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ETF Arbitrage
Ben R. Marshall* Massey University
Nhut H. Nguyen University of Auckland
Nuttawat Visaltanachoti Massey University
Abstract The prices of S&P 500 ETFs diverge on an intraday basis. This allows arbitrageurs to profit from a pairs trading strategy of going long (short) the underpriced (overpriced) ETF. The divergence does not seem to be driven by well-documented arbitrage risks and is generally removed quickly as rational investors exploit the inefficiency. The compensation these arbitrageurs receive is economically significant. Profits, net of spreads, average 6.7% p.a. over the 2001-2010 period for transactions involving the two US-listed S&P 500 ETFs and are considerably larger for opportunities including the US Dollar denominated Swiss-listed S&P 500 ETF.
JEL Classification: G1, G14 Keywords: Arbitrage, Pairs Trading, ETF
First Version: 23 September 2010 This Version: 16 November 2010
* Corresponding Author: School of Economics and Finance, Massey University, Private Bag 11-222, Palmerston North, New Zealand. Phone: 64 6 350 5799, Fax 64 6 3505651
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1. Introduction
Divergence in S&P 500 ETF prices creates arbitrage opportunities. These appear to be larger
than reasonable estimates of transactions costs, which suggests arbitrageurs exploiting these
deviations earn economic profits as they restore prices to equilibrium. The three ETFs we consider
are the NYSE Arca-listed SPDR Trust (ticker SPY) and iShare (ticker IVV), and the Swiss Stock
Exchange-listed iShare (ticker IUSA).1 All three ETFs are traded in US Dollars. The SPY is more
liquid than any stock or ETF (e.g. Elton et al (2004)) and the IVV is also highly liquid. Annual
profits from simple SPY – IVV arbitrage transactions average 6.7% p.a. and profits from arbitrages
involving the IUSA are considerably larger. Arbitrage opportunities are usually exploited quickly.
The median length of time to removal is less than five minutes for most strategies. Our findings
support the conclusions of Elton, Gruber, and Busse (2004) who show divergent pricing in S&P 500
index funds, which are not exchange traded, persist for long periods because there is no mechanism
for arbitragers to exploit this. We show divergent pricing is exploited relatively quickly in a setting
where arbitragers can remove it.
The term “arbitrage”, which Brealey and Myers (1996, G1) define as the “purchase of one
security and simultaneous sale of another to give a risk-free profit” is often used loosely. Risk is
frequently inherent in exploiting arbitrage. De Long, Shleifer, Summers, and Waldman (1990) note
the actions of irrational “noise” traders create the risk for arbitrageurs that prices will diverge
further rather than converge. Abreu and Brunnermeier (2002, p. 343) highlight that rational
arbitrageurs still face synchronization risk or “uncertainty regarding the timing of the price
correction” even when noise traders are not present. Mitchell, Pulvino, and Stafford (2002, p. 564)
also confirm that “a significant risk faced by an arbitrageur ..... is that the path to convergence can
be long and bumpy.” They refer to this as “horizon risk”. These risks are closely related to the 1 We are also in the process of generating results based on a raft of other S&P 500 ETFs. These include the US-listed short, 2× long, 2× short, 3× long, and 3× short ETFs, and internationally traded S&P 500 ETFs traded in different currencies. Initial results indicate more pronounced parity deviations in these ETFs.
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“margin risk” of Shleifer and Vishny (1997). Leveraged positions may have to be liquidated due to
margin calls before the final convergence occurs. Lui and Longstaff (2004) find it is often optimal
to under invest in arbitrage opportunities due to these risks, which are nicely summarized by John
Maynard Keynes in the statement “the market can stay irrational longer than you can stay solvent.”2
Noise trader, synchronization, horizon, and margin risk, which we shall jointly call
“convergence risk” are minimized in our market setting for a number of reasons. Firstly, the SPY
and IVV compete for investor funds. Their ability to closely track the underlying index is an
important aspect of this so the management of each fund have an incentive to minimize tracking
error. Secondly, as Ackert and Tian (2010) note, institutional investors can exchange each ETF for
the stocks in the underlying index. Larger ETF price divergence creates more incentive for this
activity.3
Another risk of arbitrage is fundamental risk. This refers to the fact that the two assets are
not perfect substitutes or identical in all respects. It is extremely difficult to find assets that are
completely identical. Dual class shares are likely to have different voting rights (e.g. Schultz and
Shive (2010)). Dual listed stocks in different countries are frequently subject to different
institutional features such as liquidity differences and index inclusion in one country (e.g. Froot and
Dabora (1999)). Short-selling constraints in one country may play a role and there may also be “tax-
induced investor heterogeneity” (e.g. Froot and Dabora (1999, p. 215)). While minimized,
fundamental risk does exist in our market setting. The SPY and IVV are both listed on the NYSE
Arca and are both highly liquid. They both have the aim of mirroring the S&P 500 index, but each
ETF will not have identical portfolios of securities at every point throughout the day. However, the
fact that any mispricing of these two ETFs is removed quickly suggests that arbitrageurs view them
as having little fundamental risk. The median time to removal is always less than five minutes for
the different SPY – IVV strategies. We also document that order imbalance increases when 2 http://www.maynardkeynes.org/keynes-the-speculator.html 3 See Engle and Sarkar (2006) and Aber, Li, and Can (2009) for more information. IUSA units can also be redeemed http://www.six-swiss-exchange.com/knowhow/products/funds/valuation_en.html.
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arbitrage opportunities exist. This is consistent with arbitrageurs acting to quickly exploit these
opportunities.
To our knowledge, the rapid removal of arbitrage opportunities is quite different to the
results of other studies on arbitrage in equity markets. For example, Froot and Dabora (1999) show
mispricing in stocks listed in different locations can prevail for over four years4, Mitchell, Pulvino,
and Stafford (2002) show divergence in the price of a parent company and listed subsidiary can last
for over five months5, and Schultz and Shive (2010) show mispricing in class of stock with different
voting rights can persist for two years.6 However, the relatively quick restoration of efficient prices
is consistent with Busse and Green (2002). They show that prices converge to efficient levels
following CNBC reports in one to fifteen minutes depending on whether the report is good or bad
news. Moreover, Chorida, Roll, and Subrahmanyam (2005) find that investors take between five
and sixty minutes to restore prices to efficient levels following order imbalances.
The notion that arbitrageurs can earn profits by returning prices to efficient levels is not
new.7 One of the fundamental assumptions behind the Grossman and Stiglitz (1980, p. 393) model
is that arbitrageurs “who expend resources to obtain information do receive compensation.” Our
contribution is documenting the magnitude and frequency of these opportunities in highly liquid
securities, where the traditional risks of arbitrage are minimized.
