jeff brown, doug crocker stephen foerster · focus on “unconstrained” versus “500,000 shares...
TRANSCRIPT
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Liquidity and Investment Styles
Jeff Brown,Doug Crocker
&Stephen Foerster
October 22, 2007 – Northfield Annual Research Conference
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Motivation and Purpose of Study
Overview of Results
Background
Hypotheses, Data, and Methodology
Results
Conclusions and Implications
Plan of Discussion
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Does size ,i.e., assets under management (AUM), matter?Economies of scale Difficulty of trading large blocks
Need to measure “costs”What is the true cost of trading?Is stock screening based on liquidity necessarily a cost?
Need to consider style of trading & relationship with liquidityInvestment strategyNote: liquidity as measured by trading volume
Original Motivation
Sample of Trading Volume ActivitySource: Wall Street Journal
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Issue Volume Price Chg % Chg
1 EMC Cp (EMC) 70,192,417 $20.91 0.40 1.95
2 iShrRu2000 (IWM) 54,940,853 79.82 -0.52 -0.65
3 USEC (USU) 53,788,050 10.34 0.58 5.94
4 Motorola (MOT) 42,330,388 18.62 0.57 3.16
5 Pfizer (PFE) 39,473,465 24.24 -0.18 -0.74
6 Lowes Cos (LOW) 33,081,927 28.51 -2.04 -6.68
7 Citigroup (C) 32,231,408 46.31 -0.28 -0.60
99 Macys (M) 6,225,600 31.91 -1.04 -3.16
100 SeagateTch (STX) 6,183,000 26.56 0.65 2.51
NYSE Most Active Stocks Tuesday, September 25, 2007 - 6:39 pm ET
Sample of Volume IndicatorsSource: Wall Street Journal
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To better understand stock market liquidity, measured at the individual stock level
Recall: liquidity as measured by trading volume
To better understand its potential impact on stock performance for a variety of well-known investment styles:
Value versus growth, small cap versus large cap, winners versus losers (price momentum)
Limitation: not attempting to measure optimal AUM
Purpose of Study and Limitation
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We uncover monotonic measures for trading volume across the price-to-book and market capitalization variables but not the momentum variable
Portfolio quintiles based on the trading volume: less (more) liquid stocks have lower (higher) returns
Liquidity screen “experiments”: screening out the least liquid stocks may actually improve performance
Overview of Results
SPOILER ALERT!
Background: Liquidity
Definition: “the ability to engage in rapidly trading a large number of securities at a low cost with little impact on market prices”Four dimensions:
Trading costTrading quantityPrice impactTrading speed
If liquidity is “priced” then less liquid stocks require higher gross returns to compensate 8
Background: Performance and AUM
Recall benefits and costs in terms of increased AUM:Economies of scaleDifficulty of trading large blocks
If investment strategy is the same (i.e., identifying undervalued stocks based on some metric), then trading may take longer or be more costlyModify strategy? change the potential universe of investments (e.g., screen out less liquid stocks)?
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Null hypotheses to be tested:
1. “Liquidity is not related to investment styles”
2. “Liquidity-related screens do not affect performance”
Hypotheses
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Ford Equity Research
S&P 500 and “Russell 1000” (i.e., largest 1,000 US stocks based on market cap)
Stock pricesTrading volume: trailing 3-month daily averageOther metrics (e.g., P/B, ROE, EPS growth)
July 1991 to January 2006, monthly, with four sub-periods
Data
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Figure 1: Sub-PeriodsS&P 500 Index
0
200
400
600
800
1000
1200
1400
1600
1991
06…
1991
11…
1992
04…
1992
09…
1993
02…
1993
07…
1993
12…
1994
05…
1994
10…
1995
03…
1995
08…
1996
01…
1996
06…
1996
11…
1997
04…
1997
09…
1998
02…
1998
07…
1998
12…
1999
05…
1999
10…
2000
03…
2000
08…
2001
01…
2001
06…
2001
11…
2002
04…
2002
09…
2003
02…
2003
07…
2003
12…
2004
05…
2004
10…
2005
03…
2005
08…
2006
01…
Sub-periods:1. July 1991 - Dec 19952. Jan 1996 - Aug 20003. Sep 2000 - Sep 20024. Oct 2002 - Jan 2006
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Methodology: Portfolios
Forming quintile portfolios – equally-weighted:S&P 500 (100 stocks in each portfolio)Russell 1000 (200 stocks in each)
Two liquidity measures:Trailing 3-month average daily trading volumeTurnover (annualized volume/shares outstanding)
Two portfolio formation methods:By style (e.g., P/B, size, momentum)By liquidity (e.g., trailing 3-month volume)
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Methodology: Overview(by Tables)
1. Summary statistics of individual stocks in universe2. Trading volume by investment style portfolios3. Returns by volume portfolios4. Regression analysis and significance tests [next slides]5. Summary statistics of “liquidity factor”6. Liquidity screens simulations [next slides]7. Liquidity screen simulations: further investigation
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Methodology: Regressions
Regression analysis:
rit - rft = ai + biRmRft + eit CAPM
rit - rft = ai + b1RmRft + b2SMBt + b3HML + eit Fama-French
where rit = return on Q1 (low volume portfolio)…return on Q5 (high volume portfolio)
Significant?
