futures and options.” (McGraw Hill Financial, 2013). When the securities included in the index are
no longer the best representation of the market or style, the index has to be reconstituted. Index providers
vary in the ways they maintain their indexes. S&P uses a committee to select the best fitting securities for
their equity indexes, while Russell uses a straight forward methodology to mechanically select its
constituents.
These reconstitution times require passive investment managers to update their portfolios so that their
returns reflect the returns of the updated index, i.e. minimize the tracking error. For institutional clients,
such as large pension fund sponsors, tracking error in excess of 0.10 percent a year is unacceptable (Chen,
Noronha, & Singal, 2006). Research has shown that that the trading volume on the effective date of
reconstitution is several times the normal daily volume, indicating that mangers rebalance their portfolios
on these dates (Honghui, Noronha, & Singal, 2004).

6. 5
Impact on market efficiency
In the semi-strong form of efficient capital markets, current asset prices should reflect all publicly
available information (Fama, Efficient capital markets: A review of theory and empirical work, 1970)
(Fama, Efficient capital markets: II, 1991). Of course, in order for asset prices to reflect all publicly
available information, the public has to react by trading on new information. It is therefore obvious to see
how markets would not follow the semi-strong form of efficient capital markets in the extreme where all
investors are passive investors. Even if this extreme is unlikely to materialize, large allocations to passive
investments may create inefficiencies in the markets.
A case in point for these inefficiencies is the constraint of the tracking error imposed on investment
managers. Since index providers announce the changes to the indexes in advance, but passive managers
will only rebalance their portfolios on the effective date, arbitrageurs can front-run those portfolio
managers.
It has been shown that the inclusion and exclusion of a stock in a benchmark causes abnormal returns to
the involved stocks. For example, the Russell 1000 generate cumulative excess returns of 10.9% from 2
days before the rebalance dates while stocks deleted from Russell 2000 Growth Index suffer cumulative
loss of 6.6% (Chen H.-L. , 2006). This paper will explore hypotheses for these abnormal returns in a later
section.
The combination of large amounts of assets in passive investments and the constraints of the tracking
error introduce inefficiencies, which provide an opportunity for arbitrageurs to transfer wealth from
passive investors to themselves. This wealth transfer has been estimated to cost passive investors
investing in the S&P 500 and Russell 2000 Index between $1.0 billion and $2.1 billion a year (Chen,
Noronha, & Singal, 2006).
This paper aims to explore whether this trading opportunity still exists and the proposed hypotheses for its
existence. Further, it will explore whether this trading strategy can be automated and turned into an
investment vehicle that could be held in combination with passive investments. If such an opportunity
exits, the current financial environment would predict a favorable reaction by the growing number of
passive investors since it would eliminate the above mentioned wealth transfer. Pursuing a business based
on this premise would then be of interest to providers of passive investment strategies.
Hypotheses for Index Effects
Abnormal returns attributable to index reconstitution have come to the attention of the investment
community, both in practical sense by exploiting these inefficiencies and academically by exploring the
reasons for their existence. The following six hypotheses have been proposed in various forms in different
studies, but have been summarized by (Doeswijk, 2005) as follows:
1. Price Pressure Hypothesis
In the price pressure hypothesis, and index revision causes a temporary price pressure, because
traders who are willing to provide liquidity to passive fund managers require a premium for their
services (i.e. liquidity). (Madhavan, 2003) describes the premium required by market makers
with the following expression:

7. 6
Where DesInv is the market makers desired inventory level, Inv is the market makers current
inventory and lambda is the coefficient that’s inversely related to market liquidity. Ultimately,
large deviations from target inventory levels – driven by portfolio rebalancing activities by
passive managers – will command a price that is higher or lower than their intrinsic values.
2. Imperfect substitutes hypothesis (downward sloping demand curves)
As in any microeconomic model, a permanent increase (decrease) in demand for a stock, driven
by its inclusion (exclusion) from an index, will shift the demand curve for that stock to the right
in an environment where there are no close substitutes for that stock. Since tracking error is a
major factor in selecting stocks for the portfolio, perfect substitutes are rare.
Figure 4 - Shifting a downward sloping demand curve
Source:
http://mbaecon.wikispaces.com/Demand+(include+what+is+a+demand+curve+and+what+shifts+a+demand+curve)
The change in price will permanently change as long as investors are required to hold the stock in
their index replicating portfolios. In a joint test, (Chen H.-L. , 2006) finds that In the joint test, the
price pressure hypothesis (1.) and the liquidity hypothesis (3.) explain the marginal index effect at
most by 0.12% and 3.05%, respectively, while the imperfect substitutes hypothesis explains it at
least by 9.21%.
3. Liquidity hypothesis
The liquidity hypothesis postulates that index revisions affect the liquidity of a stock, which in
turns reduces the liquidity premium required by investors. This line of reasoning would result in a
one-time permanent jump in share price. As mentioned in (2.), (Chen H.-L. , 2006) also found
support for this.
4. Information hypothesis

8. 7
The information hypothesis slightly reverses the causality relationship. This explanation states
that the decision to include a stock in a benchmark reflects its improved future potentials, and
therefore should command a higher price multiple. Consequently, while the stock remains in the
index, an investor subscribing to this hypothesis would continue to attach a higher price multiple
and the effect would then be permanent.
5. Attention hypothesis
It is believed that an index reconstitution will receive media attention and that this attention will
ultimately lead to an enlargement of the investor base for the mentioned company. Similarly to
the downward sloping demand curve, the additional demand would lead to a permanently higher
price.
6. Selection hypothesis
Selection hypothesis argues against the previously mentioned ideas, and states that excess returns
due to index reconstitutions are not robust and that the market displays a remarkable degree of
liquidity and substitutability for replacement stocks.
The original motivation for this paper is mostly in line with (1.). Since these hypotheses don’t appear to
be mutually exclusive, the trading strategy focused on exploiting the index effect should focus on trading
around the effective date to maximize the likeliness of profit – by capturing both temporary and
permanent price changes.
Data and methodology
Evaluation of the Index Effect in Canada
A large number of studies focusing on the abnormal returns due to index reconstitution have used popular
indexes such as the S&P 500, Russel 2000 and the MSCI Country Indexes. (Chen, Noronha, & Singal,
2006) define the requirements for an index to be a good target for arbitrageurs as follows:
• Index changes are transparent and known sufficiently in advance of the effective date
• The index is heavily used by passive index funds
• Fund managers are constrained to trade on the effective day by tracking error or other
performance metrics
While the constituents for the S&P 500 are decided by a committee – and therefore a less transparent than
-, it is the index to which the largest amount of assets are indexed to in passive strategies. On the other
hand the Russell 2000 is a prime candidate for index effect trading strategies. The constituents are
decided mainly on market capitalization. The predictability of changes in the Russell 2000 are straight
forward enough that brokerage houses now send reports to their clients on the expected changes to the
index before the reconstitution date. These predictions have been shown to be 90-95% accurate.

9. 8
Accordingly, economically significant trading opportunities can be expected to be traded away by a large
investor base.
In order for this research to be valuable, an index that can reasonably be expected to offer index effect
arbitrage opportunities should be used. The topic of discussion going forward is the S&P/TSX Composite
index for the following reasons:
• Index construction methodology is reasonably transparent (in line with S&P 500). See Appendix I
• The index is broadly accepted as the benchmark representing the Canadian Equity Markets
• Its subindexes are used for specific passive fund mandates
Data Sources
Investigation of the existence of index effect in the SP/TSX Composite
The reliability of the findings in this study is highly dependent on the quality of data used. For this reason,
the following data is sourced from Compustat:
• Historical index constituent data
• Historical share prices and dividends
• Share adjustment factors to adjust for changes in shares outstanding
The historical levels of the index are sourced from Yahoo! Finance. The time period for the study is
between January 1 2010 and February 14 2014.
Methodology
It is common practice to use event studies in the investigation of index effects. This paper will comply
with this practice specifically as outlined in (Glenn V. Henderson, 1990). The outline of this process is as
follows:
1. Define the date upon which the market would have received the news (i.e. addition or deletion
from index)
2. Characterize the returns on the individual companies in the absence of this news
3. Measure the difference between observed returns and “no-news” returns for each firm – the
abnormal returns
4. Aggregate the abnormal returns across firms and across time
5. Statistically test the aggregated returns to determine whether the abnormal returns are
significant a, if so, for how long.
Henderson describes various options for each step outlined above. Specifically the determination of
abnormal returns is of interest in this study. The no-news price in an event will be the daily index return
and the excess return will be defined as the daily return on the stock (including dividends) minus the daily
return for the index. The excess returns are then called market-adjusted returns. While there are more
sophisticated techniques employed in practice to determine excess returns, (Glenn V. Henderson, 1990)
has provided evidence that the power of this technique is comparable to that of the regression-based
methodologies. This technique should therefore be sufficient for our preliminary analysis.