So why are arbitrage opportunities between ETFs on the same underlying index created in
the first instance? While not the focus of this paper, we offer two possible explanations. Firstly, the
divergent prices may be due to small differences in the composition of the basket of securities each
ETF uses to track the S&P 500. This may be in the form of differences in the proportion allocated to
a given stock between the funds. As noted in the SPDR prospectus8, the trustees are permitted to
4 See Froot and Dabora (1999) Figure 1 on page 193. 5 See Mitchell, Pulvino, and Stafford (2002) Figure 1 on page 568. 6 See Schultz and Shive (2009) Figure 2 on page 4. 7 We refer to the Jensen (1978) definition of market efficiency which suggests efficient pricing occurs when the benefits from exploiting an inefficiency are not larger than the costs incurred. 8 2010 SPDR Prospectus, page 45. https://www.spdrs.com/product/fund.seam?ticker=spy
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allow a certain amount of “misweighting” between each stock in the SPDR and the S&P 500 index
each day. It is only when the “misweighting” in a stock exceeds 150% of this amount that a re-
balancing is required. There may also be differences in the actual securities held by each fund. The
IVV fund documentation highlights that it uses a “representative index sampling strategy”9. It does
not always hold all 500 stocks of the S&P 500. It is therefore possible that the prices of each ETF
accurately reflect the value of their underlying securities. An alternative explanation is that
irrational investors misprice the SPY and IVV (given the securities they hold) for short periods of
time. In the case of the IUSA, where market makers are responsible for posting two-way quotes,
there can be sizeable deviations (up to 5%) between these and the indicative net asset value of the
S&P 500.10 The potential for large deviations in the prices of ETFs relative to their underlying
indices has been investigated by regulators following the May 6, 2010 “Flash Crash”. As the joint
SEC / CFTC Flash Crash report11 notes, ETFs accounted for 70% of all US-listed securities that
declined by 60% or more. We show that ETFs traded at discounts to the S&P 500 index of in excess
of 10% during the flash crash. ETF price movements were not synchronized which allowed for
large “potential arbitrage opportunities” but we exclude all of these from our sample as many trades
were later reversed by exchanges.
Our paper contributes to a growing literature on arbitrage opportunities across equities.
These strategies, which are variously referred to as “convergence trading”, “pairs trading”, and
“statistical arbitrage” involve exploiting mispricing in equities with different levels of fundamental
risk. Previously mentioned papers include Froot and Dabora (1999), Mitchell, Pulvino, and
Stafford (2002), and Schultz and Shive (2010). The following is an incomplete summary of other
work in this area. Gatev, Goetzmann, and Rouwenhorst (2003) document that a strategy of selecting
“pairs” of stocks according to how much stock prices have moved together in the past and then
implementing a simple trading rule based on daily data generates profits that exceed transactions 9 2010 iShare Prospectus, page 1. http://us.ishares.com/product_info/fund/overview/IVV.htm 10 See Milonas and Rompotis (2010) for more detail. 11 http://www.cftc.gov/stellent/groups/public/@otherif/documents/ifdocs/opa-jointreport-sec-051810.pdf
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costs. Engleberg, Gao, and Jagannathan (2010) add to this work by showing that profits to this
strategy are lower when the initial divergence is due to value-relevant news relating to one of the
stocks and higher when the initial divergence is due to news that affects the liquidity of one of the
stocks. Gagnon and Karolyi (2010) document arbitrage opportunities between foreign stocks and
US listed ADRs at the time foreign markets close for the day. They find the deviations are usually
small, but the divergence can reach extreme levels. Moreover, Hogan, Jarrow, Teo, and Warachka
(2004) provide a framework for testing anomalies based on the principle of statistical arbitrage.
Theoretical work in this area includes Xiong (2001) and Bondarenko (2003).
The remainder of this paper is organized as follows: Section 2 contains a description of our
data and the rules we use to identify divergent prices. Our results are presented in Section 3 and
Section 4 concludes the paper.
2. Data and Arbitrage Identification
We source high-frequency data from the Thompson Reuters Tick History (TRTH) database,
which we access via the Securities Institute Research Centre of Asia-Pacific (SIRCA). TRTH data
are used by academic researchers (e.g. Fong, Holden, and Trzcinka (2010)), central banks, hedge
funds, investment banks, and regulators. More information on TRTH is available at their website.12
We follow Hendershott, Jones, and Menkveld (2010) and limit our analysis to post-decimalization
period of February 2001 onwards. Data for both SPY and IVV are available at this point, but our
IUSA data begins in June 2004. Our sample finishes in August 2010. We use data from the primary
listing venue for each ETF. For the SPY and IVV this was the AMEX prior to its takeover by
NYSE Euronext in 2008 and NYSE Arca following that point. The primary listing of the ISUA is
the Swiss Stock Exchange.
12 http://thomsonreuters.com/products_services/financial/financial_products/quantitave_research_trading/tick_history
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It is clear that the S&P 500 ETFs diverge from the S&P 500 index on an intraday basis.
Figure 1 shows deviations from parity (using one-minute intervals) between the IVV and S&P 500
index during the 1.30pm – 2.30pm period on September 29, 2008. This was a particularly volatile
day of trading so the deviations are larger and more frequent than those on some other days, but this
example does serve to illustrate that the ETFs frequently move from trading at a premium to a
discount versus the S&P 500 index. While the ETF price deviations from the S&P 500 index
depicted in Figure 1 are a necessary condition for arbitrage opportunities to exist they are not
sufficient. For this there needs to be deviations between ETFs that can be exploited. We outline the
algorithm used to test for these arbitrage results below.
[Insert Figure 1 Here]
We adopt the data cleaning approach advocated by Schultz and Shive (2010), which
involves deleting observations with any of the following characteristics:
1. Quotes posted outside normal trading hours.
2. Quotes posted in the first and last five minutes of regular trading.13
3. Bid price greater than or equal to the corresponding ask price for the same ETF.
4. Ask price four times or more larger than the bid price for the same ETF.
5. Bid-bid or ask-ask return for the same ETF is greater than 25% or less than -25%.
6. Bid price SPY / Ask price IVV > 1.5 or bid price IVV / ask price SPY > 1.5.
7. Observations on May 6, 2010, the day of the Flash Crash.14
The description above is based on SPY and IVV but exactly the same comparisons and
observation deletions take place between both SPY and IUSA and IVV and IUSA.15 Criteria 1. and
13 This is broadly consistent with Schultz and Shive (2010) who omit quotes from the first and last four minutes of trading. 14 This day was not in the Schultz and Shive (2010) sample. 15 The IUSA trades in units that represent 10% of the S&P 500 so we multiple this series by 10 to begin with.