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Methodology: Simulations
Unconstrained long/short portfolio returns:PB: Value/growthSize: Small cap/large capMomentum: Winners/losers
Constrained returns – screen out stocks based on minimum liquidity:
Liquidity as measured by trailing trading volume
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Figure 2a: S&P 500 Stocks Volume(average daily trading volume in 100s of shares)
0
20,000
40,000
60,000
80,000
100,000
120,000
140,000
160,000
180,000
1991
0719
9202
1992
0919
9304
1993
1119
9406
1995
0119
9508
1996
0319
9610
1997
0519
9712
1998
0719
9902
1999
0920
0004
2000
1120
0106
2002
0120
0208
2003
0320
0310
2004
0520
0412
2005
07
AllQ1Q2Q3Q4Q5
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Figure 2b: Russell 1000 Stocks Volume(average daily trading volume in 100s of shares)
0
20,000
40,000
60,000
80,000
100,000
120,000
1991
07
1992
02
1992
09
1993
04
1993
11
1994
06
1995
01
1995
08
1996
03
1996
10
1997
05
1997
12
1998
07
1999
02
1999
09
2000
04
2000
11
2001
06
2002
01
2002
08
2003
03
2003
10
2004
05
2004
12
2005
07
AllQ1Q2Q3Q4Q5
Table 1: Summary Statistics1991-2006
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S&P 500 Russell 1000Price-earnings ratio (x) 20.42 26.20Price-book ratio (x) 5.03 5.40Return on equity (%) 19.16 17.94Earnings per share 5-yr ann growth (%) 3.83 6.181-month return (%) 1.16 1.103-month return (%) 3.48 3.326-month return (%) 6.80 6.4912-month return (%) 13.74 13.22Market cap ($mil) 15021.66 10696.72Shares outstanding (mil) 524.67 393.91Share price ($) 29.45 30.473-month avg daily volume (mil shs) 2.722.72 1.911.91Turnover (x) 1.37 1.42
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Table 2a: Trading Volume by Investment Style(average daily trading volume in 100s of shares)
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Table 2b: Trading Volume by Investment Style(average daily trading volume in 100s of shares)
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Table 3a: 12-Month Returns(Q1 is smallest volume portfolio and Q5 is largest)
Sub-periods:1. July 1991 - Dec 19952. Dec 1995 - Aug 20003. Aug 2000 - Sep 20024. Sep 2002 - Jan 2006
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Table 3b: 12-Month Returns(Q1 is smallest volume portfolio and Q5 is largest)
Sub-periods:1. July 1991 - Dec 19952. Dec 1995 - Aug 20003. Aug 2000 - Sep 20024. Sep 2002 - Jan 2006
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Table 4a: Regression Analysis(Liquidity portfolios and Fama-French model)
*significant
rit - rft = ai + b1RmRft + b2SMBt + b3HML + eit
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Table 4b: Regression Analysis(Liquidity portfolios and Fama-French model)
*significant
rit - rft = ai + b1RmRft + b2SMBt + b3HML + eit
Table 5: Liquidity Factor(highest minus lowest volume quintile monthly returns)
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S&P 500 Russell 1000Summary StatisticsMean 0.67 0.93Median 0.78 0.71Minimum -19.22 -15.25Maximum 15.08 15.13Std. Dev. 4.81 4.71CorrelationsPB -0.39 -0.51MKT -0.23 -0.07MOM -0.49 -0.15HML -0.74 -0.76SMB 0.24 0.28
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Table 6a: Liquidity Screen SimulationsS&P 500
Unconstrained
(benchmark)
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Table 6b: Liquidity Screen SimulationsRussell 1000
Unconstrained
(benchmark)
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Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume”
Results are robust to different measures of holding period returns (1-month, 3-months, 6-months)Both the “long” portfolio (value/small/winner) and “short” (growth/large/loser) returns increase but the “long” returns increase moreSurprisingly, average price of stocks decline“Quality” of stocks (as measured by ROE and EPS growth) generally improves
Table 7: Further Investigation
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Trading volume is related to investment styles
Less (more) liquid stocks have lower (higher) returns
Liquid screen experiment: screening out the least liquid stocks may actually improve performance
Caveats: measuring liquidity, universe, sample period
Conclusions and Implications
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Questions…?
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TABLES AND FIGURES:
Liquidity and Investment Styles
by Jeff Brown*, Highstreet Asset Management Inc.
Doug Crocker*, Highstreet Asset Management Inc. and
Stephen Foerster**, Ivey Business School, University of Western Ontario
Current Version: October 3, 2007
Abstract The purpose of this study is to better understand stock market liquidity, measured at the individual stock level, and its potential impact on stock performance for a variety of well-known investment styles. In this study, we focus on two universes of generally liquid stocks, the stocks that make up the Standard & Poor’s (S&P) 500 Index, and a broader index of the top 1,000 stocks measured by market capitalization (closely mimicking the Russell 1000 Index stocks). We choose these universes because they are a primary focus of U.S. institutional investors such as mutual fund managers and pension fund managers. We show that liquidity, as measured by trailing 3-month trading volume, is monotonically related to price-to-book and market capitalization, and both past 6-month “winners” and “losers” tend to experience higher trading volume. When we sort stocks based on trading volume we find that, surprisingly, the more liquid stocks tend to have higher returns than the less liquid stocks overall and in most sub-periods except down markets. CAPM and Fama-French model regressions show that the most liquid quintile of stocks experiences significant superior performance in the overall period. We create a new measure that we call the liquidity factor, in the spirit of the Fama-French factors, and investigate its properties. Finally, we show that a liquidity screen (i.e., removing less liquid stocks from a long-short strategy) may actually improve performance for these particular universes of stocks. JEL Codes: G11, G12, G23 Keywords: Liquidity, Investment Styles, Assets Under Management, Factors, Asset Pricing
*Brown, CFA, is the Chief Investment Officer and Crocker is the Chief Risk Officer of Highstreet Asset Management Inc.**Foerster, PhD, CFA, is the Paul Desmarais/London Life Faculty Fellowship in Finance at the Ivey Business School. We wish to thank Lukasz Pomorski and seminar participants at Highstreet Asset Management and the Northern Finance Association meetings (2007). The research assistance of Fred Steciuk is gratefully acknowledged. Please address all correspondence to Steve Foerster: Richard Ivey School of Business, The University of Western Ontario, London, Ontario, Canada, N6A 3K7; Phone: 1-519-661-3726; Fax: 1-519-661-3485; E-mail: [email protected].