10. 9
Once abnormal returns are calculated, they will be averaged by other observations that are observed on
the same day relative to the event. To understand the pre-event cumulative abnormal returns, a time series
of cumulative returns can be constructed, which is called cumulative abnormal returns (CAR):
Where T is the time of the event and t is all calendar days 40 days before the event.
S&P/TSX Composite
Eligibility
The following criteria have to be met for a stock to be considered for inclusion in the S&P/TSX
Composite (McGraw Hill Financial, 2013).
• Market Capitalization
o Based on the volume weighted average price (VWAP) over the last three trading days
of the month-end prior to the Quarterly Review, the security must represent a
minimum weight of 0.05% of the index, after including the Quoted Market Value
(QMV) of that security in the total float capitalization of the index. In the event that
any Index Security has a weight of more than 10% at any month-end, the minimum
weights for the purpose of inclusion will be based on the S&P/TSX Capped
Composite.
o The security must have a minimum VWAP of C$ 1 over the past three months and
over the last three trading days of the month-end prior to the Quarterly Review.
• Liquidity
o Total number of shares traded at Canadian trading venues in the previous 12 months
divided by float adjusted shares outstanding at the end of the period has to be greater
than 0.5.
• Domicile
o Issuers must be incorporated under Canadian federal, provincial or territorial
jurisdictions and listed on the TSX.
• Timing
o Regular additions and deletions are made during the Quarterly Reviews.
Securities under consideration for addition to or deletion from the index will
be assessed by the Index Committee on the basis of the six-month data
ending the month prior to the Quarterly Review.
o The Quarterly Review months are March, June, September and December.
o All additions, deletions and share changes are effective after the close of trading on
the third Friday of the quarterly month.
o Whenever possible, announcements of additions or deletions of stocks or other index
adjustments are made five trading days before the adjustments are implemented. In
those cases when it is not possible to trade a stock five days after an announcement,

11. 10
the announcement period may be shortened. However, the implementation of an
index adjustment will never be earlier than the market close of the day following the
announcement.
Index and Stock Price Data
The constituent data for the S&P/TSX Composite was acquired from Compustat for the period between
January 1, 2010 and February 14, 2014. During this period 79 stocks were removed and 109 stocks were
added. There were 241 constituents in the index at the end of the period.
105 of the 109 additions and 41 of the 79 deletions took place during the Quarterly Review. The
following analysis will only refer to these additions and deletions when analyzing index effects.
Daily index levels and constituent stock prices were also collected for the same period.
Cumulative Abnormal Returns
Cumulative abnormal returns (CAR) are examined for the stocks that were added or removed during the
quarterly review. A time period of 40 calendar days are used as the CAR window. Day 0 is the effective
day of the rebalance and day -39 is 39 calendar days before the effective date.
Additions
Abnormal returns are calculated for each of the to-be-included stocks based on their relative returns to the
S&P/TSX Composite index. The significance of the abnormal returns is calculated using the Student’s t-
distribution. Based on the sample data the returns on the following days are significant: -10, -20, -21 and -
25.
The abnormal returns on day -10 are expected, because this is the fifth trading day before the index
changes become effective and TSX aims to announce the changes to the index on this date. The abnormal
returns are shown on Figure 5 – Additions Daily AR. Abnormal returns between day -25 and -20 are high
on average and would likely be significant with a larger sample. An optimal trading strategy should
therefore initiate the long positions 25 calendar days before the index rebalance.