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2. mean arbitrage opportunities between the SPY and IVV are able to be opened and closed
between 9.35am and 3.55pm Eastern Standard Time. However, there is typically only a one hour
fifty overlap between 9.35am Eastern Standard Time and 5.25pm Central European Time, which is
five minutes before the IUSA finishes trading for the day on the Swiss Stock Exchange.16 In our
paper, arbitrage opportunities involving the IUSA are limited to this period. It is quite possible that
arbitrage opportunities are, in reality, able to be opened and closed during these periods so the
imposition of 1. and 2. above leads to conservative results, which are likely to understate the
number of opportunities and average size of the profits and overstate the time an arbitrageur has to
wait before closing the position. Our assumption that trades only take place at the firm quotes in the
market is also conservative. As Schultz and Shive (2010) note, NYSE trades frequently occur at
better prices. There are approximately 553 million SPY quotes, 220 million IVV, and 1.7 million
IUSA quotes during the trading hours outlined above that pass our data cleaning process. This
represents approximately 36,000, 14,000, and 600 quotes per hour for the SPY, IVV, and IUSA
respectively.
Our profit results are very close to being “net profits.” The spread is accounted for and
market impact costs are minimal for most traders with such highly liquid instruments. The only
remaining execution costs appear to be commissions and short-selling costs, which are typically
ignored in the pairs trading literature. Goldstein, Irvine, Kandel, and Wiener (2009) show the
average one-way commission has declined over time to less than five cents per share in 2004. These
have declined further since this point with 2010 NYSE documentation stating commissions of 0.15
– 0.3 cents per share for those with direct access to NYSE Arca.17 Moreover, D’Avolio (2002)
estimate that S&P 500 stocks can be borrowed at less than 0.25% per annum, or approximately
0.0007% per day. Given these minimal costs, we suggest that the profits we document are close to
the actual profits large hedge funds / institutions could earn by exploiting these arbitrage
16 This is fifty minutes and two hours fifty minutes for small periods when day light saving periods do not align. 17 http://www.nyse.com/pdfs/NYSE_Arca_Marketplace_Fees_11_5_2010-Clean.pdf
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opportunities. However, we apply a profit threshold of 0.2% as a conservative measure to ensure
our sample is not dominated by the numerous smaller divergences.
The speed at which orders can be executed has declined over time. Bacidore, Ross, and
Sofianos (2003) find that the average order-to-execution time for NYSE orders in 1999 was 22.5
seconds. Garvey and Wu (2009) document a mean (median) execution time of 12 (4) seconds for
the 1999-2003 period. Hendershott and Moulton (2009) show execution times declined to less than
one second in 2006/2007 and Hasbrouck and Saar (2010) find some traders now react to market
events within 2-3 milliseconds. However, we take the conservative approach and assume the orders
take 15 seconds to be executed. For quotes to be included as valid quotes, both ETF quotes need to
have been updated in the last five minutes. Our algorithm, which we explain in terms of the SPY
and IVV, but is identical when the IUSA takes the place of either SPY or IVV, is as follows:
1. If bid SPY / ask IVV ≥ 1.002 or bid IVV / ask SPY ≥ 1.002 a potential arbitrage opening
trade is identified.
2. The actual arbitrage opening trade is opened at the first set of quotes for each ETF that
appear 15 seconds after the potential opening arbitrage trade is identified. We assume that
conditional limit, “fill or kill” orders are used that equate to a minimum opening profit of
0.2%.
3. In the case of the short SPY / long IVV trade, SPY ask and IVV bid prices are monitored.
When a situation of IVV bid / SPY ask ≥ 1 is observed a potential arbitrage closing trade is
identified. If a short IVV / long SPY trade was opened IVV ask and SPY bid prices are
monitored and a potential arbitrage closing trade is identified when SPY bid / IVV ask ≥ 1.
If 0.2% profit has been secured when the trade is opened we assume an arbitrageur is happy
to close the trade at prices that do not result in further profit.
4. The actual arbitrage closing trade occurs at the first set of quotes for each ETF that appear
15 seconds after the potential closing arbitrage trade is identified. We again assume that
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conditional limit, “fill or kill” orders are used that equate to a minimum closing profit of
0.2%.
We also test scenarios where an arbitrageur requires an opening profit of 0.3% and 0.4% and
is happy taking a closing loss of up to 0.1% and 0.2% respectively to leave overall profits of 0.2%
or more. These two strategies require less than total price convergence for arbitrages to be closed so
are likely to be able to be closed more quickly.
An example of an arbitrage opportunity included in our results is provided in Figure 2. At
14.40 on November 11, 2002, the bid price of the SPY was $84.08 and the ask price of the IVV was
$83.82. These prices prevailed for 15 seconds so we assume an arbitrageur could sell at the SPY bid
and buy at the IVV ask and lock in profit of 0.31% (84.08 / 83.82 – 1), which is realized at
convergence. The arbitrageur is now long the IVV and short the SPY. She maintains this position
until 15.06 when the IVV bid and SPY ask converge at 83.50 for a period longer than 15 seconds.
At this point, positions are closed at no further profit or loss, leaving overall profits of 0.31%. It is
important to note that this percentage profit calculation (and all others in this paper) implicitly
assumes that opening capital equivalent to the size of the long position is required. In reality,
proceeds from the short position could be applied to finance the long position so the net opening
would be substantially lower. The percentage profit numbers we report are therefore conservative.
[Insert Figure 2 Here]
3. Results
Profit results for our basic and alternative scenarios are presented in Table 1. All three
strategies identify arbitrage opportunities with profits of 0.2% and larger. The base strategy requires
divergence between the bid price of ETF 1 and the ask price of ETF 2 of at least 0.2% for a trade to
be opened and the bid price of ETF 2 to be equal to or greater than the ask price of ETF 1 for a trade
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to be closed. The second and third strategies require profits of 0.3% and 0.4% respectively for
trades to be opened and convergence equating to losses of no more than -0.1% and -0.2%
respectively for trades to be closed. Each arbitrage is opened and closed within normal trading
hours (excluding the first and last 5 minutes of trading) at quotes that prevail 15 seconds after each
of the criteria are met. We measure the yearly returns an arbitrageur would make over the February
2001 – August 2010 period for the SPY and IVV and the June 2004 – August 2010 period for
opportunities involving the IUSA. These returns are simply the sum of all profits within a year. We
assume an arbitrageur invests the same capital in each opportunity rather than reinvest the profits. In
Table 1 we report summary statistics for the yearly profits and the average number of opportunities
there are per year. Our results are very conservative as we only consider arbitrages generated with
quotes posted in normal trading hours (excluding the first and last five minutes). In reality
arbitrageurs could exploit divergent quotes after-hours and improve their profitability.
