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1 Liquidity and Investment Styles Jeff Brown, Doug Crocker & Stephen Foerster October 22, 2007 – Northfield Annual Research Conference

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Page 1: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Liquidity and Investment Styles

Jeff Brown,Doug Crocker

&Stephen Foerster

October 22, 2007 – Northfield Annual Research Conference

Page 2: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Motivation and Purpose of Study

Overview of Results

Background

Hypotheses, Data, and Methodology

Results

Conclusions and Implications

Plan of Discussion

Page 3: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 4: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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

Page 5: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

Sample of Volume IndicatorsSource: Wall Street Journal

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Page 6: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 7: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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!

Page 8: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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

Page 9: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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Page 10: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 11: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 12: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Figure 1: Sub-PeriodsS&P 500 Index

0

200

400

600

800

1000

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1600

1991

06…

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Sub-periods:1. July 1991 - Dec 19952. Jan 1996 - Aug 20003. Sep 2000 - Sep 20024. Oct 2002 - Jan 2006

Page 13: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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)

Page 14: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 15: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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?

Page 16: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 17: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

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180,000

1991

0719

9202

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9304

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9406

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0119

9508

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0319

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1120

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07

AllQ1Q2Q3Q4Q5

Page 18: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Figure 2b: Russell 1000 Stocks Volume(average daily trading volume in 100s of shares)

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40,000

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120,000

1991

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Page 19: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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

Page 20: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 2a: Trading Volume by Investment Style(average daily trading volume in 100s of shares)

Page 21: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 2b: Trading Volume by Investment Style(average daily trading volume in 100s of shares)

Page 22: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 23: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 24: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 4a: Regression Analysis(Liquidity portfolios and Fama-French model)

*significant

rit - rft = ai + b1RmRft + b2SMBt + b3HML + eit

Page 25: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 4b: Regression Analysis(Liquidity portfolios and Fama-French model)

*significant

rit - rft = ai + b1RmRft + b2SMBt + b3HML + eit

Page 26: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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

Page 27: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 6a: Liquidity Screen SimulationsS&P 500

Unconstrained

(benchmark)

Page 28: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Table 6b: Liquidity Screen SimulationsRussell 1000

Unconstrained

(benchmark)

Page 29: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 30: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 31: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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Questions…?

Page 32: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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].

Page 33: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 34: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 35: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

Page 36: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

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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

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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

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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

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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

Page 43: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

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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

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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

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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

Page 47: Jeff Brown, Doug Crocker Stephen Foerster · Focus on “unconstrained” versus “500,000 shares minimum average daily trading volume” Results are robust to different measures

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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

0

20,000

40,000

60,000

80,000

100,000

120,000

140,000

160,000

180,000

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

Panel B: Top 1,000 Stocks

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