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Table 1 Summary Statistics, 1991-2006
Summary statistics for S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B) based on monthly data from July 1991 to January 2006 by Ford Equity Research. Sub-period results are presented for July 1991 to December 1995 (Sub1), January 1996 to August 2000 (Sub2), September 2000 to September 2002 (Sub3) and October 2002 to January 2006 (Sub4).Variables include price-earnings ratio (PE), price-to-book ratio (PB), return on equity percentage (ROE), 1-month return (Ret1mo), 3-month return (Ret3mo), 6-month return (Ret6mo), 12-month return (Ret12mo), average daily trading volume (hundreds of shares) measured on a rolling 3-month basis (Dvol3mo), earnings per share 5-year average growth (EPS5yrg), market capitalization of equity measured in millions of dollars (Mktcap), common shares outstanding in millions (Shs), average share price (Price), and turnover as measured by the annualized trading volume as a percentage of shares outstanding (Tunro). Panel A: S&P 500 Stocks Overall Sub1 Sub2 Sub3 Sub4 PE 20.42 15.59 22.65 23.69 21.77 PB 5.03 4.37 5.57 5.35 4.99 ROE 19.16 18.42 20.04 19.18 18.89 Ret1mo 1.16 1.29 1.36 -0.56 1.79 Ret3mo 3.48 3.90 3.99 -1.20 5.12 Ret6mo 6.80 8.03 7.73 -3.76 10.43 Ret12mo 13.74 16.03 15.10 -3.93 19.80 Dvol3mo 27191.21 14697.67 25620.25 38830.92 38982.03 EPS5yrg 3.83 2.07 7.20 4.87 0.83 Mktcap 15021.66 6552.25 16929.23 20762.65 20196.64 Shs 524.67 410.37 524.14 611.69 625.31 Price 29.45 20.95 32.70 32.67 34.37 Turno 1.37 0.83 1.19 1.98 1.97 Panel B: Top 1,000 Stocks PE 26.20 17.38 31.62 32.79 26.38 PB 5.40 4.09 6.77 5.81 4.99 ROE 17.94 17.48 18.94 17.50 17.44 Ret1mo 1.10 1.23 1.47 -1.17 1.81 Ret3mo 3.32 3.72 4.15 -2.62 5.32 Ret6mo 6.49 7.56 7.77 -5.52 10.78 Ret12mo 13.22 15.03 14.90 -5.86 20.35 Dvol3mo 19078.42 12133.76 18311.71 26099.07 25139.22 EPS5yrg 6.18 4.78 8.86 6.36 4.20 Mktcap 10696.72 4799.36 11741.65 14125.80 15052.10 Shs 393.91 317.96 384.60 443.79 478.30 Price 30.47 20.83 33.89 33.63 36.71 Turno 1.42 0.90 1.40 2.01 1.80
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Table 2 Trading Volume and Turnover, 1991-2006
Summary of S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B): average daily trading volume (hundreds of shares) measured on a rolling 3-month basis (Dvol3mo), and turnover as measured by the annualized trading volume as a percentage of shares outstanding (Turno) from July 1991 to January 2006 by Ford Equity Research. Sub-period results are presented for July 1991 to December 1995 (Sub1), January 1996 to August 2000 (Sub2), September 2000 to September 2002 (Sub3) and October 2002 to January 2006 (Sub4). Data are for the lowest (1) and highest (5) quintiles sorted by price-to-book (PB), market capitalization (MKT), and momentum as measured by the previous 6-month return (MOM). Panel A: S&P500 Stocks
Dvol3mo Turno Overall Sub1 Sub2 Sub3 Sub4 Overall Sub1 Sub2 Sub3 Sub4
PB1 15850 6400 8763 30616 29300 1.343 0.834 1.120 1.992 1.934 PB2 16924 8811 12360 23625 30078 1.267 0.775 1.093 1.730 1.888 PB3 20138 10907 18035 27211 31124 1.282 0.787 1.136 1.759 1.858 PB4 31983 16537 25947 52438 48503 1.369 0.787 1.192 1.989 2.016 PB5 51061 30833 62997 60265 55905 1.596 0.975 1.422 2.406 2.171
MKT1 8507 2399 5487 13320 17973 1.643 0.939 1.308 2.306 2.646 MKT2 12674 5958 9445 21347 20840 1.535 0.938 1.261 2.346 2.216 MKT3 17863 11267 12977 27565 27545 1.397 0.862 1.163 2.107 2.001 MKT4 26511 15347 26779 33745 36687 1.280 0.766 1.226 1.785 1.734 MKT5 70401 38518 73413 98179 91865 1.004 0.654 1.005 1.332 1.272
MOM1 32076 12442 21611 75149 46309 1.796 1.001 1.494 3.336 2.329 MOM2 21963 10917 16671 37089 34829 1.155 0.704 0.992 1.712 1.644 MOM3 20990 10466 17871 30837 33409 1.069 0.660 0.926 1.486 1.559 MOM4 21796 11561 21463 25108 34011 1.133 0.695 0.974 1.435 1.760 MOM5 39132 28101 50486 25971 46352 1.705 1.099 1.577 1.907 2.576
Panel B: Top 1,000 Stocks PB1 10818 5089 6478 20870 18349 1.001 0.639 0.810 1.585 1.391 PB2 11136 5947 8912 14910 18898 1.075 0.651 0.937 1.499 1.575 PB3 14469 8801 13905 18193 20581 1.230 0.788 1.148 1.689 1.654 PB4 22873 14495 21053 33788 29909 1.561 0.956 1.568 2.217 1.954 PB5 36096 26337 41211 42735 37960 2.254 1.468 2.542 3.043 2.418