Average yearly profits to an arbitrageur applying the base pairs trading rule we document
earlier on the SPY and IVV over the 2001 – 2010 period are 6.67%. This mean return is generated
by an average of 20 opportunities per year. Profits of 19.70% could have been made in 2002 due to
the large number of opportunities (63). Mean profits decline to 4.74% and 4.05% respectively when
the 0.3% / -0.1% (opening / closing) and 0.4% / -0.2% thresholds are applied. The profits to each
opportunity within the alternative strategies are, on average, larger but there are fewer arbitrages to
be exploited. The results for each of the three strategies are not mutually exclusive. If an instance of
arbitrage has a profit 0.5%, it will appear in each scenario.
The Panel B and C results indicate profits are considerably larger when strategies involving
the IUSA are considered. More opportunities are generated each year on average. There are an
average of 45 and 31 per year for the SPY – IUSA and IVV – IUSA base strategies respectively
compared to just 20 for the SPY – IVV. This is despite there only typically being a 1 hour 50
minute overlap period we use between the US and Swiss markets. The cross-border arbitrage
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opportunities are not only more frequent, they are also more profitable. While there are just over
double the number of opportunities between the SPY – IUSA compared to the SPY – IVV, mean
yearly profits are 28.91% compared to 6.67%. Average yearly profits for the IVV – IUSA of
24.13% are also considerably larger than those for the SPY and IVV. It is also noticeable that there
is less of a decline in the Panel B and C results when the threshold for opening a arbitrage
transaction is increased to 0.3% and 0.4%. Mean profits for these thresholds also remain a lot closer
to those for the base case of 0.2% / 0.0% than they did in Panel A. Taken together, the results
suggest there is a relatively higher proportion of higher profit results in arbitrage transactions
involving the IUSA.
[Insert Table 1 Here]
The Table 2 results are by transaction. From Panel A it is clear that opportunities that are
exploited by long SPY / short IVV and long IVV / short SPY trades are almost equally likely (98
versus 104). The mean profits are also very similar (0.34% versus 0.32%). There are more instances
of long SPY / short IVV arbitrages when either the 0.3% / -0.1% or 0.4% / -0.2% rules are applied,
but the mean profits are similar to their long IVV / short SPY equivalents. This suggests both ETFs
become over (under) valued by similar amounts during the ten-year period. Profits are higher when
the 0.3% and 0.4% opening thresholds are applied, but this higher limit results in fewer
opportunities.
As documented in Table 1, arbitrage opportunities involving the IUSA are more prevalent
than those limited to the SPY and IVV. While the total numbers are similar in Panels B and C to
Panel A, there are three years less data for the IUSA so the total number per year is considerably
higher in Panels B and C. The difference in total numbers per hour even more pronounced given we
typically only use a 1 hour 50 minute period (the exchange opening overlap) in Panels B and C.
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Average profits per transaction for the base 0.2% / 0.0% strategy are 0.70% and 0.68% for SPY –
IUSA transactions and 0.80% and 0.75% for IVV – IUSA transactions. Each of these are double the
0.34% and 0.32% profits reported for the SPY – IVV. There are more long IUSA / short IVV
arbitrage opportunities when the 0.4% / -0.2% rule is applied rather than the 0.2% / 0.0% rule (142
versus 127). At first glance this seems counterintuitive. How can a stricter rule result in more
opportunities? The answer lies in the shorter length of time arbitrage trades are open for on average
and our rule preventing multiple arbitrages in the same ETF pair being opened at the same time.
The 0.4% / -0.2% only requires prices to move to within 0.2% of complete convergence for trades
to be closed. This happens more quickly on average, which allows other opportunities to be opened.
The Appendix 1 results show there is no consistent trend of profits being dramatically higher
at the beginning of the day for SPY – IVV arbitrages. However, it does appear as if the most
profitable opportunities involving the IUSA occur within the first 25 minute period of 9.35 – 9.59
a.m. EST.18 There is no trend of the profits of opportunities involving the IUSA declining over time.
However, there have been few opportunities involving the SPY and IVV in the last two years.
[Insert Table 2 Here]
Table 3 includes two types of durations. The first “duration of profit opportunities” refers to
the length of time that divergent quotes allowing arbitrage profits persist for. For the 0.2% / 0.0%
strategy this is the length of time that quotes allow for opening profits of 0.0% or greater. For the
0.3% / -0.1% the threshold is 0.1%. Since the rule involves closing positions at up to 0.1% less than
total convergence, the arbitrageur needs a minimum of 0.1% divergence before opening a position
to ensure overall profit of not less than 0%. Once the quote divergence declines below this level the
profit opportunity is assumed to have finished. The 0.4% / -0.2% scenario has a threshold of 0.2%. 18 The overlap period we consider, which excludes the first and last five minutes of trading of the US and Swiss market respectively is typically 1 hour and 50 minutes (09.35 EST – 11.25 EST), but it can be as long as 2 hours and 50 minutes (09.35 EST – 12.25 EST) when day light savings changes are not aligned.
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Each duration is measured as time in addition to the 15 second delay that is imposed once the
arbitrage opportunity is first identified. This ensures that it is a conservative indication of the length
of time an arbitrageur has to actually exploit the opportunity. The second duration is “duration of
open positions.” This is the length of time between arbitrage positions being opened and closed.
The duration of profit opportunities are lower than the equivalent duration of open positions. By
definition a profitable arbitrage opportunity has to be removed before an arbitrage can be closed
assuming spreads are positive. For instance, when the SPY trades at a sufficient premium to the
IVV an arbitrageur will open a short SPY / long IVV position at the SPY bid and IVV ask. The
profitability of this strategy will be removed once the SPY bid equals the IVV ask. The time this
takes is “duration of profit opportunities”. However, an arbitrageur needs to close their position by
buying the SPY at the ask and selling the IVV at the bid. They cannot do this until these two prices
converge. The time this takes is what we term “duration of open positions”. It is worth emphasizing
that the duration of open position numbers are conservative as we limit our analysis to quotes
posted within normal trading hours (excluding the first and last five minutes of trading). In reality
arbitrageurs could close out their positions using after-hours quotes and this would reduce the
duration.
The divergent pricing which creates the arbitrage opportunities is removed relatively
quickly. There are some outlier observations which inflate the mean duration of profit opportunities,
but even with these included the overall mean duration across all Table 3 scenarios is just over ten
hours. Arbitrage opportunities involving long SPY / short IVV positions last considerably longer
than other opportunities (means of 27.74 – 44.12 hours). The average of the mean durations across
the other opportunities is less than five hours. Given the outliers, the median results give a better
picture of how quickly arbitrage opportunities are removed. The majority of medians are less than
five minutes and, across each of the strategies, the largest median is just 17 minutes. This sort of
time frame is broadly consistent with other strands of the market efficiency literature. Busse and
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Green (2002) show prices converge to efficient levels in one to five minutes and Chordia, Roll, and
Subrahmanyam (2005) document a return to efficient pricing in five – sixty minutes.
