1) Index fund rebalancing can impose hidden costs on investors due to liquidity constraints when funds buy or sell large positions in constituent stocks. This impacts funds tracking indexes with high turnover like the Russell 2000 more than the S&P 500. 2) Two competing theories explain this - conventional view says arbitrageurs exploit rebalancing for profit, while counterintuitive view says funds face liquidity constraints due to large demand shocks. 3) Evidence shows longer notification periods before Russell 2000 changes reduces stock-specific costs, supporting liquidity constraints view. Cost impact is much higher for Russell 2000 than S&P 500 due to higher turnover.

1. Arbitrageurs
Rent Seekers & Liquidity Providers
Gaetan Lion
May 2014
1

2. Trading ahead of index fund rebalancing
“… estimated [costs] to be at least 21 to 28 bp
annually for S&P 500 index funds, and at least
38 to 77 bp per year for Russell 2000 funds.”
Wikipedia article on High Frequency Trading
2

3. 3
Annualized net returns over past 1 yr, 5 yr, and 10 yr
1 yr 5 yr 10 yr
Vanguard S&P 500 21.80% 21.15% 7.41%
S&P 500 Index 21.86% 21.16% 7.42%
Vanguard Small Cap Index25.29% 26.80% 9.91%
Small Cap Index* 25.33% 26.74% 9.84%
Yearly operating expenses
Vanguard S&P 500 0.05%
Vanguard Small Cap Index 0.09%
Vanguard Index Funds track the Indices nearly perfectly!
The Small Cap Index consists of:
Russell 2000 through May 16, 2003
MSCI US Small Cap 1750 through January 30, 2013
CRSP US Small Cap Index thereafter

4. 4
This paper is Wikipedia’s source on costs to Index funds.
“Because the cost is suffered by the benchmark index
itself, it will remain hidden from index investors who
simply focus on the explicit fees of index funds and their
performance relative to the index.” pg. 272

5. 5
S&P 500. - 10 to + 10 trading days around
Effective Trading Day

6. S&P 500. Extending horizon to 120 trading days
after Effective Trading Day
6

7. Russell 2000. - 30 to + 10 trading days
7
The above are for stocks that cross only the lower cut-off of the Russell 2000. The
ones crossing the higher cut-off (in-&-out of Russell 1000) are not be affected.

8. Russell 2000 extending horizon to – 50 + 120
trading days
8

9. Two competing theories and solutions
9
Theory/Author(s) Problem Solution
Conventional
Chen (2006)
Gastineau (2002)
The cost impact on
Indexers is solely due
to Arbitrageurs.
No pre-announcement to
eliminate Arbitrageurs
opportunity to extract profits
at index’s costs.
Counterintuitive
Petajisto (2010)
Indexers run into
liquidity constraints
buying or selling large
positions (i.e. 10%) of
stocks.
Make index changes visible
with long pre-announcement
periods to reduce liquidity
constraints and cost to the
index.

10. Petajisto’s Argument
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“If index funds suddenly and unexpectedly rushed out to buy
10% [representative level] of all the shares of a firm [S&P 500
addition], who would sell those shares to them?” For a $10
billion market cap firm, that would be a $1 billion demand
shock that would have a dramatic price impact.
This is why S&P preannounces the index changes five trading
days before the effective day of the change, as they want to
give active traders enough time to get ready to meet such large
demand. Thus, arbitrageurs provide the liquidity to meet
indexers demand.

11. Supporting Petajisto’s position
11
S&P 500, 5 trading day lead time
Russell 2000, 21 trading day lead time
The stock cost impact is a lot lower for the Russell 2000
where traders have a 21 trading day lead time vs. the S&P
500 where they have only a 5 trading day lead time.

12. Measuring impact on S&P 500
12
S&P 500 Addition S&P 500 Deletion Add. & Del.
A B C = A x B A B C = A x B Total
Market Cap* Cost per stock Impact M. Cap* Cost per stock Impact Impact
# out of 500 Impact on S&P 500 # out of 500 Impact on S&P 500 on S&P 500
1990 11 0.1% 3.6% 0.00% 7 0.1% -22.3% -0.02% 0.02%
1991 10 0.1% 9.1% 0.01% 5 0.1% -43.1% -0.03% 0.04%
1992 6 0.1% 3.3% 0.00% 5 0.1% -39.4% -0.02% 0.03%
1993 7 0.1% 5.1% 0.00% 6 0.1% -6.0% 0.00% 0.01%
1994 13 0.2% 6.4% 0.01% 13 0.2% -5.0% -0.01% 0.02%
1995 23 0.3% 8.1% 0.03% 14 0.2% -7.8% -0.01% 0.04%
1996 20 0.3% 7.4% 0.02% 14 0.2% -7.4% -0.01% 0.03%
1997 24 0.3% 11.8% 0.04% 7 0.1% -5.3% 0.00% 0.05%
1998 37 0.6% 12.7% 0.07% 10 0.1% -13.1% -0.02% 0.09%
1999 38 0.6% 10.4% 0.06% 11 0.1% -10.9% -0.01% 0.08%
2000 48 0.8% 14.4% 0.12% 23 0.3% -17.8% -0.06% 0.18%
2001 27 0.4% 4.2% 0.02% 14 0.2% -20.2% -0.03% 0.05%
2002 21 0.3% 7.6% 0.02% 16 0.2% -22.1% -0.05% 0.07%
2003 8 0.1% -1.1% 0.00% 2 0.0% -32.1% -0.01% 0.01%
2004 14 0.2% 4.3% 0.01% 7 0.1% -5.0% 0.00% 0.01%
2005 14 0.2% 4.6% 0.01% 2 0.0% -22.2% -0.01% 0.01%
Weighted Avg. 9.2% 0.048% 10 -15.2% -0.026% 0.074%
Petajisto Avg. 8.8% -15.1%
* GL's estimate