MKT1 6624 5077 5532 8556 9033 1.611 1.111 1.572 2.100 2.035 MKT2 9166 6539 8185 11953 12344 1.640 1.078 1.596 2.248 2.083 MKT3 13652 8506 12544 19268 18642 1.593 0.951 1.552 2.336 2.050 MKT4 19829 12559 16978 27468 28862 1.381 0.781 1.339 2.104 1.798 MKT5 46121 27989 48320 63249 56815 0.895 0.583 0.945 1.245 1.026
MOM1 23826 11131 17448 52698 31851 1.756 1.008 1.577 3.417 1.977 MOM2 15067 7724 12493 24813 22491 1.076 0.651 0.991 1.652 1.410 MOM3 14199 8399 13165 18640 20701 1.019 0.640 0.937 1.408 1.402 MOM4 15288 10106 16659 16143 19829 1.161 0.737 1.142 1.425 1.594 MOM5 27012 23309 31794 18201 30824 2.108 1.467 2.357 2.131 2.609
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Table 3 Performance of Portfolios Sorted by Trading Volume, 1991-2006
Holding period return percentage for S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B) formed into quintiles (where Q1 is the lowest and Q5 is the highest) on the basis of average daily trading volume measured on a rolling 3-month basis. Returns (percentages) are presented over 1-month, 3-month, 6-month and 12-month holding periods. Sub-period results are presented for July 1991 to December 1995 (Sub1), January 1996 to August 2000 (Sub2), September 2000 to September 2002 (Sub3) and October 2002 to January 2006 (Sub4). Panel A: S&P500 Stocks
Overall Sub1 Sub2 Sub3 Sub41-month return
Q1 0.86 0.83 0.55 0.61 1.49Q2 1.11 1.34 0.91 0.10 1.72Q3 1.09 1.20 1.10 -0.26 1.79Q4 1.21 1.39 1.52 -0.86 1.84Q5 1.53 1.69 2.72 -2.37 2.09
3-month return Q1 2.64 2.68 1.57 2.18 4.36Q2 3.45 3.94 3.15 0.54 5.05Q3 3.22 3.66 3.18 -0.52 5.02Q4 3.51 4.09 4.21 -2.19 5.30Q5 4.58 5.13 7.86 -6.03 5.86
6-month return Q1 5.08 5.80 2.83 2.08 9.11Q2 6.60 7.67 6.15 -1.11 10.60Q3 6.32 7.34 6.39 -2.71 10.49Q4 6.78 8.56 8.01 -5.99 10.63Q5 9.21 10.76 15.25 -11.07 11.32
12-month return Q1 10.32 11.44 6.53 3.42 18.44Q2 11.95 13.94 10.19 -1.37 20.07Q3 13.11 15.50 12.43 -2.55 20.61Q4 14.00 17.36 15.76 -7.11 20.20Q5 19.34 21.93 30.60 -12.07 19.69
Panel B: Top 1,000 Stocks Overall Sub 1 Sub 2 Sub 3 Sub 4
0.72 0.64 0.60 -0.40 1.710.91 1.08 0.89 -0.35 1.521.07 1.34 1.15 -0.83 1.801.11 1.27 1.57 -1.52 1.911.66 1.84 3.13 -2.75 2.11
2.41 2.20 1.94 -0.49 5.152.76 3.22 2.48 -0.42 4.543.19 3.94 3.18 -1.90 5.393.25 3.70 4.22 -3.59 5.574.98 5.54 8.95 -6.71 5.97
4.93 4.74 3.95 -1.88 10.815.11 6.32 4.35 -2.10 9.065.95 7.55 5.52 -4.46 10.906.52 7.75 8.01 -7.26 11.409.96 11.44 17.02 -11.91 11.74
10.16 9.69 7.53 -1.16 21.559.83 11.89 7.91 -1.77 16.97
11.25 14.26 9.01 -5.37 20.7113.57 15.87 15.68 -8.54 21.3221.31 23.47 34.40 -12.48 21.20
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Table 4 CAPM and Fama-French Three Factor Adjusted Portfolio Performance, 1991-2006
S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B) are formed into quintile portfolios (where Q1 is the lowest and Q5 is the highest) on the basis of average daily trading volume measured on a rolling 3-month basis. Monthly portfolio returns in excess of risk-free returns are regressed on market excess returns RmRf (i.e., the CAPM) and on the Fama-French three-factors: RmRf, SMB and HML (see Ken French website for details). The intercept term (α), slope (β), adjusted R-squared (R2) and t-statistics (in parentheses) are presented for each portfolio. Panel A: S&P500 Stocks
CAPM Fama-French alpha RmRf R2 alpha RmRf SMB HML R2
Overall coefficient 0.24 0.94 -0.09 0.43 0.01 1.13 (t-stat) (1.71) (27.74) 0.82 (-0.85) (11.77) (0.48) (39.71) 0.91Q1 coefficient 0.07 0.74 -0.20 0.72 0.11 1.03 (t-stat) (0.32) (13.82) 0.52 (-2.96) (12.41) (2.30) (23.13) 0.76Q2 coefficient 0.30 0.78 -0.20 0.65 0.01 1.06 (t-stat) (1.51) (16.49) 0.61 (-1.55) (14.32) (0.18) (30.11) 0.84Q3 coefficient 0.25 0.83 -0.16 0.53 0.01 1.06 (t-stat) (1.42) (19.77) 0.69 (-1.19) (11.57) (0.25) (30.00) 0.84Q4 coefficient 0.30 0.94 -0.04 0.44 -0.01 1.13 (t-stat) (1.91) (25.14) 0.79 (-0.34) (10.61) (-0.31) (35.06) 0.88Q5 coefficient 0.30 1.42 0.44 -0.18 -0.04 1.35 (t-stat) (1.75) (34.64) 0.87 (2.53) (-2.97) (-0.83) (28.78) 0.88
Panel B: Top 1,000 Stocks
CAPM Fama-French alpha RmRf R2 alpha RmRf SMB HML R2