The medians of the six strategies we test involving the SPY and IVV are lower on average
(2.19 minutes) than those of six strategies involving the SPY and IUSA (2.58 minutes) and IVV and
IUSA (6.52 minutes). It seems reasonable to expect arbitrageurs to react more quickly when
opportunities present themselves within one market (i.e. SPY – IVV opportunities), but the fact that
cross-border opportunities have such low medians appears to be an indication of just how prevalent
cross-border arbitrage is in S&P 500 ETFs. Busse and Green (2002) find that mispricing that
requires short-selling to be exploited persists for longer than when a long position can remove it.
The fact that durations are similar in our setting regardless of which ETF is sold short indicates that
short-selling constraints are not a major factor in any of the ETFs we consider.
The Panel A results indicate the duration of open positions are considerably lower for long
IVV / short SPY transactions than long SPY / short IVV transactions. There is noticeable positive
skewness, however the median duration for the base 0.2% / 0.0% long IVV / short SPY arbitrages is
0.39 hours or 23 minutes. The equivalent median for long SPY / short IVV arbitrages is 85 minutes.
Open positions can be closed more quickly under the 0.3% / -0.1% and 0.4% / -0.2% strategies.
Under the latter the requirement of less than complete convergence results in median durations
dropping to 10-12 minutes. Long SPY / short IUSA arbitrages are closed quickly. The median
duration of open positions for the base strategy is just 17 minutes. On the other hand, long IUSA /
short SPY arbitrage opportunities take a median of 72 hours to be closed. Both these times decline
when the modified strategies which require less than complete convergence are applied. A similar
theme of disparity in durations between long and short IUSA positions is evident in opportunities
involving the IVV. Median durations are just 3 minutes when long IVV positions are taken yet the
median increases to 192 hours when arbitrages require short IVV positions.
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[Insert Table 3 Here]
We now turn our attention to considering market characteristics before each arbitrage
opportunity is created and during each arbitrage opportunity and comparing these to other periods.
The time period before an arbitrage opportunity is created (“before”) is the 30 minute prior period.
“During” is the period between an arbitrage position being opened and closed. We calculate a range
of variables across one-minute intervals. The first is Order Imbalance, which is the absolute value
of the difference between the value of buy transactions and sell transactions divided by the sum of
these two values. We measure the absolute value as the order imbalance could be from either the
buy side or sell side of the order for each of ETF pairs. A high value for Order Imbalance indicates
a one-sided market, where as a low value close to zero indicates little order imbalance. Our second
measure is Ln(Value). This is the natural logarithm of total value of trades in both ETFs. Volatility
is the squared one-minute mid-point return. Spread is the average relative spread within each one-
minute interval.
We run the regression specified below over all one-minute intervals:
Market_Characteristict = αt + β1*DBefore,t + β2*DAfter,t + Controls + εt
where:
Market_Characteristict = each of the four market characteristics.
DBefore = 1 if the one-minute interval is 30 minutes or less before an arbitrage opportunity
DAfter = 1 if the one-minute interval during an arbitrage opportunity
Controls = time of the day dummy variables and 10 lags of the Market Characteristic
17
The “Before” and “During” columns in Table 4 contain the increases / decreases in each
variable in these periods respectively over the level of that variable in other (non before or during)
periods and associated t-statistics in parentheses. We also report the results to F-test (p-values in
parentheses) pertaining to the null hypothesis that the before and during coefficients are equal. The
Table 4 results indicate order imbalance increase when arbitrage opportunities are present in each of
the three ETF pairs. This appears to be consistent with our earlier finding of arbitrage opportunities
being removed relatively quickly on average. Arbitrageurs seem to actively exploit opportunities as
they arise. Arbitrage opportunities appear to exist in relatively illiquid times in the ETFs. The value
of trades is consistently lower in the During period and the spread is higher in SPY – IVV pair.
Volatility is elevated when arbitrage profits are available in the SPY – IVV pair but there is no
evidence of this in the other two pairs.
There is strong evidence that order imbalance is atypical in the Before period for SPY – IVV
arbitrages. This indicates that a one-sided market in at least one of the ETFs creates the
environment for the arbitrage opportunity. However, this result is not consistent across the other
pairs. None of the other market characteristics are consistently different in the Before period to
unconditional periods either, which leaves somewhat of a puzzle in terms of what leads to these
opportunities being generated in the first instance.
Divergent pricing in ETFs has recently captured the attention of regulators. The May 6,
2010 “Flash Crash” has been the catalyst for regulators to look at the reasons behind ETF pricing
deviations from the indices they seek to mirror. In their joint report19, the SEC and CFTC note that
ETFs made up 70% of all US-listed securities that plunged 60% or more on May 6. The SEC /
CFTC report suggests that one explanation for this might be institutions using ETFs as a quick way
of reducing market exposure. Another possible explanation is the use of stop-loss market orders in
ETFs by individual investors. Borkovec, Domowitz, Serbin, and Yegerman (2010, p. 1) suggest that
19 The report is entitled “Preliminary Findings Regarding the Market Events of May 6, 2010” and is available here: http://www.cftc.gov/stellent/groups/public/@otherif/documents/ifdocs/opa-jointreport-sec-051810.pdf
18
the failure in ETF price discovery during this event was due to “an extreme deterioration in
liquidity, both in absolute terms and relative to individual securities in the baskets tracked by the
funds.”
We plot the deviations of the SPY and IVV from the level of the S&P 500 index at one-
minute intervals during the 2.30pm – 3.30pm period on May 6, 2010 in Figure 3. Numbers greater
(less) than zero indicate the ETF is trading at a premium (discount). The black bars represent the
total SPY variation and the entire white bar (including the black portion) represents the IVV
variation. Figure 3 makes it clear that the IVV was more affected than the SPY. Its deviations from
parity range from +4% to -10%. It is also evident that the ETFs change from trading at a large
premium one minute (2.45pm) to a large discount the next minute (2.46pm). On one occasion
(2.49pm) the SPY is trading at a premium of over 2% and the IVV is trading at a discount of more
than -2%. As mentioned previously, we do not include any observations from May 6, 2010 in our
formal analysis.
[Insert Figure 3 Here]
4. Conclusions
The prices of S&P 500 ETFs diverge on an intraday basis. Arbitrageurs who exploit these
deviations in the two US-listed ETFs using a pairs trading strategy of selling (buying) the over
(under) priced ETF would have earned average annual profits of 6.7% over the 2001 – 2010 period.