12. 11
Figure 5 – Additions Daily AR
Figure 6 – Additions Average CAR
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
9.0%
10.0%
-39 -35 -33 -31 -27 -25 -21 -19 -17 -13 -11 -7 -5 -3

13. 12
Figure 7 - Additions Average CAR per year
Deletions
Similar to the additions, the abnormal returns and the t-statistics for each of the calendar days is shown on
the figure below. An inconsistency in the data is present, because the additions are shown as effective as
of the Monday following the index change announcements, while deletions are effective as of the Sunday
following the announcement. The following days are significant in negative abnormal returns: -6, -10, -
26, -30, -34, -37.
Figure 8 - Deletions Daily AR
-0.1
-0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
-39 -35 -33 -31 -27 -25 -21 -19 -17 -13 -11 -7 -5 -3
2010
2011
2012
2013
-5
-4
-3
-2
-1
0
1
2
3
-5.0%
-4.0%
-3.0%
-2.0%
-1.0%
0.0%
1.0%
2.0%
3.0%
-39 -37 -33 -31 -27 -25 -23 -19 -17 -13 -11 -9 -5 -3 t
average

14. 13
Figure 9 - Deletions Average CAR
Figure 10 - Deletions Average CAR per year
Findings
The study finds that the index effects due to the inclusion or exclusion of a stock in a major index
generates abnormal returns around the date of index reconstitution. Recent data suggest that cumulative
abnormal returns are positive for newly added constituents and negative for dropped constituents for the
40 calendar days leading up to the index reconstitution date. These effects have been shown consistently
for index changes for the years 2010 – 2013.
-0.25
-0.2
-0.15
-0.1
-0.05
0
-39 -37 -33 -31 -27 -25 -23 -19 -17 -13 -11 -9 -5 -3
CAR
CAR
-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
-39 -37 -33 -31 -27 -25 -23 -19 -17 -13 -11 -9 -5 -3
2011
2012
2013

15. 14
Extensions
As outlined in the introduction of the paper, passive investors could benefit from an investment vehicle
that produces the abnormal returns due to index reconstitutions. An extension of this study would explore
the ex-ante trading strategy, which identifies the stocks which are added and removed from the index,
before the announcement is made. The index construction methodology clearly outlines the eligibility of a
stock for the index and the data is mainly publicly available. The most relevant data points are price,
liquidity and relative market capitalization. Adjusting for float introduces some complexities.

16. 15
Appendix I – S&P/TSX Composite Rebalancing Methodology
Rebalancing
The index is reviewed quarterly and all Index Securities that, in the opinion of the Index Committee, do
not meet the Buffer Rules are removed. Added securities, if any, are selected using the Eligibility Criteria.
1. Securities under consideration for addition to or deletion from the index are assessed by the Index
Committee on the basis of the six-month data ending the month prior to the Quarterly Review. The
Quarterly Review months are March, June, September and December. Publicly available information up
to and including the month end preceding the Quarterly Review month, which pertains to shares
outstanding (rounded to the nearest thousand), is considered in the Quarterly Review. Investable Weight
Factor (IWF) updates are only made annually at the September Quarterly Review. All additions, deletions
and share changes are effective after the close of trading on the third Friday of the quarterly month.
For details regarding Investable Weight Factors (IWF) and Float Adjustment please refer to S&P Dow
Jones Indices’ Float Adjustment Methodology available at www.spdji.com.
Securities that the Index Committee determines meet the Eligibility Criteria are added to the index after
the close on the third Friday of the Quarterly Review month.
2. Securities removed from the index as a result of the Quarterly Review are not eligible for re-inclusion
for a period of 12 full calendar months following removal. The Index Committee may, nevertheless, add a
security at an earlier date if, in the opinion of the Index Committee, the issuer’s business has been
substantially restructured.
3. Index Securities that the Index Committee determines fail to meet Buffer Rules are removed from the
index after the close on the third Friday of the Quarterly Review month.
4. A press release is issued to the market within 10 business days after the start of the rebalancing month
announcing the additions and deletions, as well as the new float shares for index calculation.
Frequency. Rebalancings occur quarterly. Intra-quarter changes are made on an as needed basis. Changes
occur in response to corporate actions and market developments. The target announcement period is two-
to-five business days, but exceptions may apply due to unexpected corporate activity.

17. 16
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