Overall coefficient 0.15 0.98 -0.06 0.24 0.16 1.05 (t-stat) (1.85) (49.06) 0.93 (-0.90) (10.96) (9.07) (61.24) 0.96Q1 coefficient -0.02 0.67 -0.28 0.45 0.16 0.84 (t-stat) (-0.16) (21.36) 0.73 (-4.15) (13.81) (6.17) (33.17) 0.87Q2 coefficient 0.10 0.77 -0.28 0.48 0.14 0.96 (t-stat) (0.72) (22.55) 0.75 (-2.69) (13.07) (4.83) (33.73) 0.87Q3 coefficient 0.18 0.90 -0.13 0.36 0.20 1.02 (t-stat) (1.55) (32.16) 0.86 (-1.42) (11.74) (8.03) (42.66) 0.92Q4 coefficient 0.12 1.06 -0.09 0.23 0.22 1.12 (t-stat) (1.02) (37.75) 0.89 (-0.87) (6.39) (7.66) (40.45) 0.92Q5 coefficient 0.39 1.48 0.61 -0.30 0.09 1.33 (t-stat) (2.39) (38.32) 0.89 (4.21) (-6.11) (2.15) (34.56) 0.92
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Table 5 Liquidity Factor Measure Summary Statistics, 1991-2006
The liquidity factor measure is calculated monthly as the difference between the return on the highest quintile portfolio (Q5) of S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B) measured by the average daily trading volume over the past 3-months and the return on the corresponding lowest quintile portfolio (Q1) from July 1991 to January 2006. Sub-period results are presented for July 1991 to December 1995 (Sub1), January 1996 to August 2000 (Sub2), September 2000 to September 2002 (Sub3) and October 2002 to January 2006 (Sub4). Summary statistics include the mean, median, minimum, maximum, and standard deviation. Correlations are measured against the monthly return difference of the lowest quintile of S&P 500 stocks (P1) versus highest quintile (P5) as sorted by price-to-book (PB) and market capitalization (MKT), and between P5 and P1 for momentum as measured by the previous 6-month return (MOM), as well the Fama-French factors: SMB, and HML (see Ken French website for details). Panel A: S&P500 Stocks Overall Sub1 Sub2 Sub3 Sub4Summary Statistics Mean 0.67 0.89 2.17 -2.98 0.59Median 0.78 0.93 1.40 -4.36 1.03Minimum -19.22 -2.37 -11.66 -19.22 -7.84Maximum 15.08 4.19 15.08 13.43 10.59Std. Dev. 4.81 1.66 5.02 8.32 3.20Correlations PB -0.389 -0.452 -0.840 -0.045 0.299MKT -0.226 -0.334 -0.687 0.061 0.560MOM -0.490 -0.184 0.231 -0.890 -0.560HML -0.744 -0.565 -0.785 -0.865 -0.342SMB 0.238 -0.131 0.350 0.251 0.465
Panel B: Top 1,000 Stocks Overall Sub1 Sub2 Sub3 Sub4Summary Statistics Mean 0.93 1.13 2.43 -2.98 0.70Median 0.71 1.01 2.00 -4.12 0.27Minimum -15.25 -2.99 -5.98 -15.25 -7.43Maximum 15.13 7.92 15.13 15.13 12.76Std. Dev. 4.71 2.20 4.41 7.66 3.38Correlations PB -0.511 -0.588 -0.748 -0.258 0.272MKT -0.069 0.210 -0.104 0.168 0.123MOM -0.152 0.150 0.556 -0.897 -0.533HML -0.760 -0.551 -0.817 -0.785 -0.625SMB 0.281 0.127 0.397 0.379 0.260
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Table 6 Liquidity Screen Simulations
“Long and short strategy” return percentage for S&P 500 stocks (panel A) and largest 1,000 U.S. stocks by market capitalization (panel B) quintile portfolios sorted by various metrics (P1 is the lowest quintile and P5 is the highest quintile) based on price-to-book (PB) in Panel A, market capitalization (MKT) in Panel B, and price momentum as measured by the previous 6-month return (MOM) in Panel C. The holding period is 12 months. Data are from July 1991 to January 2006 (Overall) by Ford Equity Research. Sub-period results are presented for July 1991 to December 1995 (Sub1), January 1996 to August 2000 (Sub2), September 2000 to September 2002 (Sub3) and October 2002 to January 2006 (Sub4). “Constraint” represents a screen for the minimum average daily trading volume (number of shares) measured on a rolling 3-month basis; “0” indicates the no constraint scenario. “P1 (P5) Screen Avg %” represents the average percentage of P1 (P5) quintile stocks, across all months in the sample, which were eliminated due to the minimum volume constraint. Panel A: S&P500 Stocks
12-Month Return % P1 Screen Avg % P5 Screen Avg % Constraint Overall Sub1 Sub2 Sub3 Sub4 Overall Sub1 Sub2 Sub3 Sub4 Overall Sub1 Sub2 Sub3 Sub4 Price-to-Book (PB) P1-P5
0 6.42 7.32 -2.03 9.46 15.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 6.72 8.18 -2.01 9.60 15.14 3.26 8.63 1.70 0.40 0.00 0.49 1.57 0.00 0.00 0.00