Considerably larger profits would have been earned if the same strategy had been applied to the US
Dollar denominated Swiss-listed S&P 500 ETF. The profits we document in these highly liquid
securities account for the bid-ask spread and appear not to be fully explained by traditional limits to
arbitrage. Arbitrage opportunities tend to be exploited quickly. The median time until profit
19
opportunities disappear is typically less than five minutes. It takes longer for an arbitrageur to close
their open positions because an arbitrageur who entered a long SPY / short IVV position at the SPY
ask (IVV bid) has to wait for the SPY bid and IVV ask prices to converge before they can close
their positions. An arbitrageur exploiting long IVV / short SPY opportunities has positions open for
a median time of just 23 minutes. Other arbitrages take longer to converge, but unlike many
settings, the divergences do not last for months and years. This suggests that noise trader /
synchronization / horizon / margin risk is not a major factor in our setting. The reasonably rapid
convergence also implies that ETFs on the same underlying index are seen as perfect substitutes for
each other. Fundamental risk does not appear to be pervasive. In summary, our results provide
support for the Grossman and Stiglitz (1980) proposition that arbitrageurs receive compensation for
obtaining information and restoring prices to equilibrium.
During the May 6, 2010 Flash Crash a disproportionate number of ETFs were among those
securities that experienced the largest price declines. The prices of ETFs also temporarily diverged
by large amounts (greater than 10%) from their “true value” based on the indices they track. This
point has not been missed by regulators, such as the SEC, who have investigated why this occurred.
There are many extensions to our core finding, which we are in the process of investigating.
Investors now have access to a short (inverse) S&P 500 ETF, 2×, and 3× leveraged ETFs, and
inverse 2×, and 3× leveraged ETFs. Our initial (as yet unreported) results suggest even more price
divergence in these instruments. S&P 500 ETFs are also traded in different currencies in a range of
countries. These provide more fertile ground to test ETF arbitrage on and we are actively pursuing
this. Our setting is unique in that we know what the “fundamental value” of S&P 500 at each point
in time. We plan to investigate the relation between deviations from this fundamental value in each
ETF and the arbitrage opportunities that are created.
20
References Aber, Jack W., Li, Dan., and Luc Can. (2009). Price volatility and tracking ability of ETFs. Journal
of Asset Management, 10, 210-221. Abreu, Dilip and Markus K. Brunnermeier. (2002). Synchronization risk and delayed arbitrage.
Journal of Financial Economics, 66, 341–360 Ackert, Lucy F. and Yisong S. Tian. (2000). Arbitrage and valuation in the market for Standard and
Poor's Depositary Receipts. Financial Management, 29(3), 71-87. Bacidore, Jeffrey, Ross, Katharine., and George Sofianos. (2003). Quantifying market order
execution quality at the NYSE. Journal of Financial Markets, 6, 281–307. Bondarenko, Oleg. (2003). Statistical arbitrage and securities prices. Review of Financial Studies,
16(3), 875-919. Borkovec, Milan., Domowitz, Ian., Serbin, Vitaly., and Henry Yegerman. (2010). Liquidity and
price discovery in exchange traded funds: One of several possible lessons from the flash crash. ITG Investment Group. http://www.itg.com/news_events/ITG-Paper-LiquidityPriceDiscovery.pdf
Brealey, Richard A. and Stewart C. Myers. (1996). Principles of corporate finance. 5th edition.
McGraw-Hill, New York. Busse, Jeffrey and Clifford T. Green. (2002). Market efficiency in real time. Journal of Financial
Economics, 65, 415-437. Chordia, Tarun, Roll, Richard, and Avanidhar Subrahmanyam. (2005). Evidence on the speed of
convergence to market efficiency. Journal of Financial Economics, 76, 271-292. D’Avolio, Gene. (2002). The market for borrowing stock. Journal of Financial Economics, 66 (2–
3), 271–306. De Long, J. Bradford, Andrei Shleifer, Lawrence H. Summers, and Robert J Waldmann. (1990).
Noise trader risk in financial markets, Journal of Political Economy 98, 703-738.
Elton, Edwin J., Gruber, Martin J. and Jeffrey A. Busse. (2004). Are investors rational? Choices among index funds. Journal of Finance, 59(1), 261-288.
Engle, Robert and Debojyoti Sarkar. (2006). Premiums-discounts and exchange traded funds. Journal of Derivatives, Summer, 27-45.
Engleberg, Joseph, Gao, Pengjie, and Ravi Jagannathan. (2010). An anatomy of pairs trading: the role of idiosyncratic news common information and liquidity. SSRN Working Paper: http://ssrn.com/abstract=1330689
Fong, Kingsley., Holden, Craig., and Charles Trzcinka. (2010). Can global stock market liquidity be
measured? SSRN Working Paper: http://ssrn.com/abstract=1558447
21
Froot, Kenneth. A. and Emil. M. Dabora. (1999). How are stock prices affected by the location of trade? Journal of Financial Economics, 53, 189-216.
Garvey, Ryan and Fei Wu (2009) Intraday time and order execution quality dimensions. Journal of
Financial Markets, 12, 203-228. Gagnon, Louis and G. Andrew Karolyi. (2010). Multi-market trading and arbitrage. Journal of
Financial Economics, 97, 53-80. Gatev, Evan, Goetzmann, William N. and K. Geert Rouwenhorst. (2003). Pairs trading:
Performance of a relative value arbitrage rule. Review of Financial Studies, 19(3), 797-827. Goldstein, Michael A., Irvine, Paul., Kandel, Eugene., and Zvi Wiener. (2009). Brokerage
commissions and institutional trading patterns. Review of Financial Studies, 22(12), 5175-5212.
Grossman, Stanford J. and Joseph E. Stiglitz. (1980). On the impossibility of informationally
efficient markets, American Economic Review 70, 393-408.
Hasbrouck, Joel and Gideon Saar. (2010). Low-latency trading. SSRN Working Paper: http://ssrn.com/abstract=1695460
Hendershott, Terrence., Jones, Charles M., and Albert J. Menkveld. (2010). Does algorithmic
trading improve liquidity? Journal of Finance – Forthcoming. Hendershott, Terrence and Pamela C. Moulton. (2009). Speed and stock market quality: The
NYSE’s hybrid. SSRN Working Paper: http://ssrn.com/abstract=1159773 Hogan, Steve., Jarrow, Robert., Teo, Melvyn., and Mitch Warachka. (2004). Testing market
efficiency using statistical arbitrage with applications to momentum and value strategies. Journal of Financial Economics, 73, 525-565.
Jensen, Michael C. (1978). Some anomalous evidence regarding market efficiency, Journal of
Financial Economics, 6, 95-101.