13. Measuring impact on Russell 2000
13
Russell Addition from below Russell Deletion from below Add. & Del.
A B C = A x B A B C = A x B Total
Market Cap Cost per stock Impact M. Cap* Cost per stock Impact Impact
# out of 2000 Impact on R 2000 # out of 2000 Impact on R 2000 on R 2000
1990 284 7.3% 3.5% 0.26% 174 2.3% -3.7% -0.09% 0.34%
1991 403 18.3% 2.2% 0.40% 344 2.3% -6.0% -0.14% 0.54%
1992 439 17.4% -1.6% -0.28% 388 3.8% -7.4% -0.28% 0.00%
1993 344 13.0% 1.0% 0.13% 314 3.9% -3.4% -0.13% 0.26%
1994 462 18.1% -0.4% -0.07% 415 6.4% -3.0% -0.19% 0.12%
1995 363 11.6% 7.0% 0.81% 251 3.9% -3.7% -0.14% 0.96%
1996 413 14.1% -3.5% -0.49% 312 4.8% -10.1% -0.48% -0.01%
1997 436 14.3% 8.0% 1.14% 320 4.7% -7.1% -0.33% 1.48%
1998 427 14.0% -0.1% -0.01% 243 4.2% -5.3% -0.22% 0.21%
1999 412 13.7% 9.6% 1.32% 250 3.9% -7.9% -0.31% 1.62%
2000 546 20.0% 31.0% 6.20% 334 4.8% -5.1% -0.24% 6.44%
2001 501 12.3% 5.6% 0.69% 279 1.8% -5.6% -0.10% 0.79%
2002 382 9.0% 8.5% 0.77% 233 1.9% -10.0% -0.19% 0.96%
2003 283 6.3% 1.1% 0.07% 187 1.6% 5.6% 0.09% -0.02%
2004 310 6.8% -2.0% -0.14% 214 2.5% -1.6% -0.04% -0.10%
2005 206 4.1% 6.0% 0.25% 215 2.1% 1.4% 0.03% 0.22%
Weighted Avg. 5.5% 0.905% 280 -5.1% -0.210% 1.115%
Petajisto Avg. 4.7% -4.6%

14. Different impact estimates over 1990-2005 period
14
GL replication is close to Petajisto’s empirical 2 mth lag strategy
(instead of his calculated estimates). In the 2 month lag strategy,
he uses an Index fund that would rebalance two months later then
the Index, thus avoiding much of the earlier impact on the specific
stocks that are added or deleted.
S&P 500 R. 2000
Petajisto
Empirical a) 2 mth lag strategy 0.09% 1.20%
Calculated b) Abstract conclusion-Low 0.21% 0.38%
Calculated c) Abstract conclusion-High 0.28% 0.77%
Calculated GL replication 0.07% 1.12%

15. The 2 month lag strategy
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With the S&P 500 you can see that the directional gap in cost impact between Additions
and Deletions has dramatically narrowed between the rebalancing trading day vs. 60 days
(42 trading days) later. This shows that waiting out 2 months to rebalance would work.
However, when looking at the Russell 2000, you can’t say the same thing. That spread
has barely moved.

16. Why is impact so much greater on R 2000?
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It is because of the much higher stock turnover.
Avg. stock turnover = Avg. market cap stock additions/Total market
cap + Avg. market cap of stock deletions/Total market cap
S&P 500 R. 2000
A Average stock turnover 0.4% 16.0%
B Median impact per stock addition 6.9% 2.9%
C Median impact per stock deletion -15.5% -5.2%
D = A(B-C) Overall impact on index 0.09% 1.28%

17. How to reduce the cost impact on Index Funds?
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1) Preannouncements with longer lead time to reduce the stock
specific cost (as demonstrated when comparing the 21 trading
days of Russell 2000 vs. 5 trading days of S&P 500);
2) Hold broad-based indices to reduce stock turnover. The Wilshire
5000 has a stock turnover a lot lower than the S&P 500.
3) Use the Russell 1000. This is pretty much an arbitrage free
index. That’s because the stocks that get in or out of the Russell
1000 are traded with the Russell 2000 indexers. There is no
arbitrage opportunity or liquidity constraints here. Petajisto has
documented that for the Russell 1000 the stock specific cost is
essentially 0% (Russell 2000 upper cutoff).