100,000 7.01 8.96 -1.86 9.66 15.14 7.95 18.91 6.21 0.92 0.00 2.35 6.57 1.02 0.00 0.00 500,000 8.40 13.54 -1.47 9.08 14.83 40.12 69.46 47.98 15.68 4.78 17.99 34.11 16.79 6.68 4.98
1,000,000 10.13 15.55 0.28 10.14 16.62 62.02 86.22 74.86 40.44 24.88 35.19 54.98 33.93 17.84 21.08 Market Capitalization (MKT) P1-P5
0 3.87 1.06 -7.11 20.26 12.77 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 4.33 2.23 -6.86 20.42 12.77 6.02 16.00 3.21 0.40 0.00 0.00 0.00 0.00 0.00 0.00
100,000 5.06 4.29 -6.58 20.45 12.77 15.64 38.07 11.64 1.16 0.00 0.04 0.13 0.00 0.00 0.00 500,000 14.90 24.66 3.35 20.92 14.13 59.14 89.67 69.50 34.96 18.55 4.30 12.00 1.66 0.00 0.28
1,000,000 25.56 39.37 20.42 22.35 16.13 79.75 97.31 89.66 65.92 50.83 11.87 30.87 6.79 0.24 0.60 Price Momentum (MOM) P5-P1
0 3.50 3.54 5.31 3.15 1.13 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 3.44 3.29 5.37 3.15 1.13 1.87 5.20 0.84 0.00 0.00 0.81 2.26 0.34 0.00 0.00
100,000 3.61 3.79 5.41 3.15 1.13 4.86 12.63 2.93 0.20 0.00 2.78 7.96 0.95 0.12 0.00 500,000 4.30 5.82 4.96 3.68 1.72 30.65 56.19 36.11 5.68 4.15 23.52 47.63 19.91 11.32 3.65
1,000,000 4.50 5.40 5.42 3.39 2.68 49.38 76.31 58.95 15.28 20.93 41.83 66.15 38.89 34.76 17.53
8
Table 6 (continued) Liquidity Screen Simulations
Panel B: Top 1,000 Stocks 12-Month Return % P1 Screen Avg % P5 Screen Avg % Constraint Overall Sub1 Sub2 Sub3 Sub4 Overall Sub1 Sub2 Sub3 Sub4 Overall Sub1 Sub2 Sub3 Sub4 Price-to-Book (PB) P1-P5
0 4.73 5.57 -3.16 10.66 10.95 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 5.00 6.13 -2.92 10.86 10.91 10.17 15.66 8.85 7.66 6.19 2.32 5.65 1.00 0.70 0.69
100,000 4.88 6.45 -3.51 10.58 10.95 17.93 28.04 16.63 11.54 10.08 6.66 14.74 3.53 1.70 3.23 500,000 5.04 7.36 -3.78 8.91 11.85 57.01 77.04 63.84 38.14 32.20 28.46 46.23 25.71 16.82 15.60
1,000,000 5.52 8.44 -3.97 7.37 13.70 74.03 88.59 82.75 58.16 52.09 46.73 63.09 45.29 33.22 35.11 Market Capitalization (MKT) P1-P5
0 1.84 1.79 -4.24 12.35 3.85 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 2.25 3.31 -4.55 12.17 4.15 9.44 20.74 5.77 3.96 2.76 4.94 7.20 5.11 3.74 2.41
100,000 3.32 5.79 -3.77 11.70 4.69 21.42 43.25 17.26 8.30 5.96 8.24 10.49 8.72 6.38 5.70 500,000 12.72 21.11 9.41 8.68 8.57 68.56 86.00 70.37 55.62 50.58 21.75 30.71 19.18 14.42 17.81
1,000,000 22.50 31.29 25.83 10.10 13.71 85.31 92.98 87.27 79.12 76.06 33.50 51.60 30.49 19.36 22.10 Price Momentum (MOM) P5-P1
0 6.56 3.52 12.41 10.15 0.23 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 50,000 6.80 3.86 12.47 10.51 0.51 6.00 11.19 4.33 3.56 2.85 3.61 6.27 2.68 2.54 1.98
100,000 7.29 4.58 13.21 10.53 0.63 11.62 22.09 8.99 5.42 5.03 7.87 13.99 6.20 4.80 3.86 500,000 9.68 8.47 16.38 9.99 1.76 40.47 64.52 43.68 16.14 18.71 36.73 56.02 33.80 29.22 19.48
1,000,000 11.29 10.51 18.33 9.75 3.46 58.20 80.38 64.55 28.00 38.23 55.36 71.40 53.75 52.88 37.53
9
Table 7a Liquidity Screen Simulations: Further Investigation
Further investigation of long/short strategies for S&P 500 stocks based on monthly data from July 1991 to January 2006 by Ford Equity Research. P1 is the lowest quintile and P5 is the highest quintile based on price-to-book (PB), market capitalization (MKT), and price momentum as measured by the previous 6-month return (MOM). Panel A is the unconstrained strategy, Panel B screens for stocks in the strategy with a minimum average daily trading volume (number of shares) on a rolling 3-month basis of 500,000 shares, and Panel C reports the difference between unconstrained and constrained variables. Variables include 1-month return (Ret1mo), 3-month return (Ret3mo), 6-month return (Ret6mo), 12-month return (Ret12mo), price-earnings ratio (PE), price-to-book ratio (PB), return on equity percentage (ROE), average daily trading volume (hundreds of shares) measured on a rolling 3-month basis (Dvol3mo), earnings per share 5-year average growth (EPS5yrg), market capitalization of equity measured in millions of dollars (Mktcap), common shares outstanding in millions (Shs), past 6-month return (past6mo), average share price (Price), and turnover as measured by the annualized trading volume as a percentage of shares outstanding (Tunro).