Lui, Jun and Francis A. Longstaff. (2004). Losing money on arbitrage: Optimal dynamic portfolio choice in markets with arbitrage opportunities. Review of Financial Studies, 17(3), 611-641.
Mitchell, Mark., Pulvino, Todd., and Erik Stafford. (2002). Limited arbitrage in equity markets.
Journal of Finance, 57(2), 551-584. Schultz, Paul and Sophie Shive. (2010). Mispricing of dual-class shares: Profit opportunities,
arbitrage, and trading. Journal of Financial Economics, 98, 524-549. Shleifer, Andrei. and Robert W. Vishny. (1997). The limits of arbitrage. Journal of Finance, 52, 35-
55.
Xiong, Wei. (2001). Convergence trading with wealth effects: An amplification mechanism in financial markets. Journal of Financial Economics, 62, 247–292
22
Table 1 Annual Arbitrage Profits Threshold Average % Profit Statistics (p.a.)
% No. By Year Mean Median Min Max Std Dev
Panel A: SPY-IVV
0.2 / 0.0 20 6.67 4.75 0.00 19.70 6.12 0.3 / -0.1 12 4.74 4.42 0.00 8.81 3.19 0.4 / -0.2 10 4.05 3.73 0.00 9.64 2.93
Panel B: SPY-IUSA
0.2 / 0.0 42 28.91 23.94 9.79 54.68 14.69 0.3 / -0.1 38 28.19 19.14 8.45 58.44 18.79 0.4 / -0.2 34 26.73 15.99 6.73 56.20 20.22
Panel C: IVV-IUSA
0.2 / 0.0 31 24.13 20.67 6.98 52.67 14.95 0.3 / -0.1 30 23.02 18.29 7.60 51.37 14.71 0.4 / -0.2 29 21.34 16.28 6.65 49.23 14.70
This table contains summary statistics for the percentage total profits (assuming no compounding) earned by an arbitrageur each year. SPY – IVV results covers the February 2001 – August 2010 period. Other results span the 2004 – 2010 period. Our data are sourced from the Thompson Reuters Tick History (TRTH) database, which we access via SIRCA. SPY, IVV, and IUSA refer to the, the US-listed SPDR, S&P 500 iShare, and the Swiss-listed S&P 500 iShare respectively. Average No. By Year refers to the average number of arbitrage opportunities per year. Threshold % relates to the three strategies we test. 0.2 / 0.0 requires quote divergence equating to at least 0.2% profit for a trade to be opened and complete convergence (0% profit) for a trade to be closed. 0.3 / -0.1 and 0.4 / -0.2 require quote divergence equating to 0.3% and 0.4% profit, or more, respectively for a trade to be opened and convergence equating to losses of no more than 0.1% and 0.2% respectively when the trade is closed.
23
Table 2 Arbitrage Profits By Transaction Type
Threshold Total % Profit % Number Mean Median Min Max Std Dev
Panel A: SPY-IVV
Long SPY Short IVV 0.2 / 0.0 98 0.34 0.27 0.20 1.87 0.21 Long SPY Short IVV 0.3 / -0.1 80 0.39 0.33 0.21 2.06 0.25 Long SPY Short IVV 0.4 / -0.2 68 0.42 0.36 0.21 2.61 0.31 Long IVV Short SPY 0.2 / 0.0 104 0.32 0.28 0.20 1.27 0.28 Long IVV Short SPY 0.3 / -0.1 41 0.39 0.32 0.22 1.19 0.32 Long IVV Short SPY 0.4 / -0.2 27 0.45 0.39 0.21 1.19 0.39
Panel B: SPY-IUSA
Long SPY Short IUSA 0.2 / 0.0 130 0.70 0.55 0.20 2.99 0.50 Long SPY Short IUSA 0.3 / -0.1 112 0.72 0.58 0.20 2.99 0.52 Long SPY Short IUSA 0.4 / -0.2 89 0.79 0.71 0.21 2.99 0.54 Long IUSA Short SPY 0.2 / 0.0 163 0.68 0.51 0.20 3.74 0.51 Long IUSA Short SPY 0.3 / -0.1 157 0.74 0.55 0.20 3.74 0.55 Long IUSA Short SPY 0.4 / -0.2 151 0.77 0.56 0.21 3.96 0.56
Panel C: IVV-IUSA
Long IVV Short IUSA 0.2 / 0.0 92 0.80 0.64 0.21 2.96 0.57 Long IVV Short IUSA 0.3 / -0.1 69 0.86 0.75 0.22 2.96 0.57 Long IVV Short IUSA 0.4 / -0.2 59 0.90 0.77 0.24 2.96 0.58 Long IUSA Short IVV 0.2 / 0.0 127 0.75 0.58 0.21 3.67 0.58 Long IUSA Short IVV 0.3 / -0.1 140 0.72 0.58 0.20 3.67 0.58 Long IUSA Short IVV 0.4 / -0.2 142 0.68 0.50 0.21 3.67 0.50
The table contains profit summary statistics by opportunity. All other descriptions are as per Table 1.
24
Table 3 Arbitrage Durations By Transaction Type
Threshold Duration of Profit Opportunities Duration of Open Positions % Mean Median Mean Median
Panel A: SPY-IVV
Long SPY Short IVV 0.2 / 0.0 27.74 0.04 429.10 1.42 Long SPY Short IVV 0.3 / -0.1 44.12 0.06 319.62 0.27 Long SPY Short IVV 0.4 / -0.2 39.81 0.05 228.93 0.18 Long IVV Short SPY 0.2 / 0.0 5.43 0.02 35.33 0.39 Long IVV Short SPY 0.3 / -0.1 12.90 0.02 30.89 0.06 Long IVV Short SPY 0.4 / -0.2 8.66 0.03 35.11 0.20
Panel B: SPY-IUSA
Long SPY Short IUSA 0.2 / 0.0 1.15 0.02 35.05 0.29 Long SPY Short IUSA 0.3 / -0.1 1.07 0.02 16.86 0.05 Long SPY Short IUSA 0.4 / -0.2 1.33 0.02 6.21 0.03 Long IUSA Short SPY 0.2 / 0.0 4.03 0.09 190.33 72.04 Long IUSA Short SPY 0.3 / -0.1 3.88 0.07 147.59 71.97 Long IUSA Short SPY 0.4 / -0.2 3.00 0.04 114.27 24.16
Panel C: IVV-IUSA
Long IVV Short IUSA 0.2 / 0.0 0.53 0.02 11.75 0.05 Long IVV Short IUSA 0.3 / -0.1 0.35 0.02 0.81 0.03 Long IVV Short IUSA 0.4 / -0.2 0.40 0.02 0.80 0.03 Long IUSA Short IVV 0.2 / 0.0 12.83 0.29 352.61 192.00 Long IUSA Short IVV 0.3 / -0.1 11.52 0.17 260.88 143.99 Long IUSA Short IVV 0.4 / -0.2 5.88 0.13 198.73 71.99
The table contains summary statistics in hours for the length of time arbitrage profits greater than zero last for. We call this “Duration of Profit Opportunity.” For the 0.2% / 0.0% rule this is the length of time until quote divergence declines to a point where profits greater than 0% are no longer available. For the 0.3% / -0.1% (0.4% / -0.2%) rules this is the length of time that quote divergence leading to profits of greater than 0.1% and 0.2% respectively remain for. The mean and median length of time arbitrage positions are “open” for is also documented. All other descriptions are as per Table 1.
25
Table 4 Market Characteristics Before and During Arbitrage Opportunities
Before During F-Test
Panel A: SPY-IVV
Order Imbalance 3.62 4.38 0.41 (3.15) (15.37) (0.52)
ln(Value) 0.02 -0.37 32.57 (-0.47) (-9.84) (0.00)
Volatility 0.21 0.49 3.49 (-1.46) (26.73) (0.06)
Spread 0.03 0.14 11.94 (1.24) (6.85) (0.00)
Panel B: SPY-IUSA
Order Imbalance 11.80 14.43 0.11 (1.56) (5.80) (0.74)
ln(Value) -0.54 -1.30 3.86 (-1.65) (-5.63) (0.05)
Volatility 0.43 -0.99 0.36 (0.19) (-1.32) (0.55)
Spread 0.23 -0.06 1.9 (1.74) (-0.37) (0.17)
Panel C: IVV-IUSA
Order Imbalance -6.15 8.27 0.82 (-0.39) (5.88) (0.37)
ln(Value) 0.03 -1.43 7.88 (0.06) (-11.22) (0.01)
Volatility 3.30 -0.18 2.36 (1.48) (-0.49) (0.12)
Spread -0.85 0.14 27.33 (-6.04) (1.08) (0.00)
This table contains regression results for four market characteristics. The first number is the percentage that the market characteristic is higher or lower in the Before or During period than its unconditional level. The Before period is the 30 minutes prior to an arbitrage opportunity being created. The During period is when an arbitrage is open. The numbers in parentheses in the Before and During columns are t-statistics. The F-Test column contains the F Statistic (and p-value in parentheses) for the test of the null hypothesis that the coefficients of each characteristic are equal between the Before and During periods.
26
Figure 1 IVV Deviations from the S&P 500, September 29, 2008
Deviations from parity between the IVV and S&P 500 during one-minute intervals on 29 September 2008. Numbers greater (less) than zero indicate the IVV is trading at a premium (discount).
‐1.25%
‐0.75%
‐0.25%
0.25%
0.75%
1.25%1:30
p.m
.
1:40
p.m
.
1:50
p.m
.
2:00
p.m
.
2:10
p.m
.
2:20
p.m
.
2:30
p.m
.
27
Figure 2 Arbitrage Example November 11, 2002
An arbitrage that was opened at 14.40 by selling (buying) the SPY (IVV) at the bid (ask) and closed at 15.06 by selling (buying) the IVV (SPY) at the bid (ask). Profit of 0.274% was realized from this trade.
83.20
83.40
83.60
83.80
84.00
84.20
84.40
14.30
14.31
14.32
14.33
14.34
14.35
14.36
14.37
14.38
14.39
14.40
14.41
14.42
14.43
14.44
14.45
14.46
14.47
14.48
14.49
14.50
14.51
14.52
14.53
14.54
14.55
14.56
14.57
14.58
14.59
15.00
15.01
15.02
15.03
15.04
15.05
15.06
15.07
15.08
15.09
15.10
SPY‐BID SPY‐ASK IVV‐BID IVV‐ASK
Arbitrage Opened
Arbitrage Closed
28
Figure 3 IVV and SPY Deviations from the S&P 500 During Flash Crash (May 6, 2010)
Deviations from parity between the IVV and S&P 500 and SPY and S&P 500 during one-minute intervals during the Flash Crash on May 6, 2010. Numbers greater (less) than zero indicate the IVV is trading at a premium (discount).
‐12.00%
‐10.00%
‐8.00%
‐6.00%
‐4.00%
‐2.00%
0.00%
2.00%
4.00%
6.00%2:30:00 p.m.
2:35:00 p.m.
2:40:00 p.m.
2:45:00 p.m.
2:50:00 p.m.
2:55:00 p.m.
3:00:00 p.m.
3:05:00 p.m.
3:10:00 p.m.
3:15:00 p.m.
3:20:00 p.m.
3:25:00 p.m.
3:30:00 p.m.
IVV
SPY
29
Appendix 1 Average Profits By Time of Day and Year
Long SPY Short IVV
Long IVV Short SPY
Long SPY Short IUSA
Long IUSA Short SPY
Long IVV Short IUSA
Long IUSA Short IVV
Panel A: Time of Day
9.35-9.59 0.39 0.32 0.87 0.80 0.99 0.99 10.00-10.29 0.33 0.31 1.20 0.38 0.39 0.46 10.30-10.59 0.28 0.32 0.45 0.43 0.46 0.47 11.00-11.29 0.27 0.38 0.34 0.32 0.34 0.54 11.30-11.59 0.33 0.24 0.26 0.92 0.64 0.41 12.00-12.29 0.27 0.27 - 0.31 - 0.36 12.30-12.59 0.22 0.37 - - - - 1.00-1.29 0.26 0.24 - - - - 1.30-1.59 0.39 0.43 - - - - 2.00-2.29 0.32 0.32 - - - - 2.30-2.59 0.53 0.29 - - - - 3.00-3.29 0.39 0.27 - - - - 3.30-3.55 0.24 0.49 - - - -
Panel B: By Year
2001 0.32 0.40 - - - - 2002 0.33 0.31 - - - - 2003 0.31 0.30 - - - - 2004 0.28 0.23 0.74 0.54 0.83 0.52 2005 0.36 0.32 0.48 0.88 0.70 0.77 2006 0.26 0.27 0.51 0.53 0.54 0.48 2007 0.36 0.51 0.73 0.61 0.81 0.85 2008 0.35 0.50 0.90 0.89 0.80 0.96 2009 1.87 - 1.20 0.85 1.47 1.20 2010 - - 0.91 0.77 1.09 1.00
The appendix contains mean arbitrage by time of the day and by year. These relate to the strategy that requires profits of 0.2% or more for a position to be opened and complete convergence for a trade to be closed. Time of the day is New York time. All other descriptions are as per Table 1.