Panel A: Unconstrained Differences: Across Portfolios Variable
PB P1 (value)
MKT P1 (small)
MOMP5 (winners)
PBP5 (growth)
MKT P5 (large)
MOMP1 (losers) PB MKT MOM
Ret1mo 1.58 1.41 1.20 0.94 1.00 1.27 0.64 0.41 -0.07Ret3mo 4.65 4.21 3.79 2.91 2.91 3.40 1.74 1.31 0.39Ret6mo 8.98 8.05 8.24 5.75 5.82 6.15 3.24 2.23 2.09Ret12mo 18.17 16.17 16.29 11.75 12.30 12.79 6.42 3.87 3.50PE 13.16 15.57 26.88 31.46 25.88 16.93 -18.30 -10.32 9.95PB 1.21 5.60 6.63 15.70 5.29 4.78 -14.49 0.31 1.84ROE 10.79 18.81 19.62 37.30 21.18 19.34 -26.51 -2.37 0.28Dvol3mo 15849.76 8542.94 39131.63 51060.57 70176.35 32075.52 -35210.81 -61633.41 7056.11EPS5yrg -3.02 -3.87 2.99 8.53 7.82 1.99 -11.55 -11.69 1.00Mktcap 6475.65 1670.10 15845.63 27191.10 51381.79 10985.52 -20715.45 -49711.69 4860.12Shs 284.55 104.90 573.10 894.77 1607.13 457.99 -610.22 -1502.23 115.11Past6mo -2.25 0.71 38.02 13.31 8.90 -21.44 -15.56 -8.19 59.46Price 23.65 20.27 31.08 32.59 36.94 23.68 -8.93 -16.67 7.40Turno 1.34 1.64 1.70 1.60 1.00 1.80 -0.25 0.64 -0.09
10
Table 7a (continued)
Liquidity Screen Simulations: Further Investigation
Panel B: 500,000 Minimum Average Daily Volume Differences: Across Portfolios Variable
PB P1 (value)
MKT P1 (small)
MOMP5 (winners)
PBP5 (growth)
MKT P5 (large)
MOMP1 (losers) PB MKT
MOM
Ret1mo 1.81 2.22 1.40 1.11 1.02 1.38 0.69 1.21 0.02 Ret3mo 5.41 6.39 4.32 3.32 3.03 3.72 2.09 3.36 0.60 Ret6mo 10.62 13.11 9.59 6.70 5.97 6.88 3.92 7.15 2.71 Ret12mo 22.11 27.53 18.97 13.72 12.63 14.67 8.40 14.90 4.30 PE 13.18 16.44 28.22 32.97 25.97 17.90 -19.80 -9.53 10.33 PB 1.23 6.73 6.83 14.12 5.33 4.46 -12.90 1.40 2.38 ROE 11.10 19.86 20.07 35.11 21.36 19.52 -24.01 -1.50 0.56 Dvol3mo 21580.22 14629.27 50277.75 60406.01 72101.81 40368.43 -38825.79 -57472.53 9909.32 EPS5yrg -2.38 -2.85 4.02 9.64 7.98 3.83 -12.02 -10.83 0.19 Mktcap 8442.02 1777.02 18482.35 30708.84 52014.69 13308.67 -22266.82 -50237.67 5173.68 Shs 399.40 155.76 744.87 1074.46 1661.54 596.63 -675.06 -1505.78 148.25 Past6mo -2.17 0.60 39.37 14.42 8.86 -22.03 -16.59 -8.26 61.40 Price 21.72 13.94 28.84 31.44 35.47 22.12 -9.72 -21.53 6.72 Turno 1.51 2.39 1.85 1.70 1.02 2.00 -0.19 1.38 -0.15
11
Table 7a (continued) Liquidity Screen Simulations: Further Investigation
Panel C: Differences Constrained versus Unconstrained Variable
PBP1 (value)
MKTP1 (small)
MOMP5 (winners)
PB P5 (growth)
MKTP5 (large)
MOMP1 (losers)
Ret1mo 0.22 0.81 0.20 0.17 0.01 0.11Ret3mo 0.76 2.17 0.53 0.41 0.12 0.31Ret6mo 1.64 5.06 1.35 0.95 0.15 0.73Ret12mo 3.94 11.37 2.68 1.97 0.33 1.88PE 0.02 0.87 1.34 1.52 0.08 0.97PB 0.01 1.13 0.21 -1.58 0.04 -0.32ROE 0.30 1.05 0.45 -2.20 0.17 0.17Dvol3mo 5730.46 6086.33 11146.12 9345.44 1925.45 8292.91EPS5yrg 0.64 1.02 1.03 1.10 0.17 1.84Mktcap 1966.37 106.92 2636.72 3517.74 632.90 2323.16Shs 114.85 50.86 171.78 179.69 54.40 138.64Past6mo 0.07 -0.11 1.35 1.11 -0.04 -0.58Price -1.94 -6.33 -2.24 -1.15 -1.47 -1.56Turno 0.17 0.75 0.14 0.10 0.01 0.21
12
Table 7b Liquidity Screen Simulations: Further Investigation
Further investigation of long/short strategies for the largest 1,000 U.S. stocks by market capitalization based on monthly data from July 1991 to January 2006 by Ford Equity Research. P1 is the lowest quintile and P5 is the highest quintile based on price-to-book (PB), market capitalization (MKT), and price momentum as measured by the previous 6-month return (MOM). Panel A is the unconstrained strategy, Panel B screens for stocks in the strategy with a minimum average daily trading volume (number of shares) on a rolling 3-month basis of 500,000 shares, and Panel C reports the difference between unconstrained and constrained variables. Variables include 1-month return (Ret1mo), 3-month return (Ret3mo), 6-month return (Ret6mo), 12-month return (Ret12mo), price-earnings ratio (PE), price-to-book ratio (PB), return on equity percentage (ROE), average daily trading volume (hundreds of shares) measured on a rolling 3-month basis (Dvol3mo), earnings per share 5-year average growth (EPS5yrg), market capitalization of equity measured in millions of dollars (Mktcap), common shares outstanding in millions (Shs), past 6-month return (past6mo), average share price (Price), and turnover as measured by the annualized trading volume as a percentage of shares outstanding (Tunro).
Panel A: Unconstrained Differences: Across Portfolios Variable
PB P1 (value)
MKT P1 (small)
MOMP5 (winners)
PBP5 (growth)
MKT P5 (large)
MOMP1 (losers) PB MKT MOM
Ret1mo 1.42 1.12 1.37 1.01 0.94 0.91 0.42 0.18 0.46Ret3mo 4.13 3.51 4.35 3.08 2.84 2.40 1.05 0.67 1.96Ret6mo 8.10 6.88 8.95 5.93 5.71 4.35 2.17 1.17 4.59Ret12mo 16.76 13.86 17.10 12.03 12.02 10.54 4.73 1.84 6.56PE 15.62 25.03 39.36 47.40 27.32 22.78 -31.79 -2.29 16.58PB 1.26 5.45 8.22 17.17 4.96 4.56 -15.91 0.49 3.66ROE 10.20 17.29 19.02 34.09 18.79 17.73 -23.88 -1.50 1.29Dvol3mo 10818.49 6623.52 27012.12 36095.82 46121.05 23826.49 -25277.33 -39497.54 3185.63EPS5yrg -0.15 5.70 6.23 10.85 6.46 5.74 -11.00 -0.76 0.49Mktcap 6639.54 1590.56 8864.24 15735.73 37784.99 9357.11 -9096.19 -36194.43 -492.87Shs 284.55 104.90 573.10 894.77 1607.13 457.99 -610.22 -1502.23 115.11Past6mo 0.88 10.79 49.31 23.23 9.46 -19.31 -22.34 1.33 68.62Price 26.77 25.22 32.30 34.65 36.39 26.62 -7.87 -11.17 5.69Turno 1.00 1.61 2.11 2.25 0.89 1.76 -1.25 0.72 0.35
13
Table 7b (continued)
Liquidity Screen Simulations: Further Investigation
Panel B: 500,000 Minimum Average Daily Volume Differences: Across Portfolios Variable
PB P1 (value)
MKT P1 (small)
MOMP5 (winners)
PBP5 (growth)
MKTP5 (large)
MOMP1 (losers) PB MKT
MOM
Ret1mo 1.71 1.89 1.78 1.31 0.97 0.99 0.40 0.91 0.79 Ret3mo 4.82 5.66 5.46 3.83 2.92 2.62 0.99 2.74 2.84 Ret6mo 9.68 11.55 11.52 7.56 5.91 5.07 2.12 5.64 6.45 Ret12mo 20.85 25.24 22.48 15.81 12.51 12.80 5.04 12.72 9.68 PE 15.22 32.39 42.68 50.02 28.23 24.22 -34.80 4.16 18.45 PB 1.25 6.29 8.69 15.61 5.40 4.98 -14.36 0.89 3.71 ROE 10.70 17.92 19.61 31.61 20.09 18.79 -20.91 -2.17 0.82 Dvol3mo 20064.52 19203.19 42167.67 49303.59 57165.11 35380.55 -29239.07 -37961.92 6787.11 EPS5yrg -0.18 7.90 7.33 12.01 7.43 7.45 -12.19 0.48 -0.12 Mktcap 8362.39 1601.32 10950.50 19261.38 40157.82 11273.01 -10898.99 -38556.49 -322.51 Shs 433.49 148.63 510.49 738.07 1349.81 525.86 -304.57 -1201.18 -15.37 Past6mo -0.33 15.31 52.13 24.55 9.98 -20.90 -24.87 5.32 73.03 Price 21.15 16.96 27.47 30.69 34.35 22.69 -9.54 -17.39 4.78 Turno 1.48 3.28 2.67 2.67 1.07 2.33 -1.19 2.21 0.34
14
Table 7b (continued) Liquidity Screen Simulations: Further Investigation
Panel C: Differences Constrained versus Unconstrained Variable
PBP1 (value)
MKTP1 (small)
MOMP5 (winners)
PBP5 (growth)
MKTP5 (large)
MOMP1 (losers)
Ret1mo 0.29 0.77 0.41 0.31 0.03 0.08Ret3mo 0.70 2.16 1.10 0.75 0.08 0.22Ret6mo 1.58 4.66 2.57 1.63 0.20 0.72Ret12mo 4.09 11.38 5.38 3.78 0.50 2.26PE -0.40 7.36 3.31 2.62 0.91 1.44PB 0.00 0.84 0.46 -1.56 0.44 0.41ROE 0.50 0.63 0.59 -2.47 1.30 1.06Dvol3mo 9246.02 12579.67 15155.55 13207.77 11044.06 11554.06EPS5yrg -0.03 2.20 1.10 1.16 0.97 1.71Mktcap 1722.85 10.76 2086.26 3525.66 2372.83 1915.90Shs 148.94 43.73 -62.61 -156.71 -257.32 67.87Past6mo -1.21 4.52 2.82 1.32 0.52 -1.59Price -5.63 -8.27 -4.83 -3.96 -2.05 -3.92Turno 0.48 1.67 0.56 0.41 0.18 0.57
15
Figure 1 Graph of S&P500 Index July 1991 to January 2006. Sub-periods are indicated as: pre-tech bubble run-up, July 1991 to December 1995 (sub-period 1); tech bubble run-up, January 2006 to August 2000 (sub-period 2); post-bubble decline, September 2000 to September 2002 (sub-period 3) and post-bubble period, October 2002 to January 2006 (sub-period 4).
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Sub-periods:1. July 1991 - Dec 19952. Jan 1996 - Aug 20003. Sep 2000 - Sep 20024. Oct 2002 - Jan 2006
16
Figure 2 Comparison of average daily trading volume (hundreds of shares) measured on a rolling 3-month basis for S&P 500 stocks (panel A) and largest 1,000 U.S. stocks sorted by market capitalization (panel B), sorted into quintiles with Q1 (Q5) having the lowest (highest) average trading volume; monthly observations from July 1991 to January 2006. Panel A: S&P500 Stocks
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Panel B: Top 1,000 Stocks
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